%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.63", %%% date = "09 January 2026", %%% time = "10:15:52 MDT", %%% filename = "talg.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "28677 37180 209138 1842733", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "ACM Transactions on Algorithms; bibliography; %%% TALG", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE BibTeX bibliography for %%% ACM Transactions on Algorithms (CODEN ????, %%% ISSN 1549-6325), covering all journal issues %%% from 2005 -- date. %%% %%% At version 1.63, the COMPLETE journal %%% coverage looked like this: %%% %%% 2005 ( 20) 2013 ( 21) 2021 ( 37) %%% 2006 ( 37) 2014 ( 37) 2022 ( 41) %%% 2007 ( 52) 2015 ( 20) 2023 ( 39) %%% 2008 ( 66) 2016 ( 74) 2024 ( 38) %%% 2009 ( 54) 2017 ( 38) 2025 ( 48) %%% 2010 ( 66) 2018 ( 53) 2026 ( 12) %%% 2011 ( 41) 2019 ( 55) %%% 2012 ( 57) 2020 ( 54) %%% %%% Article: 960 %%% %%% Total entries: 960 %%% %%% The journal Web page can be found at: %%% %%% http://talg.acm.org/ %%% %%% The journal table of contents pages are at: %%% %%% http://www.acm.org/talg/ %%% http://portal.acm.org/browse_dl.cfm?idx=J982 %%% https://dl.acm.org/loi/talg %%% %%% Qualified subscribers can retrieve the full %%% text of recent articles in PDF form. %%% %%% The initial draft was extracted from the ACM %%% Web pages. %%% %%% ACM copyrights explicitly permit abstracting %%% with credit, so article abstracts, keywords, %%% and subject classifications have been %%% included in this bibliography wherever %%% available. Article reviews have been %%% omitted, until their copyright status has %%% been clarified. %%% %%% bibsource keys in the bibliography entries %%% below indicate the entry originally came %%% from the computer science bibliography %%% archive, even though it has likely since %%% been corrected and updated. %%% %%% URL keys in the bibliography point to %%% World Wide Web locations of additional %%% information about the entry. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted in %%% publication order, using ``bibsort -byvolume.'' %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{ "\hyphenation{Ka-wa-ra-ba-ya-shi Ma-kar-y-chev Thu-ri-mel-la Ver-strae-te}" # "\input bibnames.sty" # "\input path.sty" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" # "\ifx \undefined \MST \def \MST {{\rm MST}}\fi" # "\ifx \undefined \occ \def \occ {{\rm occ}}\fi" # "\ifx \undefined \polylog \def \polylog {{\rm polylog}}\fi" # "\ifx \undefined \polyloglog \def \polyloglog {{\rm polyloglog}}\fi" # "\ifx \undefined \poly \def \poly {{\rm poly}}\fi" # "\ifx \undefined \rank \def \rank {{\rm rank}}\fi" # "\ifx \undefined \select \def \select {{\rm select}}\fi" # "\ifx \undefined \SORT \def \SORT {{\rm SORT}}\fi" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-nhfb = "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"} %%% ==================================================================== %%% Journal abbreviations: @String{j-TALG = "ACM Transactions on Algorithms"} %%% ==================================================================== %%% Bibliography entries: @Article{Gabow:2005:EF, author = "Harold N. Gabow", title = "{Editor}'s foreword", journal = j-TALG, volume = "1", number = "1", pages = "1--1", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Yuster:2005:FSM, author = "Raphael Yuster and Uri Zwick", title = "Fast sparse matrix multiplication", journal = j-TALG, volume = "1", number = "1", pages = "2--13", month = jul, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1077464.1077466", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let $A$ and $B$ be two $ n \times n$ matrices over a ring $R$ (e.g., the reals or the integers) each containing at most $m$ nonzero elements. We present a new algorithm that multiplies $A$ and $B$ using $ O(m^{0.7}n^{1.2} + n^2 + o(1))$ algebraic operations (i.e., multiplications, additions and subtractions) over $R$. The na{\"\i}ve matrix multiplication algorithm, on the other hand, may need to perform $ \Omega (m n)$ operations to accomplish the same task. For $ m \leq n^{1.14}$, the new algorithm performs an almost optimal number of only $ n^2 + o(1)$ operations. For $ m \leq n^{1.68}$, the new algorithm is also faster than the best known matrix multiplication algorithm for dense matrices which uses $ O(n^{2.38})$ algebraic operations. The new algorithm is obtained using a surprisingly straightforward combination of a simple combinatorial idea and existing fast rectangular matrix multiplication algorithms. We also obtain improved algorithms for the multiplication of more than two sparse matrices. As the known fast rectangular matrix multiplication algorithms are far from being practical, our result, at least for now, is only of theoretical value.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Edmonds:2005:MAL, author = "Jeff Edmonds and Kirk Pruhs", title = "A maiden analysis of longest wait first", journal = j-TALG, volume = "1", number = "1", pages = "14--32", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2005:FPA, author = "Erik D. Demaine and Fedor V. Fomin and Mohammadtaghi Hajiaghayi and Dimitrios M. Thilikos", title = "Fixed-parameter algorithms for $ (k, r)$-center in planar graphs and map graphs", journal = j-TALG, volume = "1", number = "1", pages = "33--47", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Adler:2005:PMM, author = "Micah Adler and Dan Rubenstein", title = "Pricing multicasting in more flexible network models", journal = j-TALG, volume = "1", number = "1", pages = "48--73", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Even:2005:NDP, author = "Guy Even and Guy Kortsarz and Wolfgang Slany", title = "On network design problems: fixed cost flows and the covering {Steiner} problem", journal = j-TALG, volume = "1", number = "1", pages = "74--101", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alstrup:2005:BBC, author = "Stephen Alstrup and Thore Husfeldt and Theis Rauhe and Mikkel Thorup", title = "Black box for constant-time insertion in priority queues (note)", journal = j-TALG, volume = "1", number = "1", pages = "102--106", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Vinkemeier:2005:LTA, author = "Doratha E. Drake Vinkemeier and Stefan Hougardy", title = "A linear-time approximation algorithm for weighted matchings in graphs", journal = j-TALG, volume = "1", number = "1", pages = "107--122", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Grabner:2005:ALC, author = "Peter J. Grabner and Clemens Heuberger and Helmut Prodinger and J{\"o}rg M. Thuswaldner", title = "Analysis of linear combination algorithms in cryptography", journal = j-TALG, volume = "1", number = "1", pages = "123--142", month = jul, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1077464.1077473", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Several cryptosystems rely on fast calculations of linear combinations in groups. One way to achieve this is to use joint signed binary digit expansions of small ``weight.'' We study two algorithms, one based on nonadjacent forms of the coefficients of the linear combination, the other based on a certain joint sparse form specifically adapted to this problem. Both methods are sped up using the sliding windows approach combined with precomputed lookup tables. We give explicit and asymptotic results for the number of group operations needed, assuming uniform distribution of the coefficients. Expected values, variances and a central limit theorem are proved using generating functions. Furthermore, we provide a new algorithm that calculates the digits of an optimal expansion of pairs of integers from left to right. This avoids storing the whole expansion, which is needed with the previously known right-to-left methods, and allows an online computation.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cechlarova:2005:GSR, author = "Katar{\'\i}na Cechl{\'a}rov{\'a} and Tam{\'a}s Fleiner", title = "On a generalization of the stable roommates problem", journal = j-TALG, volume = "1", number = "1", pages = "143--156", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Khuller:2005:PC, author = "Samir Khuller", title = "Problems column", journal = j-TALG, volume = "1", number = "1", pages = "157--159", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Johnson:2005:NCC, author = "David S. Johnson", title = "The {NP}-completeness column", journal = j-TALG, volume = "1", number = "1", pages = "160--176", month = jul, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:55 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Janson:2005:IDL, author = "Svante Janson", title = "Individual displacements for linear probing hashing with different insertion policies", journal = j-TALG, volume = "1", number = "2", pages = "177--213", month = oct, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1103963.1103964", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the distribution of the individual displacements in hashing with linear probing for three different versions: First Come, Last Come and Robin Hood. Asymptotic distributions and their moments are found when the size of the hash table tends to infinity with the proportion of occupied cells converging to some $ \alpha $, $ 0 < \alpha < 1 $. (In the case of Last Come, the results are more complicated and less complete than in the other cases.) We also show, using the diagonal Poisson transform studied by Poblete, Viola and Munro, that exact expressions for finite $m$ and $n$ can be obtained from the limits as $ m, n \rightarrow \infty $. We end with some results, conjectures and questions about the shape of the limit distributions. These have some relevance for computer applications.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Viola:2005:EDI, author = "Alfredo Viola", title = "Exact distribution of individual displacements in linear probing hashing", journal = j-TALG, volume = "1", number = "2", pages = "214--242", month = oct, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1103963.1103965", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This paper studies the distribution of individual displacements for the standard and the Robin Hood linear probing hashing algorithms. When a table of size $m$ has $n$ elements, the distribution of the search cost of a random element is studied for both algorithms. Specifically, exact distributions for fixed $m$ and $n$ are found as well as when the table is $ \alpha $-full, and $ \alpha $ strictly smaller than 1. Moreover, for full tables, limit laws for both algorithms are derived.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alstrup:2005:MIF, author = "Stephen Alstrup and Jacob Holm and Mikkel Thorup and Kristian De Lichtenberg", title = "Maintaining information in fully dynamic trees with top trees", journal = j-TALG, volume = "1", number = "2", pages = "243--264", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jothi:2005:AAC, author = "Raja Jothi and Balaji Raghavachari", title = "Approximation algorithms for the capacitated minimum spanning tree problem and its variants in network design", journal = j-TALG, volume = "1", number = "2", pages = "265--282", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2005:CAS, author = "Michael Elkin", title = "Computing almost shortest paths", journal = j-TALG, volume = "1", number = "2", pages = "283--323", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Carvalho:2005:VAE, author = "Marcelo H. {De Carvalho} and Joseph Cheriyan", title = "An {$ O(V E) $} algorithm for ear decompositions of matching-covered graphs", journal = j-TALG, volume = "1", number = "2", pages = "324--337", month = oct, year = "2005", CODEN = "????", DOI = "https://doi.org/10.1145/1103963.1103969", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Goel:2005:AMF, author = "Ashish Goel and Adam Meyerson and Serge Plotkin", title = "Approximate majorization and fair online load balancing", journal = j-TALG, volume = "1", number = "2", pages = "338--349", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chrobak:2005:GAM, author = "Marek Chrobak and Petr Kolman and Ji{\v{r}}{\'\i} Sgall", title = "The greedy algorithm for the minimum common string partition problem", journal = j-TALG, volume = "1", number = "2", pages = "350--366", month = oct, year = "2005", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Dec 13 18:19:56 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Sawada:2006:GRF, author = "Joe Sawada", title = "Generating rooted and free plane trees", journal = j-TALG, volume = "2", number = "1", pages = "1--13", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hegde:2006:FSE, author = "Rajneesh Hegde", title = "Finding $3$-shredders efficiently", journal = j-TALG, volume = "2", number = "1", pages = "14--43", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gramm:2006:PMA, author = "Jens Gramm and Jiong Guo and Rolf Niedermeier", title = "Pattern matching for arc-annotated sequences", journal = j-TALG, volume = "2", number = "1", pages = "44--65", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hassin:2006:MGV, author = "Refael Hassin and Asaf Levin", title = "The minimum generalized vertex cover problem", journal = j-TALG, volume = "2", number = "1", pages = "66--78", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Epstein:2006:OSS, author = "Leah Epstein and Rob {Van Stee}", title = "Online scheduling of splittable tasks", journal = j-TALG, volume = "2", number = "1", pages = "79--94", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gonzalez:2006:MTC, author = "Teofilo F. Gonzalez and Joseph Y.-T. Leung and Michael Pinedo", title = "Minimizing total completion time on uniform machines with deadline constraints", journal = j-TALG, volume = "2", number = "1", pages = "95--115", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gandhi:2006:IRD, author = "Rajiv Gandhi and Magn{\'u}s M. Halld{\'o}rsson and Guy Kortsarz and Hadas Shachnai", title = "Improved results for data migration and open shop scheduling", journal = j-TALG, volume = "2", number = "1", pages = "116--129", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", note = "See corrigendum \cite{Gandhi:2013:CIR}.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Khuller:2006:PC, author = "Samir Khuller", title = "Problems column", journal = j-TALG, volume = "2", number = "1", pages = "130--134", month = jan, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Fri May 26 08:40:43 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Korsh:2006:LGC, author = "James Korsh and Paul Lafollette", title = "A loopless {Gray} code for rooted trees", journal = j-TALG, volume = "2", number = "2", pages = "135--152", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alon:2006:ACS, author = "Noga Alon and Dana Moshkovitz and Shmuel Safra", title = "Algorithmic construction of sets for {$k$}-restrictions", journal = j-TALG, volume = "2", number = "2", pages = "153--177", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lau:2006:BRG, author = "Lap Chi Lau", title = "Bipartite roots of graphs", journal = j-TALG, volume = "2", number = "2", pages = "178--208", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2006:EAB, author = "Pankaj K. Agarwal and Boris Aronov and Vladlen Koltun", title = "Efficient algorithms for bichromatic separability", journal = j-TALG, volume = "2", number = "2", pages = "209--227", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Epstein:2006:SU, author = "Leah Epstein and Rob {Van Stee}", title = "This side up!", journal = j-TALG, volume = "2", number = "2", pages = "228--243", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Huo:2006:MMF, author = "Yumei Huo and Joseph Y.-T. Leung", title = "Minimizing mean flow time for {UET} tasks", journal = j-TALG, volume = "2", number = "2", pages = "244--262", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hassin:2006:RST, author = "Refael Hassin and Danny Segev", title = "Robust subgraphs for trees and paths", journal = j-TALG, volume = "2", number = "2", pages = "263--281", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Azar:2006:IAC, author = "Yossi Azar and Yossi Richter", title = "An improved algorithm for {CIOQ} switches", journal = j-TALG, volume = "2", number = "2", pages = "282--295", month = apr, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Wed Aug 23 05:38:18 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Berend:2006:CMP, author = "Daniel Berend and Amir Sapir", title = "The cyclic multi-peg {Tower of Hanoi}", journal = j-TALG, volume = "2", number = "3", pages = "297--317", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Drmota:2006:RFA, author = "Michael Drmota and Helmut Prodinger", title = "The register function for $t$-ary trees", journal = j-TALG, volume = "2", number = "3", pages = "318--334", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kowalik:2006:OBL, author = "Lukasz Kowalik and Maciej Kurowski", title = "Oracles for bounded-length shortest paths in planar graphs", journal = j-TALG, volume = "2", number = "3", pages = "335--363", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Katriel:2006:OTO, author = "Irit Katriel and Hans L. Bodlaender", title = "Online topological ordering", journal = j-TALG, volume = "2", number = "3", pages = "364--379", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Duncan:2006:OCG, author = "Christian A. Duncan and Stephen G. Kobourov and V. S. Anil Kumar", title = "Optimal constrained graph exploration", journal = j-TALG, volume = "2", number = "3", pages = "380--402", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Raman:2006:FFP, author = "Venkatesh Raman and Saket Saurabh and C. R. Subramanian", title = "Faster fixed parameter tractable algorithms for finding feedback vertex sets", journal = j-TALG, volume = "2", number = "3", pages = "403--415", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jansen:2006:AAS, author = "Klaus Jansen and Hu Zhang", title = "An approximation algorithm for scheduling malleable tasks under general precedence constraints", journal = j-TALG, volume = "2", number = "3", pages = "416--434", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Feigenbaum:2006:SMC, author = "Joan Feigenbaum and Yuval Ishai and Tal Malkin and Kobbi Nissim and Martin J. Strauss and Rebecca N. Wright", title = "Secure multiparty computation of approximations", journal = j-TALG, volume = "2", number = "3", pages = "435--472", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Johnson:2006:NCC, author = "David S. Johnson", title = "The {NP}-completeness column: {The} many limits on approximation", journal = j-TALG, volume = "2", number = "3", pages = "473--489", month = jul, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Thu Sep 21 08:13:30 MDT 2006", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lopez-Ortiz:2006:F, author = "Alejandro L{\'o}pez-Ortiz and J. Ian Munro", title = "Foreword", journal = j-TALG, volume = "2", number = "4", pages = "491--491", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2006:QAM, author = "David Eppstein", title = "Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms", journal = j-TALG, volume = "2", number = "4", pages = "492--509", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Geary:2006:SOT, author = "Richard F. Geary and Rajeev Raman and Venkatesh Raman", title = "Succinct ordinal trees with level-ancestor queries", journal = j-TALG, volume = "2", number = "4", pages = "510--534", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mendelson:2006:MPQ, author = "Ran Mendelson and Robert E. Tarjan and Mikkel Thorup and Uri Zwick", title = "Melding priority queues", journal = j-TALG, volume = "2", number = "4", pages = "535--556", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baswana:2006:ADO, author = "Surender Baswana and Sandeep Sen", title = "Approximate distance oracles for unweighted graphs in expected {$ O(n^2) $} time", journal = j-TALG, volume = "2", number = "4", pages = "557--577", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demetrescu:2006:EAD, author = "Camil Demetrescu and Giuseppe F. Italiano", title = "Experimental analysis of dynamic all pairs shortest path algorithms", journal = j-TALG, volume = "2", number = "4", pages = "578--601", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Irving:2006:RMM, author = "Robert W. Irving and Telikepalli Kavitha and Kurt Mehlhorn and Dimitrios Michail and Katarzyna E. Paluch", title = "Rank-maximal matchings", journal = j-TALG, volume = "2", number = "4", pages = "602--610", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Foschini:2006:WIE, author = "Luca Foschini and Roberto Grossi and Ankur Gupta and Jeffrey Scott Vitter", title = "When indexing equals compression: {Experiments} with compressing suffix arrays and applications", journal = j-TALG, volume = "2", number = "4", pages = "611--639", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alon:2006:GAO, author = "Noga Alon and Baruch Awerbuch and Yossi Azar and Niv Buchbinder and Joseph (Seffi) Naor", title = "A general approach to online network optimization problems", journal = j-TALG, volume = "2", number = "4", pages = "640--660", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Evans:2006:OSV, author = "William Evans and David Kirkpatrick", title = "Optimally scheduling video-on-demand to minimize delay when sender and receiver bandwidth may differ", journal = j-TALG, volume = "2", number = "4", pages = "661--678", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Beier:2006:CES, author = "Rene Beier and Artur Czumaj and Piotr Krysta and Berthold V{\"o}cking", title = "Computing equilibria for a service provider game with (Im)perfect information", journal = j-TALG, volume = "2", number = "4", pages = "679--706", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Moore:2006:GQF, author = "Cristopher Moore and Daniel Rockmore and Alexander Russell", title = "Generic quantum {Fourier} transforms", journal = j-TALG, volume = "2", number = "4", pages = "707--723", month = oct, year = "2006", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Archer:2007:FPM, author = "Aaron Archer and {\'E}va Tardos", title = "Frugal path mechanisms", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bhatia:2007:AAB, author = "Randeep Bhatia and Julia Chuzhoy and Ari Freund and Joseph (Seffi) Naor", title = "Algorithmic aspects of bandwidth trading", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Carmo:2007:QPI, author = "Renato Carmo and Tom{\'a}s Feder and Yoshiharu Kohayakawa and Eduardo Laber and Rajeev Motwani and Liadan O'Callaghan and Rina Panigrahy and Dilys Thomas", title = "Querying priced information in databases: {The} conjunctive case", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ciriani:2007:DSS, author = "Valentina Ciriani and Paolo Ferragina and Fabrizio Luccio and S. Muthukrishnan", title = "A data structure for a sequence of string accesses in external memory", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cormode:2007:SED, author = "Graham Cormode and S. Muthukrishnan", title = "The string edit distance matching problem with moves", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The edit distance between two strings $S$ and $R$ is defined to be the minimum number of character inserts, deletes, and changes needed to convert $R$ to S. Given a text string $t$ of length $n$, and a pattern string $p$ of length $m$, informally, the string edit distance matching problem is to compute the smallest edit distance between $p$ and substrings of $t$. We relax the problem so that: (a) we allow an additional operation, namely, substring moves; and (b) we allow approximation of this string edit distance. Our result is a near-linear time deterministic algorithm to produce a factor of $ O(\log n \log \star n)$ approximation to the string edit distance with moves. This is the first known significantly subquadratic algorithm for a string edit distance problem in which the distance involves nontrivial alignments. Our results are obtained by embedding strings into $ L_1$ vector space using a simplified parsing technique, which we call edit-sensitive parsing (ESP).", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Czumaj:2007:TBW, author = "Artur Czumaj and Berthold V{\"o}cking", title = "Tight bounds for worst-case equilibria", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2007:IAR, author = "Michael Elkin and Guy Kortsarz", title = "An improved algorithm for radio broadcast", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2007:FSI, author = "David Eppstein", title = "Foreword to special issue on {SODA 2002}", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hershberger:2007:DSS, author = "John Hershberger and Subhash Suri and Amit Bhosle", title = "On the difficulty of some shortest path problems", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pandurangan:2007:EBB, author = "Gopal Pandurangan and Eli Upfal", title = "Entropy-based bounds for online algorithms", journal = j-TALG, volume = "3", number = "1", pages = "??--??", month = feb, year = "2007", CODEN = "????", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Apr 14 10:58:14 MDT 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Voronenko:2007:MMC, author = "Yevgen Voronenko and Markus P{\"u}schel", title = "Multiplierless multiple constant multiplication", journal = j-TALG, volume = "3", number = "2", pages = "11:1--11:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240234", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A variable can be multiplied by a given set of fixed-point constants using a multiplier block that consists exclusively of additions, subtractions, and shifts. The generation of a multiplier block from the set of constants is known as the multiple constant multiplication (MCM) problem. Finding the optimal solution, namely, the one with the fewest number of additions and subtractions, is known to be NP-complete. We propose a new algorithm for the MCM problem, which produces solutions that require up to 20\% less additions and subtractions than the best previously known algorithm. At the same time our algorithm, in contrast to the closest competing algorithm, is not limited by the constant bitwidths. We present our algorithm using a unifying formal framework for the best, graph-based MCM algorithms and provide a detailed runtime analysis and experimental evaluation. We show that our algorithm can handle problem sizes as large as 100 32-bit constants in a time acceptable for most applications. The implementation of the new algorithm is available at \path =www.spiral.net=.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Addition chains; directed graph; FIR filter; fixed-point arithmetic; strength reduction", } @Article{Chern:2007:PCR, author = "Hua-Huai Chern and Michael Fuchs and Hsien-Kuei Hwang", title = "Phase changes in random point quadtrees", journal = j-TALG, volume = "3", number = "2", pages = "12:1--12:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240235", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that a wide class of linear cost measures (such as the number of leaves) in random $d$-dimensional point quadtrees undergo a change in limit laws: If the dimension $ d = 1, \ldots, 8 $, then the limit law is normal; if $ d \geq 9 $ then there is no convergence to a fixed limit law. Stronger approximation results such as convergence rates and local limit theorems are also derived for the number of leaves, additional phase changes being unveiled. Our approach is new and very general, and also applicable to other classes of search trees. A brief discussion of Devroye's grid trees (covering $m$-ary search trees and quadtrees as special cases) is given. We also propose an efficient numerical procedure for computing the constants involved to high precision.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "analysis in distribution of algorithms; Asymptotic transfer; central limit theorems; depth; differential equations; grid trees; local limit theorems; Mellin transforms; page usage; phase transitions; quadtrees; total path length", } @Article{Demaine:2007:RDS, author = "Erik D. Demaine and John Iacono and Stefan Langerman", title = "Retroactive data structures", journal = j-TALG, volume = "3", number = "2", pages = "13:1--13:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240236", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present, but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. The data structure allows arbitrary insertion and deletion of operations at arbitrary times, subject only to consistency requirements. We initiate the study of retroactive data structures by formally defining the model and its variants. We prove that, unlike persistence, efficient retroactivity is not always achievable. Thus, we present efficient retroactive data structures for queues, doubly ended queues, priority queues, union-find, and decomposable search structures.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "History; persistence; point location; rollback; time travel", } @Article{Hayward:2007:IAW, author = "Ryan B. Hayward and Jeremy P. Spinrad and R. Sritharan", title = "Improved algorithms for weakly chordal graphs", journal = j-TALG, volume = "3", number = "2", pages = "14:1--14:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240237", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We use a new structural theorem on the presence of two-pairs in weakly chordal graphs to develop improved algorithms. For the recognition problem, we reduce the time complexity from {$ O(m n^2) $} to {$ O(m^2) $} and the space complexity from {$ O(n^3) $} to {$ O(m + n) $}, and also produce a hole or antihole if the input graph is not weakly chordal. For the optimization problems, the complexity of the clique and coloring problems is reduced from {$ O(m n^2) $} to {$ O(n^3) $} and the complexity of the independent set and clique cover problems is improved from {$ O(n^4) $} to {$ O(m n) $}. The space complexity of our optimization algorithms is {$ O(m + n) $}.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "coloring; graph algorithms; Perfect graphs; recognition; weakly chordal", } @Article{Kavitha:2007:SSM, author = "Telikepalli Kavitha and Kurt Mehlhorn and Dimitrios Michail and Katarzyna E. Paluch", title = "Strongly stable matchings in time {$ O(n m) $} and extension to the hospitals-residents problem", journal = j-TALG, volume = "3", number = "2", pages = "15:1--15:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240238", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An instance of the stable marriage problem is an undirected bipartite graph {$ G = (X \cup W, E) $} with linearly ordered adjacency lists with ties allowed in the ordering. A matching {$M$} is a set of edges, no two of which share an endpoint. An edge {$ e = (a, b) \in E \setminus M $} is a blocking edge for {$M$} if {$a$} is either unmatched or strictly prefers {$b$} to its partner in {$M$}, and {$b$} is unmatched, strictly prefers {$a$} to its partner in {$M$}, or is indifferent between them. A matching is strongly stable if there is no blocking edge with respect to it. We give an {$ O(n m) $} algorithm for computing strongly stable matchings, where {$n$} is the number of vertices and {$m$} the number of edges. The previous best algorithm had running time {$ O(m^2) $}. We also study this problem in the hospitals-residents setting, which is a many-to-one extension of the aforementioned problem. We give an {$ O(m \sum_{h \in H} p_h) $} algorithm for computing a strongly stable matching in the hospitals-residents problem, where {$ p_h $} is the quota of a hospital {$h$}. The previous best algorithm had running time {$ O(m^2) $}.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Bipartite matching; level maximal; stable marriage; strong stability", } @Article{Bagchi:2007:DSR, author = "Amitabha Bagchi and Amitabh Chaudhary and David Eppstein and Michael T. Goodrich", title = "Deterministic sampling and range counting in geometric data streams", journal = j-TALG, volume = "3", number = "2", pages = "16:1--16:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240239", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present memory-efficient deterministic algorithms for constructing $ \epsilon $-nets and $ \epsilon $-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are at least inverse-polylogarithmic. We also include a lower bound for noniceberg geometric queries.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Data streams; epsilon nets; geometric data; iceberg queries; range counting; robust statistics; sampling; streaming algorithms", } @Article{Arya:2007:SEB, author = "Sunil Arya and Theocharis Malamatos and David M. Mount", title = "A simple entropy-based algorithm for planar point location", journal = j-TALG, volume = "3", number = "2", pages = "17:1--17:17", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240240", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a planar polygonal subdivision {$S$}, point location involves preprocessing this subdivision into a data structure so that given any query point {$q$}, the cell of the subdivision containing {$q$} can be determined efficiently. Suppose that for each cell {$z$} in the subdivision, the probability $ p_z $ that a query point lies within this cell is also given. The goal is to design the data structure to minimize the average search time. This problem has been considered before, but existing data structures are all quite complicated. It has long been known that the entropy {$H$} of the probability distribution is the dominant term in the lower bound on the average-case search time. In this article, we show that a very simple modification of a well-known randomized incremental algorithm can be applied to produce a data structure of expected linear size that can answer point-location queries in {$ O(H) $} average time. We also present empirical evidence for the practical efficiency of this approach.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "entropy; expected-case complexity; Point location; polygonal subdivision; randomized algorithms; trapezoidal maps", } @Article{Kauers:2007:ADZ, author = "Manuel Kauers", title = "An algorithm for deciding zero equivalence of nested polynomially recurrent sequences", journal = j-TALG, volume = "3", number = "2", pages = "18:1--18:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240241", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce the class of nested polynomially recurrent sequences which includes a large number of sequences that are of combinatorial interest. We present an algorithm for deciding zero equivalence of these sequences, thereby providing a new algorithm for proving identities among combinatorial sequences: In order to prove an identity, decide by the algorithm whether the difference of lefthand-side and righthand-side is identically zero. This algorithm is able to treat mathematical objects which are not covered by any other known symbolic method for proving combinatorial identities. Despite its theoretical flavor and high complexity, an implementation of the algorithm can be successfully applied to nontrivial examples.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "combinatorial sequences; nested polynomially recurrent sequences; Symbolic computation; zero equivalence", } @Article{Amir:2007:DTS, author = "Amihood Amir and Gad M. Landau and Moshe Lewenstein and Dina Sokol", title = "Dynamic text and static pattern matching", journal = j-TALG, volume = "3", number = "2", pages = "19:1--19:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240242", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we address a new version of dynamic pattern matching. The dynamic text and static pattern matching problem is the problem of finding a static pattern in a text that is continuously being updated. The goal is to report all new occurrences of the pattern in the text after each text update. We present an algorithm for solving the problem where the text update operation is changing the symbol value of a text location. Given a text of length $n$ and a pattern of length $m$, our algorithm preprocesses the text in time {$ O(n \log \log m) $}, and the pattern in time {$ O(m \log m) $}. The extra space used is {$ O(n + m \log m) $}. Following each text update, the algorithm deletes all prior occurrences of the pattern that no longer match, and reports all new occurrences of the pattern in the text in {$ O(\log \log m) $} time. We note that the complexity is not proportional to the number of pattern occurrences, since all new occurrences can be reported in a succinct form.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "border trees; Dynamic text; static pattern", } @Article{Ferragina:2007:CRS, author = "Paolo Ferragina and Giovanni Manzini and Veli M{\"a}kinen and Gonzalo Navarro", title = "Compressed representations of sequences and full-text indexes", journal = j-TALG, volume = "3", number = "2", pages = "20:1--20:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240243", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a sequence {$ S = s_1 s_2 \ldots s_n $} of integers smaller than {$ r = O(\polylog (n)) $}, we show how {$S$} can be represented using {$ n H_0 (S) + o(n) $} bits, so that we can know any {$ s_q $}, as well as answer rank and select queries on {$S$}, in constant time. {$ H_0 (S) $} is the zero-order empirical entropy of {$S$} and {$ n H_0 (S) $} provides an information-theoretic lower bound to the bit storage of any sequence {$S$} via a fixed encoding of its symbols. This extends previous results on binary sequences, and improves previous results on general sequences where those queries are answered in {$ O(\log r) $} time. For larger {$r$}, we can still represent {$S$} in {$ n H_0 (S) + o(n \log r) $} bits and answer queries in {$ O(\log r / \log \log n) $} time.\par Another contribution of this article is to show how to combine our compressed representation of integer sequences with a compression boosting technique to design compressed full-text indexes that scale well with the size of the input alphabet {$ \Sigma $}. Specifically, we design a variant of the FM-index that indexes a string {$ T[1, n] $} within {$ n H_k(T) + o(n) $} bits of storage, where {$ H_k(T) $} is the {$k$} th-order empirical entropy of {$T$}. This space bound holds simultaneously for all {$ k \leq \alpha \log | \Sigma | n $}, constant {$ 0 < \alpha < 1 $}, and {$ | \Sigma | = O(\polylog (n)) $}. This index counts the occurrences of an arbitrary pattern {$ P[1, p] $} as a substring of {$T$} in {$ O(p) $} time; it locates each pattern occurrence in {$ O(\log 1 + \varepsilon n) $} time for any constant {$ 0 < \varepsilon < 1 $}; and reports a text substring of length {$ \ell $} in {$ O(\ell + \log 1 + \varepsilon n) $} time.\par Compared to all previous works, our index is the first that removes the alphabet-size dependance from all query times, in particular, counting time is linear in the pattern length. Still, our index uses essentially the same space of the {$k$} th-order entropy of the text {$T$}, which is the best space obtained in previous work. We can also handle larger alphabets of size {$ | \Sigma | = O(n \beta) $}, for any {$ 0 < \beta < 1 $}, by paying {$ o(n \log | \Sigma |) $} extra space and multiplying all query times by {$ O(\log | \Sigma | / \log \log n) $}.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Burrows--Wheeler transform; compression boosting; entropy; rank and select; text compression; Text indexing; wavelet tree", } @Article{Chan:2007:CID, author = "Ho-Leung Chan and Wing-Kai Hon and Tak-Wah Lam and Kunihiko Sadakane", title = "Compressed indexes for dynamic text collections", journal = j-TALG, volume = "3", number = "2", pages = "21:1--21:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240244", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$T$} be a string with {$n$} characters over an alphabet of constant size. A recent breakthrough on compressed indexing allows us to build an index for {$T$} in optimal space (i.e., {$ O(n) $} bits), while supporting very efficient pattern matching [Ferragina and Manzini 2000; Grossi and Vitter 2000]. Yet the compressed nature of such indexes also makes them difficult to update dynamically.\par This article extends the work on optimal-space indexing to a dynamic collection of texts. Our first result is a compressed solution to the library management problem, where we show an index of {$ O(n) $} bits for a text collection {$L$} of total length {$n$}, which can be updated in {$ O(| T | \log n) $} time when a text {$T$} is inserted or deleted from {$L$}; also, the index supports searching the occurrences of any pattern {$P$} in all texts in {$L$} in {$ O(|P| \log n + {\rm occ} \log 2 n) $} time, where {\rm occ} is the number of occurrences.\par Our second result is a compressed solution to the dictionary matching problem, where we show an index of {$ O(d) $} bits for a pattern collection {$D$} of total length {$d$}, which can be updated in {$ O(|P| \log 2 d) $} time when a pattern {$P$} is inserted or deleted from {$D$}; also, the index supports searching the occurrences of all patterns of {$D$} in any text {$T$} in {$ O((|T| + {\rm occ}) \log 2 d) $} time. When compared with the {$ O(d \log d) $}-bit suffix-tree-based solution of Amir et al. [1995], the compact solution increases the query time by roughly a factor of {$ \log d $} only.\par The solution to the dictionary matching problem is based on a new compressed representation of a suffix tree. Precisely, we give an {$ O(n) $}-bit representation of a suffix tree for a dynamic collection of texts whose total length is {$n$}, which supports insertion and deletion of a text {$T$} in {$ O(|T| \log 2 n) $} time, as well as all suffix tree traversal operations, including forward and backward suffix links. This work can be regarded as a generalization of the compressed representation of static texts. In the study of the aforementioned result, we also derive the first {$ O(n) $}-bit representation for maintaining {$n$} pairs of balanced parentheses in {$ O(\log n / \log \log n) $} time per operation, matching the time complexity of the previous {$ O(n \log n) $}-bit solution.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Compressed suffix tree; string matching", } @Article{Boyar:2007:RWO, author = "Joan Boyar and Lene M. Favrholdt", title = "The relative worst order ratio for online algorithms", journal = j-TALG, volume = "3", number = "2", pages = "22:1--22:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240245", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We define a new measure for the quality of online algorithms, the relative worst order ratio, using ideas from the max/max ratio [Ben-David and Borodin 1994] and from the random order ratio [Kenyon 1996]. The new ratio is used to compare online algorithms directly by taking the ratio of their performances on their respective worst permutations of a worst-case sequence.\par Two variants of the bin packing problem are considered: the classical bin packing problem, where the goal is to fit all items in as few bins as possible, and the dual bin packing problem, which is the problem of maximizing the number of items packed in a fixed number of bins. Several known algorithms are compared using this new measure, and a new, simple variant of first-fit is proposed for dual bin packing.\par Many of our results are consistent with those previously obtained with the competitive ratio or the competitive ratio on accommodating sequences, but new separations and easier proofs are found.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "bin packing; dual bin packing; Online; quality measure; relative worst order ratio", } @Article{Becchetti:2007:SCM, author = "L. Becchetti and J. K{\"o}nemann and S. Leonardi and M. P{\'a}al", title = "Sharing the cost more efficiently: {Improved} approximation for multicommodity rent-or-buy", journal = j-TALG, volume = "3", number = "2", pages = "23:1--23:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240246", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the multicommodity rent-or-buy (MROB) network design problems, we are given a network together with a set of $k$ terminal pairs $ (s_1, t_1), \ldots, (s_k, t_k) $. The goal is to provision the network so that a given amount of flow can be shipped between $ s_i $ and $ t_i $ for all $ 1 \leq i \leq k $ simultaneously. In order to provision the network, one can either rent capacity on edges at some cost per unit of flow, or buy them at some larger fixed cost. Bought edges have no incremental, flow-dependent cost. The overall objective is to minimize the total provisioning cost.\par Recently, Gupta et al. [2003a] presented a 12-approximation for the MROB problem. Their algorithm chooses a subset of the terminal pairs in the graph at random and then buys the edges of an approximate Steiner forest for these pairs. This technique had previously been introduced [Gupta et al. 2003b] for the single-sink rent-or-buy network design problem.\par In this article we give a 6.828-approximation for the MROB problem by refining the algorithm of Gupta et al. and simplifying their analysis. The improvement in our article is based on a more careful adaptation and simplified analysis of the primal-dual algorithm for the Steiner forest problem due to Agrawal et al. [1995]. Our result significantly reduces the gap between the single-sink and multisink case.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; cost sharing; network design; Steiner forests", } @Article{Johnson:2007:NCC, author = "David S. Johnson", title = "The {NP}-completeness column: {Finding} needles in haystacks", journal = j-TALG, volume = "3", number = "2", pages = "24:1--24:??", month = may, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1240233.1240247", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:54:42 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This is the 26th edition of a column that covers new developments in the theory of NP-completeness. The presentation is modeled on that which M. R. Garey and I used in our book ``Computers and Intractability: A Guide to the Theory of NP-Completeness,'' W. H. Freeman {\&} Co., New York, 1979, hereinafter referred to as ``[G{\&}J].'' Previous columns, the first 23 of which appeared in J. Algorithms, will be referred to by a combination of their sequence number and year of appearance, e.g., ``Column 1 [1981].'' Full bibliographic details on the previous columns, as well as downloadable unofficial versions of them, can be found at \path =http://www.research.att.com/~dsj/columns/=. This column discusses the question of whether finding an object can be computationally difficult even when we know that the object exists.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "fixed point; game theory; local search; Nash equilibrium; PLS; PPAD", } @Article{Feng:2007:FAS, author = "Jianxing Feng and Daming Zhu", title = "Faster algorithms for sorting by transpositions and sorting by block interchanges", journal = j-TALG, volume = "3", number = "3", pages = "25:1--25:14", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273341", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we present a new data structure, called the permutation tree, to improve the running time of sorting permutation by transpositions and sorting permutation by block interchanges. The existing 1.5-approximation algorithm for sorting permutation by transpositions has time complexity {$ O(n^{3 / 2} \sqrt {\log n}) $}. By means of the permutation tree, we can improve this algorithm to achieve time complexity {$ O(n \log n) $}. We can also improve the algorithm for sorting permutation by block interchanges to take its time complexity from {$ O(n^2) $} down to {$ O(n \log n) $}.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Block interchange; genome; permutation; time complexity; transposition; tree", } @Article{Gupta:2007:CPD, author = "Himanshu Gupta and Rephael Wenger", title = "Constructing pairwise disjoint paths with few links", journal = j-TALG, volume = "3", number = "3", pages = "26:1--26:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273342", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$P$} be a simple polygon and let {$ \{ (u_1, u{\prime }_1), (u_2, u{\prime }_2), \ldots, (u_m, u{\prime }_m) \} $} be a set of {$m$} pairs of distinct vertices of {$P$}, where for every distinct {$ i, j \leq m $}, there exist pairwise disjoint (nonintersecting) paths connecting {$ u_i $} to {$ u \prime_i $} and $ u_j $ to $ u \prime_j $. We wish to construct $m$ pairwise disjoint paths in the interior of {$P$} connecting {$ u_i $} to {$ u \prime_i $} for {$ i = 1, \ldots, m $}, with a minimal total number of line segments. We give an approximation algorithm that constructs such a set of paths using {$ O(M) $} line segments in {$ O(n \log m + M \log m) $} time, where {$M$} is the number of line segments in the optimal solution and {$n$} is the size of the polygon.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "isomorphic triangulations; Link paths; noncrossing; polygon", } @Article{Chekuri:2007:MDF, author = "Chandra Chekuri and Marcelo Mydlarz and F. Bruce Shepherd", title = "Multicommodity demand flow in a tree and packing integer programs", journal = j-TALG, volume = "3", number = "3", pages = "27:1--27:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273343", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider requests for capacity in a given tree network {$ T = (V, E) $} where each edge {$e$} of the tree has some integer capacity {$ u_e $}. Each request {$f$} is a node pair with an integer demand $ d_f $ and a profit $ w_f $ which is obtained if the request is satisfied. The objective is to find a set of demands that can be feasibly routed in the tree and which provides a maximum profit. This generalizes well-known problems, including the knapsack and $b$-matching problems.\par When all demands are 1, we have the integer multicommodity flow problem. Garg et al. [1997] had shown that this problem is NP-hard and gave a 2-approximation algorithm for the cardinality case (all profits are 1) via a primal-dual algorithm. Our main result establishes that the integrality gap of the natural linear programming relaxation is at most 4 for the case of arbitrary profits. Our proof is based on coloring paths on trees and this has other applications for wavelength assignment in optical network routing.\par We then consider the problem with arbitrary demands. When the maximum demand $ d_{\rm max} $ is at most the minimum edge capacity $ u_{\rm min} $, we show that the integrality gap of the LP is at most 48. This result is obtained by showing that the integrality gap for the demand version of such a problem is at most 11.542 times that for the unit-demand case. We use techniques of Kolliopoulos and Stein [2004, 2001] to obtain this. We also obtain, via this method, improved algorithms for line and ring networks. Applications and connections to other combinatorial problems are discussed.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithm; Integer multicommodity flow; integrality gap; packing integer program; tree", } @Article{Bar-Noy:2007:WSR, author = "Amotz Bar-Noy and Richard E. Ladner and Tami Tamir", title = "Windows scheduling as a restricted version of bin packing", journal = j-TALG, volume = "3", number = "3", pages = "28:1--28:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273344", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a sequence of $n$ positive integers $ w_1, w_2, \ldots, w_n $ that are associated with the items $ 1, 2, \ldots n $, respectively. In the windows scheduling problem, the goal is to schedule all the items (equal-length information pages) on broadcasting channels such that the gap between two consecutive appearances of page $i$ on any of the channels is at most $ w_i $ slots (a slot is the transmission time of one page). In the unit-fractions bin packing problem, the goal is to pack all the items in bins of unit size where the size (width) of item $i$ is $ 1 / w_i $. The optimization objective is to minimize the number of channels or bins. In the offline setting, the sequence is known in advance, whereas in the online setting, the items arrive in order and assignment decisions are irrevocable. Since a page requires at least $ 1 / w_i $ of a channel's bandwidth, it follows that windows scheduling without migration (i.e., all broadcasts of a page must be from the same channel) is a restricted version of unit-fractions bin packing.\par Let {$ H = \lceil \sum_{i = 1}^n (1 / w_i) $} be the bandwidth lower bound on the required number of bins (channels). The best-known offline algorithm for the windows scheduling problem used {$ H + O(\ln H) $} channels. This article presents an offline algorithm for the unit-fractions bin packing problem with at most {$ H + 1 $} bins. In the online setting, this article presents algorithms for both problems with {$ H + O(\sqrt {H}) $} channels or bins, where the one for the unit-fractions bin packing problem is simpler. On the other hand, this article shows that already for the unit-fractions bin packing problem, any online algorithm must use at least {$ H + \Omega (\ln H) $} bins. For instances in which the window sizes form a divisible sequence, an optimal online algorithm is presented. Finally, this article includes a new NP-hardness proof for the windows scheduling problem.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; bin-packing; online algorithms; Periodic scheduling", } @Article{Hazay:2007:APM, author = "Carmit Hazay and Moshe Lewenstein and Dina Sokol", title = "Approximate parameterized matching", journal = j-TALG, volume = "3", number = "3", pages = "29:1--29:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273345", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Two equal length strings $s$ and $ s \prime $, over alphabets {$ \Sigma s $} and {$ \Sigma s \prime $}, parameterize match if there exists a bijection {$ \pi : \Sigma s \rightarrow \Sigma s \prime $} such that {$ \pi (s) = s \prime $}, where {$ \pi (s) $} is the renaming of each character of {$s$} via $ \pi $. Parameterized matching is the problem of finding all parameterized matches of a pattern string $p$ in a text $t$, and approximate parameterized matching is the problem of finding at each location a bijection $ \pi $ that maximizes the number of characters that are mapped from $p$ to the appropriate $ |p| $-length substring of $t$.\par Parameterized matching was introduced as a model for software duplication detection in software maintenance systems and also has applications in image processing and computational biology. For example, approximate parameterized matching models image searching with variable color maps in the presence of errors.\par We consider the problem for which an error threshold, $k$, is given, and the goal is to find all locations in $t$ for which there exists a bijection $ \pi $ which maps $p$ into the appropriate $ |p| $-length substring of $t$ with at most $k$ mismatched mapped elements. Our main result is an algorithm for this problem with {$ O(n k^{1.5} + m k \log m) $} time complexity, where {$ m = | p | $} and {$ n = | t | $}. We also show that when {$ | p | = | t | = m $}, the problem is equivalent to the maximum matching problem on graphs, yielding a {$ O(m + k^{1.5}) $} solution.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Hamming distance; maximum matching; mismatch pair; parameterize match", } @Article{Halldorsson:2007:IAR, author = "Magn{\'u}s M. Halld{\'o}rsson and Kazuo Iwama and Shuichi Miyazaki and Hiroki Yanagisawa", title = "Improved approximation results for the stable marriage problem", journal = j-TALG, volume = "3", number = "3", pages = "30:1--30:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273346", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The stable marriage problem has recently been studied in its general setting, where both ties and incomplete lists are allowed. It is NP-hard to find a stable matching of maximum size, while any stable matching is a maximal matching and thus trivially we can obtain a 2-approximation algorithm.\par In this article, we give the first nontrivial result for approximation of factor less than two. Our algorithm achieves an approximation ratio of {$ 2 / (1 + L - 2) $} for instances in which only men have ties of length at most {$L$}. When both men and women are allowed to have ties but the lengths are limited to two, then we show a ratio of {$ 13 / 7 ( < 1.858) $}. We also improve the lower bound on the approximation ratio to {$ 21 / 19 ( > 1.1052) $}.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; incomplete lists; stable marriage problem; ties", } @Article{Indyk:2007:NNP, author = "Piotr Indyk and Assaf Naor", title = "Nearest-neighbor-preserving embeddings", journal = j-TALG, volume = "3", number = "3", pages = "31:1--31:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273347", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we introduce the notion of nearest-neighbor-preserving embeddings. These are randomized embeddings between two metric spaces which preserve the (approximate) nearest-neighbors. We give two examples of such embeddings for Euclidean metrics with low ``intrinsic'' dimension. Combining the embeddings with known data structures yields the best-known approximate nearest-neighbor data structures for such metrics.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "dimensionality reduction; doubling spaces; embeddings; Nearest neighbor", } @Article{Even-Dar:2007:CTN, author = "Eyal Even-Dar and Alex Kesselman and Yishay Mansour", title = "Convergence time to {Nash} equilibrium in load balancing", journal = j-TALG, volume = "3", number = "3", pages = "32:1--32:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273348", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the number of steps required to reach a pure Nash equilibrium in a load balancing scenario where each job behaves selfishly and attempts to migrate to a machine which will minimize its cost. We consider a variety of load balancing models, including identical, restricted, related, and unrelated machines. Our results have a crucial dependence on the weights assigned to jobs. We consider arbitrary weights, integer weights, $k$ distinct weights, and identical (unit) weights. We look both at an arbitrary schedule (where the only restriction is that a job migrates to a machine which lowers its cost) and specific efficient schedulers (e.g., allowing the largest weight job to move first). A by-product of our results is establishing a connection between various scheduling models and the game-theoretic notion of potential games. We show that load balancing in unrelated machines is a generalized ordinal potential game, load balancing in related machines is a weighted potential game, and load balancing in related machines and unit weight jobs is an exact potential game.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "convergence time; game theory; Nash equilibrium", } @Article{Andrews:2007:RSM, author = "Matthew Andrews and Lisa Zhang", title = "Routing and scheduling in multihop wireless networks with time-varying channels", journal = j-TALG, volume = "3", number = "3", pages = "33:1--33:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273349", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study routing and scheduling in multihop wireless networks. When data is transmitted from its source node to its destination node it may go through other wireless nodes as intermediate hops. The data transmission is node constrained, that is, every node can transmit data to at most one neighboring node per time step. The transmission rates are time varying as a result of changing wireless channel conditions.\par In this article, we assume that data arrivals and transmission rates are governed by an adversary. The power of the adversary is limited by an admissibility condition which forbids the adversary from overloading any wireless node a priori. The node-constrained transmission and time-varying nature of the transmission rates make our model different from and harder than the standard adversarial queueing model which relates to wireline networks.\par For the case in which the adversary specifies the paths that the data must follow, we design scheduling algorithms that ensure network stability. These algorithms try to give priority to the data that is closest to its source node. However, at each time step only a subset of the data queued at a node is eligible for scheduling. One of our algorithms is fully distributed.\par For the case in which the adversary does not dictate the data paths, we show how to route data so that the admissibility condition is satisfied. We can then schedule data along the chosen paths using our stable scheduling algorithms.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "routing; Scheduling; stability; time-varying; wireless network", } @Article{Naor:2007:NAP, author = "Moni Naor and Udi Wieder", title = "Novel architectures for {P2P} applications: {The} continuous-discrete approach", journal = j-TALG, volume = "3", number = "3", pages = "34:1--34:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273350", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose a new approach for constructing P2P networks based on a dynamic decomposition of a continuous space into cells corresponding to servers. We demonstrate the power of this approach by suggesting two new P2P architectures and various algorithms for them. The first serves as a DHT (distributed hash table) and the other is a dynamic expander network. The DHT network, which we call Distance Halving, allows logarithmic routing and load while preserving constant degrees. It offers an optimal tradeoff between degree and path length in the sense that degree $d$ guarantees a path length of {$ O(\log d n) $}. Another advantage over previous constructions is its relative simplicity. A major new contribution of this construction is a dynamic caching technique that maintains low load and storage, even under the occurrence of hot spots. Our second construction builds a network that is guaranteed to be an expander. The resulting topologies are simple to maintain and implement. Their simplicity makes it easy to modify and add protocols. A small variation yields a DHT which is robust against random Byzantine faults. Finally we show that, using our approach, it is possible to construct any family of constant degree graphs in a dynamic environment, though with worse parameters. Therefore, we expect that more distributed data structures could be designed and implemented in a dynamic environment.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Peer-to-peer networks; routing", } @Article{Khuller:2007:PC, author = "Samir Khuller", title = "Problems column", journal = j-TALG, volume = "3", number = "3", pages = "35:1--35:??", month = aug, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1273340.1273351", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gabow:2007:ISS, author = "H. N. Gabow and Michael A. Bender and Martin Farach-Colton", title = "Introduction to {SODA} 2002 and 2003 special issue", journal = j-TALG, volume = "3", number = "4", pages = "36:1--36:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290673", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aspnes:2007:SG, author = "James Aspnes and Gauri Shah", title = "Skip graphs", journal = j-TALG, volume = "3", number = "4", pages = "37:1--37:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290674", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are designed for use in searching peer-to-peer systems, and by providing the ability to perform queries based on key ordering, they improve on existing search tools that provide only hash table functionality. Unlike skip lists or other tree data structures, skip graphs are highly resilient, tolerating a large fraction of failed nodes without losing connectivity. In addition, simple and straightforward algorithms can be used to construct a skip graph, insert new nodes into it, search it, and detect and repair errors within it introduced due to node failures.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "overlay networks; Peer-to-peer; skip lists", } @Article{Han:2007:OPS, author = "Yijie Han", title = "Optimal parallel selection", journal = j-TALG, volume = "3", number = "4", pages = "38:1--38:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290675", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present an optimal parallel selection algorithm on the EREW PRAM. This algorithm runs in {$ O(\log n) $} time with {$ n / \log n $} processors. This complexity matches the known lower bound for parallel selection on the EREW PRAM model. We therefore close this problem which has been open for more than a decade.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "EREW PRAM; Parallel algorithms; selection", } @Article{Bansal:2007:MWF, author = "Nikhil Bansal and Kedar Dhamdhere", title = "Minimizing weighted flow time", journal = j-TALG, volume = "3", number = "4", pages = "39:1--39:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290676", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of minimizing the total weighted flow time on a single machine with preemptions. We give an online algorithm that is {$ O(k) $}-competitive for {$k$} weight classes. This implies an {$ O(\log W) $}-competitive algorithm, where {$W$} is the maximum to minimum ratio of weights. This algorithm also implies an {$ O(\log n + \log P) $}-approximation ratio for the problem, where {$P$} is the ratio of the maximum to minimum job size and {$n$} is the number of jobs. We also consider the nonclairvoyant setting where the size of a job is unknown upon its arrival and becomes known to the scheduler only when the job meets its service requirement. We consider the resource augmentation model, and give a {$ (1 + \varepsilon) $}-speed, {$ (1 + 1 / \varepsilon) $}-competitive online algorithm.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "nonclairvoyant scheduling; online algorithms; response time; Scheduling", } @Article{Fakcharoenphol:2007:TRP, author = "Jittat Fakcharoenphol and Chris Harrelson and Satish Rao", title = "The $k$-traveling repairmen problem", journal = j-TALG, volume = "3", number = "4", pages = "40:1--40:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290677", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the $k$-traveling repairmen problem, also known as the minimum latency problem, to multiple repairmen. We give a polynomial-time $ 8.497 \alpha $-approximation algorithm for this generalization, where $ \alpha $ denotes the best achievable approximation factor for the problem of finding the least-cost rooted tree spanning $i$ vertices of a metric. For the latter problem, a $ (2 + \varepsilon) $-approximation is known. Our results can be compared with the best-known approximation algorithm using similar techniques for the case $ k = 1 $, which is $ 3.59 \alpha $. Moreover, recent work of Chaudry et al. [2003] shows how to remove the factor of $ \alpha $, thus improving all of these results by that factor. We are aware of no previous work on the approximability of the present problem. In addition, we give a simple proof of the $ 3.59 \alpha $-approximation result that can be more easily extended to the case of multiple repairmen, and may be of independent interest.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Traveling salesman; vehicle routing", } @Article{Irani:2007:APS, author = "Sandy Irani and Sandeep Shukla and Rajesh Gupta", title = "Algorithms for power savings", journal = j-TALG, volume = "3", number = "4", pages = "41:1--41:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290678", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article examines two different mechanisms for saving power in battery-operated embedded systems. The first strategy is that the system can be placed in a sleep state if it is idle. However, a fixed amount of energy is required to bring the system back into an active state in which it can resume work. The second way in which power savings can be achieved is by varying the speed at which jobs are run. We utilize a power consumption curve {$ P(s) $} which indicates the power consumption level given a particular speed. We assume that {$ P(s) $} is convex, nondecreasing, and nonnegative for {$ s \geq 0 $}. The problem is to schedule arriving jobs in a way that minimizes total energy use and so that each job is completed after its release time and before its deadline. We assume that all jobs can be preempted and resumed at no cost. Although each problem has been considered separately, this is the first theoretical analysis of systems that can use both mechanisms. We give an offline algorithm that is within a factor of 2 of the optimal algorithm. We also give an online algorithm with a constant competitive ratio.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "dynamic speed scaling; online algorithms; Power savings", } @Article{Alon:2007:GSE, author = "Noga Alon and Venkatesan Guruswami and Tali Kaufman and Madhu Sudan", title = "Guessing secrets efficiently via list decoding", journal = j-TALG, volume = "3", number = "4", pages = "42:1--42:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290679", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the guessing secrets problem defined by Chung et al. [2001]. This is a variant of the standard 20 questions game where the player has a set of $ k > 1 $ secrets from a universe of {$N$} possible secrets. The player is asked Boolean questions about the secret. For each question, the player picks one of the {$k$} secrets adversarially, and answers according to this secret.\par We present an explicit set of {$ O(\log N) $} questions together with an efficient (i.e., {$ {\rm poly}(\log N) $} time) algorithm to solve the guessing secrets problem for the case of 2 secrets. This answers the main algorithmic question left unanswered by Chung et al. [2001]. The main techniques we use are small {$ \epsilon $}-biased spaces and the notion of list decoding.\par We also establish bounds on the number of questions needed to solve the {$k$}-secrets game for {$ k > 2 $}, and discuss how list decoding can be used to get partial information about the secrets, specifically to find a small core of secrets that must intersect the actual set of $k$ secrets.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "$\epsilon$-biased spaces; $k$-universal sets; 20 questions; decoding algorithms; error-correcting codes", } @Article{Raman:2007:SID, author = "Rajeev Raman and Venkatesh Raman and Srinivasa Rao Satti", title = "Succinct indexable dictionaries with applications to encoding $k$-ary trees, prefix sums and multisets", journal = j-TALG, volume = "3", number = "4", pages = "43:1--43:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290680", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the indexable dictionary problem, which consists of storing a set {$ S \subseteq \{ 0, \ldots, m - 1 \} $} for some integer {$m$} while supporting the operations of {$ \rank (x) $}, which returns the number of elements in {$S$} that are less than {$x$} if {$ x \in S $}, and {$ - 1 $} otherwise; and {$ \select (i) $}, which returns the {$i$} th smallest element in {$S$}. We give a data structure that supports both operations in {$ O(1) $} time on the RAM model and requires {$ B(n, m) + o(n) + O(\lg \lg m) $} bits to store a set of size {$n$}, where {$ B(n, m) = \lfloor \lg (m / n) \rfloor $} is the minimum number of bits required to store any {$n$}-element subset from a universe of size {$m$}. Previous dictionaries taking this space only supported (yes/no) membership queries in {$ O (1) $} time. In the cell probe model we can remove the {$ O (\lg \lg m) $} additive term in the space bound, answering a question raised by Fich and Miltersen [1995] and Pagh [2001].\par We present extensions and applications of our indexable dictionary data structure, including:\par --- an information-theoretically optimal representation of a {$k$}-ary cardinal tree that supports standard operations in constant time;\par --- a representation of a multiset of size {$n$} from {$ \{ 0, \ldots, m - 1 \} $} in {$ B(n, m + n) + o(n) $} bits that supports (appropriate generalizations of) rank and select operations in constant time; and {$ + O(\lg \lg m) $}\par --- a representation of a sequence of {$n$} nonnegative integers summing up to {$m$} in {$ B(n, m + n) + o(n) $} bits that supports prefix sum queries in constant time.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Dictionaries; multisets; perfect hashing; prefix sums; sets; succinct data structures; tries", } @Article{Janson:2007:PFS, author = "Svante Janson and Wojciech Szpankowski", title = "Partial fillup and search time in {LC} tries", journal = j-TALG, volume = "3", number = "4", pages = "44:1--44:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290681", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Andersson and Nilsson introduced in 1993 a level-compressed trie (for short, LC trie) in which a full subtree of a node is compressed to a single node of degree being the size of the subtree. Recent experimental results indicated a ``dramatic improvement'' when full subtrees are replaced by ``partially filled subtrees.'' In this article, we provide a theoretical justification of these experimental results, showing, among others, a rather moderate improvement in search time over the original LC tries. For such an analysis, we assume that $n$ strings are generated independently by a binary memoryless source, with $p$ denoting the probability of emitting a ``1'' (and $ q = 1 - p $ ). We first prove that the so-called {$ \alpha $}-fillup level {$ F_n (\alpha) $} (i.e., the largest level in a trie with {$ \alpha $} fraction of nodes present at this level) is concentrated on two values with high probability: either {$ F_n(\alpha) = k_n $} or {$ F_n ({\alpha }) = k_n + 1 $}, where {$ k_n = \log 1 / \sqrt {pq} n - |l n(p / q)| / 2 l n 3 / 2 (1 \sqrt {pq}) {\Phi } - 1 (\alpha) \sqrt {\ln n} + O(1) $} is an integer and {$ \Phi (x) $} denotes the normal distribution function. This result directly yields the typical depth (search time) {$ D_n (\alpha) $} in the {$ \alpha $}-LC tries, namely, we show that with high probability {$ D_n(\alpha) \sim C_2 \log \log n $}, where {$ C_2 = 1 / | \log (1 - h / \log (1 / \sqrt {pq}))| $} for {$ p \neq q $} and {$ h = - p \log p - q \log q $} is the Shannon entropy rate. This should be compared with recently found typical depth in the original LC tries, which is {$ C_1 \log \log n $}, where {$ C_1 = 1 / | \log (1 - h) / \log (1 / \min \{ p, 1 - p \})| $}. In conclusion, we observe that {$ \alpha $} affects only the lower term of the {$ \alpha $}-fillup level {$ F_n(\alpha) $}, and the search time in {$ \alpha $}-LC tries is of the same order as in the original LC tries.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Digital trees; level-compressed tries; partial fillup; Poissonization; probabilistic analysis; strings; trees", } @Article{Hershberger:2007:FSS, author = "John Hershberger and Matthew Maxel and Subhash Suri", title = "Finding the $k$ shortest simple paths: a new algorithm and its implementation", journal = j-TALG, volume = "3", number = "4", pages = "45:1--45:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290682", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a new algorithm to enumerate the $k$ shortest simple (loopless) paths in a directed graph and report on its implementation. Our algorithm is based on a replacement paths algorithm proposed by Hershberger and Suri [2001], and can yield a factor {$ \Theta (n) $} improvement for this problem. But there is a caveat: The fast replacement paths subroutine is known to fail for some directed graphs. However, the failure is easily detected, and so our {$k$} shortest paths algorithm optimistically uses the fast subroutine, then switches to a slower but correct algorithm if a failure is detected. Thus, the algorithm achieves its {$ \Theta (n) $} speed advantage only when the optimism is justified. Our empirical results show that the replacement paths failure is a rare phenomenon, and the new algorithm outperforms the current best algorithms; the improvement can be substantial in large graphs. For instance, on GIS map data with about 5,000 nodes and 12,000 edges, our algorithm is 4--8 times faster. In synthetic graphs modeling wireless ad hoc networks, our algorithm is about 20 times faster.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "directed paths; Loop-free paths; path equivalence class; replacement paths", } @Article{Chekuri:2007:EDP, author = "Chandra Chekuri and Sanjeev Khanna", title = "Edge-disjoint paths revisited", journal = j-TALG, volume = "3", number = "4", pages = "46:1--46:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290683", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The approximability of the maximum edge-disjoint paths problem (EDP) in directed graphs was seemingly settled by an {$ \Omega (m^{1 / 2} - \epsilon) $}-hardness result of Guruswami et al. [2003], and an {$ O(\sqrt {m}) $} approximation achievable via a natural multicommodity-flow-based LP relaxation as well as a greedy algorithm. Here {$m$} is the number of edges in the graph. We observe that the {$ \Omega (m^{1 / 2} - {\epsilon }) $}-hardness of approximation applies to sparse graphs, and hence when expressed as a function of {$n$}, that is, the number of vertices, only an {$ \Omega (n^{1 / 2} - \epsilon) $}-hardness follows. On the other hand, {$ O(\sqrt {m}) $}-approximation algorithms do not guarantee a sublinear (in terms of {$n$} ) approximation algorithm for dense graphs. We note that a similar gap exists in the known results on the integrality gap of the flow-based LP relaxation: an {$ \Omega (\sqrt {n}) $} lower bound and {$ O(\sqrt {m}) $} upper bound. Motivated by this discrepancy in the upper and lower bounds, we study algorithms for EDP in directed and undirected graphs and obtain improved approximation ratios. We show that the greedy algorithm has an approximation ratio of {$ O(\min (n^{2 / 3}, \sqrt {m})) $} in undirected graphs and a ratio of {$ O(\min (n^{4 / 5}, \sqrt {m})) $} in directed graphs. For acyclic graphs we give an {$ O(\sqrt {n} \ln n) $} approximation via LP rounding. These are the first sublinear approximation ratios for EDP. The results also extend to EDP with weights and to the uniform-capacity unsplittable flow problem (UCUFP).", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithm; Edge-disjoint paths; greedy algorithm; multicommodity flow relaxation", } @Article{Cheriyan:2007:PED, author = "Joseph Cheriyan and Mohammad R. Salavatipour", title = "Packing element-disjoint {Steiner} trees", journal = j-TALG, volume = "3", number = "4", pages = "47:1--47:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290684", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given an undirected graph {$ G(V, E) $} with terminal set {$ T \subseteq V $}, the problem of packing element-disjoint Steiner trees is to find the maximum number of Steiner trees that are disjoint on the nonterminal nodes and on the edges. The problem is known to be NP-hard to approximate within a factor of {$ \Omega (\log n) $}, where {$n$} denotes {$ |V| $}. We present a randomized {$ O(\log n) $}-approximation algorithm for this problem, thus matching the hardness lower bound. Moreover, we show a tight upper bound of {$ O(\log n) $} on the integrality ratio of a natural linear programming relaxation.", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; element-disjoint; hardness of approximation; Packing; Steiner trees", } @Article{Krivelevich:2007:AAH, author = "Michael Krivelevich and Zeev Nutov and Mohammad R. Salavatipour and Jacques Verstraete Yuster and Raphael Yuster", title = "Approximation algorithms and hardness results for cycle packing problems", journal = j-TALG, volume = "3", number = "4", pages = "48:1--48:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290685", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The cycle packing number {$ \nu e(G) $} of a graph {$G$} is the maximum number of pairwise edge-disjoint cycles in {$G$}. Computing {$ \nu e(G) $} is an NP-hard problem. We present approximation algorithms for computing {$ \nu e (G) $} in both undirected and directed graphs. In the undirected case we analyze a variant of the modified greedy algorithm suggested by Caprara et al. [2003] and show that it has approximation ratio {$ \Theta (\sqrt {\log n}) $}, where {$ n = |V(G)| $}. This improves upon the previous {$ O(\log n) $} upper bound for the approximation ratio of this algorithm. In the directed case we present a {$ \sqrt {n} $}-approximation algorithm. Finally, we give an {$ O(n^{2 / 3}) $}-approximation algorithm for the problem of finding a maximum number of edge-disjoint cycles that intersect a specified subset {$S$} of vertices. We also study generalizations of these problems. Our approximation ratios are the currently best-known ones and, in addition, provide upper bounds on the integrality gap of standard LP-relaxations of these problems. In addition, we give lower bounds for the integrality gap and approximability of {$ \nu e(G) $} in directed graphs. Specifically, we prove a lower bound of {$ \Omega (\log n / \log \log n) $} for the integrality gap of edge-disjoint cycle packing. We also show that it is quasi-NP-hard to approximate {$ \nu e(G) $} within a factor of {$ O(\log 1 - \varepsilon n) $} for any constant {$ \varepsilon > 0 $}. This improves upon the previously known APX-hardness result for this problem.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; Cycle packing; edge-disjoint; hardness of approximation; integrality gap", } @Article{Albers:2007:EEA, author = "Susanne Albers and Hiroshi Fujiwara", title = "Energy-efficient algorithms for flow time minimization", journal = j-TALG, volume = "3", number = "4", pages = "49:1--49:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290686", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study scheduling problems in battery-operated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadline-based settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variable-speed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs.\par We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unit-size jobs. We devise a deterministic constant competitive online algorithm and show that the offline problem can be solved in polynomial time.", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "competitive analysis; dynamic programming; flow time; offline algorithms; online algorithms; Variable-speed processor", } @Article{Chrobak:2007:IOA, author = "Marek Chrobak and Wojciech Jawor and Ji{\v{r}}{\'\i} Sgall and Tom{\'a}{\v{s}} Tich{\'y}", title = "Improved online algorithms for buffer management in {QoS} switches", journal = j-TALG, volume = "3", number = "4", pages = "50:1--50:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290687", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the following buffer management problem arising in QoS networks: Packets with specified weights and deadlines arrive at a network switch and need to be forwarded so that the total weight of forwarded packets is maximized. Packets not forwarded before their deadlines are lost. The main result of the article is an online $ 64 / 33 \approx 1.939 $-competitive algorithm, the first deterministic algorithm for this problem with competitive ratio below 2. For the 2-uniform case we give an algorithm with ratio $ \approx 1.377 $ and a matching lower bound.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Online algorithms; scheduling", } @Article{Hajiaghayi:2007:ORN, author = "Mohammad Taghi Hajiaghayi and Robert D. Kleinberg and Harald R{\"a}cke and Tom Leighton", title = "Oblivious routing on node-capacitated and directed graphs", journal = j-TALG, volume = "3", number = "4", pages = "51:1--51:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290688", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Oblivious routing algorithms for general undirected networks were introduced by R{\"a}cke [2002], and this work has led to many subsequent improvements and applications. Comparatively little is known about oblivious routing in general directed networks, or even in undirected networks with node capacities.\par We present the first nontrivial upper bounds for both these cases, providing algorithms for $k$-commodity oblivious routing problems with competitive ratio {$ O(\sqrt {k \log (n)}) $} for undirected node-capacitated graphs and {$ O(\sqrt {k_n} 1 / 4 \log (n)) $} for directed graphs. In the special case that all commodities have a common source or sink, our upper bound becomes {$ O(\sqrt {n} \log (n)) $} in both cases, matching the lower bound up to a factor of {$ \log (n) $}. The lower bound (which first appeared in Azar et al. [2003]) is obtained on a graph with very high degree. We show that, in fact, the degree of a graph is a crucial parameter for node-capacitated oblivious routing in undirected graphs, by providing an {$ O(\Delta \polylog (n)) $}-competitive oblivious routing scheme for graphs of degree {$ \Delta $}. For the directed case, however, we show that the lower bound of {$ \Omega (\sqrt {n}) $} still holds in low-degree graphs.\par Finally, we settle an open question about routing problems in which all commodities share a common source or sink. We show that even in this simplified scenario there are networks in which no oblivious routing algorithm can achieve a competitive ratio better than {$ \Omega (\log n) $}.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "communication networks; directed graphs; node-capacitated graphs; Oblivious routing", } @Article{Auletta:2007:RSU, author = "Vincenzo Auletta and Roberto {De Prisco} and Paolo Penna and Giuseppe Persiano", title = "Routing selfish unsplittable traffic", journal = j-TALG, volume = "3", number = "4", pages = "52:1--52:??", month = nov, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1145/1290672.1290689", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:55:31 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider general resource assignment games involving selfish users/agents in which users compete for resources and try to be assigned to those which maximize their own benefits (e.g., try to route their traffic through links which minimize the latency of their own traffic). We propose and study a mechanism design approach in which an allocation mechanism assigns users to resources and charges the users for using the resources so as to induce each user to truthfully report a private piece of information he/she holds (e.g., how much traffic he/she needs to transmit). This information is crucial for computing optimal (or close to optimal) allocations and an agent could misreport his/her information to induce the underlying allocation algorithm to output a solution which he/she likes more (e.g., which assigns better resources to him/her).\par For our resource allocation problems, we give an algorithmic characterization of the solutions for which truth-telling is a Nash equilibrium. A natural application of these results is to a scheduling/routing problem which is the mechanism design counterpart of the selfish routing game of Koutsoupias and Papadimitriou [1999]: Each selfish user wants to route a piece of unsplittable traffic using one of $m$ links of different speeds so as to minimize his/her own latency. Our mechanism design counterpart can be seen as the problem of scheduling selfish jobs on parallel related machines and is the dual of the problem of scheduling (unselfish) jobs on parallel selfish machines studied by Archer and Tardos [2001].\par Koutsoupias and Papadimitriou studied an ``anarchic'' scenario in which each user chooses his/her own link, and this may produce Nash equilibria of cost {$ \Omega (\log m / \log \log m) $} times the optimum. Our mechanism design counterpart is a possible way of reducing the effect of selfish behavior via suitable incentives to the agents (i.e., taxes for using the links). We indeed show that in the resulting game, it is possible to guarantee an approximation factor of 8 for any number of links/machines (this solution also works for online settings). However, it remains impossible to guarantee arbitrarily good approximate solutions, even for 2 links/machines and even if the allocation algorithm is allowed superpolynomial time. This result shows that our scheduling problem with selfish jobs is more difficult than the scheduling problem with selfish machines by Archer and Tardos (which admits exact solutions).\par We also study some generalizations of this basic problem.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithmic mechanism design; Nash equilibrium; scheduling; selfish routing", } @Article{Ruzic:2008:UDD, author = "Milan Ru{\v{z}}i{\'c}", title = "Uniform deterministic dictionaries", journal = j-TALG, volume = "4", number = "1", pages = "1:1--1:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328912", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a new analysis of the well-known family of multiplicative hash functions, and improved deterministic algorithms for selecting ``good'' hash functions. The main motivation is realization of deterministic dictionaries with fast lookups and reasonably fast updates. The model of computation is the Word RAM, and it is assumed that the machine word-size matches the size of keys in bits. Many of the modern solutions to the dictionary problem are weakly nonuniform, that is, they require a number of constants to be computed at ``compile time'' for the stated time bounds to hold. The currently fastest deterministic dictionary uses constants not known to be computable in polynomial time. In contrast, our dictionaries do not require any special constants or instructions, and running times are independent of word (and key) length. Our family of dynamic dictionaries achieves a performance of the following type: lookups in time {$ O(t) $} and updates in amortized time {$ O(n^{1 / t}) $}, for an appropriate parameter function {$t$}. Update procedures require division, whereas searching uses multiplication only.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Deterministic algorithms; perfect hashing", } @Article{Franceschini:2008:NSB, author = "Gianni Franceschini and Roberto Grossi", title = "No sorting? better searching!", journal = j-TALG, volume = "4", number = "1", pages = "2:1--2:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328913", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Questions about order versus disorder in systems and models have been fascinating scientists over the years. In computer science, order is intimately related to sorting, commonly meant as the task of arranging keys in increasing or decreasing order with respect to an underlying total order relation. The sorted organization is amenable for searching a set of $n$ keys, since each search requires {$ \Theta (\log n) $} comparisons in the worst case, which is optimal if the cost of a single comparison can be considered a constant. Nevertheless, we prove that disorder implicitly provides more information than order does. For the general case of searching an array of multidimensional keys whose comparison cost is proportional to their length (and hence which cannot be considered a constant), we demonstrate that ``suitable'' disorder gives better bounds than those derivable by using the natural lexicographic order.\par We start from previous work done by Andersson et al. [2001], who proved that {$ \Theta (k \log \log n / \log \log (4 + k \log \log n / \log n) + k + \log n) $} character comparisons (or probes) comprise the tight complexity for searching a plain sorted array of {$n$} keys, each of length {$k$}, arranged in lexicographic order. We describe a novel permutation of the {$n$} keys that is different from the sorted order. When keys are kept ``unsorted'' in the array according to this permutation, the complexity of searching drops to {$ \Theta (k + \log n) $} character comparisons (or probes) in the worst case, which is optimal among all possible permutations, up to a constant factor. Consequently, disorder carries more information than does order; this fact was not observable before, since the latter two bounds are {$ \Theta (\log n) $} when {$ k = O(1) $}. More implications are discussed in the article, including searching in the bit-probe model.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Implicit data structures; in-place algorithms; searching; sorting", } @Article{Kaplan:2008:THT, author = "Haim Kaplan and Robert Endre Tarjan", title = "Thin heaps, thick heaps", journal = j-TALG, volume = "4", number = "1", pages = "3:1--3:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328914", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Fibonacci heap was devised to provide an especially efficient implementation of Dijkstra's shortest path algorithm. Although asymptotically efficient, it is not as fast in practice as other heap implementations. Expanding on ideas of H{\o}yer [1995], we describe three heap implementations (two versions of thin heaps and one of thick heaps) that have the same amortized efficiency as Fibonacci heaps, but need less space and promise better practical performance. As part of our development, we fill in a gap in H{\o}yer's analysis.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "binomial queue; Data structure; decrease key operation; Fibonacci heap; heap; melding; priority queue; thick heap; thin heap", } @Article{Barbay:2008:ARA, author = "J{\'e}r{\'e}my Barbay and Claire Kenyon", title = "Alternation and redundancy analysis of the intersection problem", journal = j-TALG, volume = "4", number = "1", pages = "4:1--4:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328915", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The intersection of sorted arrays problem has applications in search engines such as Google. Previous work has proposed and compared deterministic algorithms for this problem, in an adaptive analysis based on the encoding size of a certificate of the result (cost analysis). We define the alternation analysis, based on the nondeterministic complexity of an instance. In this analysis we prove that there is a deterministic algorithm asymptotically performing as well as any randomized algorithm in the comparison model. We define the redundancy analysis, based on a measure of the internal redundancy of the instance. In this analysis we prove that any algorithm optimal in the redundancy analysis is optimal in the alternation analysis, but that there is a randomized algorithm which performs strictly better than any deterministic algorithm in the comparison model. Finally, we describe how these results can be extended beyond the comparison model.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Adaptive analysis; alternation analysis; intersection; intersection of sorted arrays; randomized algorithm; redundancy analysis", } @Article{Pettie:2008:RMS, author = "Seth Pettie and Vijaya Ramachandran", title = "Randomized minimum spanning tree algorithms using exponentially fewer random bits", journal = j-TALG, volume = "4", number = "1", pages = "5:1--5:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328916", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best-known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum spanning tree problems, and the local sorting and set maxima problems. (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear, running times.) One downside of the randomized methods for solving these problems is that they use a number of random bits linear in the size of input. In this article we develop some general methods for reducing exponentially the consumption of random bits in comparison-based algorithms. In some cases we are able to reduce the number of random bits from linear to nearly constant, without affecting the expected running time.\par Most of our results are obtained by adjusting or reorganizing existing randomized algorithms to work well with a pairwise or {$ O(1) $}-wise independent sampler. The prominent exception, and the main focus of this article, is a linear-time randomized minimum spanning tree algorithm that is not derived from the well-known Karger-Klein-Tarjan algorithm. In many ways it resembles more closely the deterministic minimum spanning tree algorithms based on soft heaps. Further, using our algorithm as a guide, we present a unified view of the existing ``nongreedy'' minimum spanning tree algorithms. Concepts from the Karger-Klein-Tarjan algorithm, such as F-lightness, MST verification, and sampled graphs, are related to the concepts of edge corruption, subgraph contractibility, and soft heaps, which are the basis of the deterministic MST algorithms of Chazelle and Pettie-Ramachandran.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Graph algorithms; minimum spanning trees; random sampling", } @Article{Roditty:2008:FSF, author = "Liam Roditty", title = "A faster and simpler fully dynamic transitive closure", journal = j-TALG, volume = "4", number = "1", pages = "6:1--6:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328917", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We obtain a new fully dynamic algorithm for maintaining the transitive closure of a directed graph. Our algorithm maintains the transitive closure matrix in a total running time of {$ O(m n + ({\rm ins} + {\rm del}) {\cdot } n^2) $}, where ins(del) is the number of insert (delete) operations performed. Here {$n$} is the number of vertices in the graph and {$m$} is the initial number of edges in the graph. Obviously, reachability queries can be answered in constant time. The algorithm uses only {$ O(n^2) $} time which is essentially optimal for maintaining the transitive closure matrix. Our algorithm can also support path queries. If {$v$} is reachable from {$u$}, the algorithm can produce a path from {$u$} to $v$ in time proportional to the length of the path. The best previously known algorithm for the problem is due to Demetrescu and Italiano [2000]. Their algorithm has a total running time of {$ O(n^3 + ({\rm ins} + {\rm del}) {\cdot } n^2) $}. The query time is also constant. In addition, we also present a simple algorithm for directed acyclic graphs (DAGs) with a total running time of {$ O(m n + {\rm ins} {\cdot } n^2 + {\rm del}) $}. Our algorithms are obtained by combining some new ideas with techniques of Italiano [1986, 1988], King [1999], King and Thorup [2001] and Frigioni et al. [2001]. We also note that our algorithms are extremely simple and can be easily implemented.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "directed graph; Dynamic graph algorithms; reachability", } @Article{Gabow:2008:FLD, author = "Harold N. Gabow and Shuxin Nie", title = "Finding a long directed cycle", journal = j-TALG, volume = "4", number = "1", pages = "7:1--7:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328918", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider a digraph with $n$ vertices. For any fixed value $k$, we present linear- and almost-linear-time algorithms to find a cycle of length $ \geq k $, if one exists. We also find a cycle that has length $ \geq \log n / \log \log n $ in polynomial time, if one exists. Under an appropriate complexity assumption it is known to be impossible to improve this guarantee by more than a $ \log \log n $ factor. Our approach is based on depth-first search.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; circumference; cycles; Hamiltonian cycles; long cycles", } @Article{Buchsbaum:2008:RLC, author = "Adam L. Buchsbaum and Emden R. Gansner and Cecilia M. Procopiuc and Suresh Venkatasubramanian", title = "Rectangular layouts and contact graphs", journal = j-TALG, volume = "4", number = "1", pages = "8:1--8:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328919", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Contact graphs of isothetic rectangles unify many concepts from applications including VLSI and architectural design, computational geometry, and GIS. Minimizing the area of their corresponding rectangular layouts is a key problem. We study the area-optimization problem and show that it is NP-hard to find a minimum-area rectangular layout of a given contact graph. We present {$ O(n) $}-time algorithms that construct {$ O(n^2) $}-area rectangular layouts for general contact graphs and {$ O(n \log n) $}-area rectangular layouts for trees. (For trees, this is an {$ O(\log n) $}-approximation algorithm.) We also present an infinite family of graphs (respectively, trees) that require {$ \Omega (n^2) $} (respectively, {$ \Omega (n \log n) $}) area.\par We derive these results by presenting a new characterization of graphs that admit rectangular layouts, using the related concept of rectangular duals. A corollary to our results relates the class of graphs that admit rectangular layouts to rectangle-of-influence drawings.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Contact graphs; rectangular duals; rectangular layouts", } @Article{Arge:2008:PRT, author = "Lars Arge and Mark {De Berg} and Herman Haverkort and Ke Yi", title = "The priority {R}-tree: a practically efficient and worst-case optimal {R}-tree", journal = j-TALG, volume = "4", number = "1", pages = "9:1--9:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328920", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the priority R-tree, or PR-tree, which is the first R-tree variant that always answers a window query using {$ O((N / B) 1 - 1 / d + T / B) $} I/Os, where {$N$} is the number of {$d$}-dimensional (hyper-) rectangles stored in the R-tree, {$B$} is the disk block size, and {$T$} is the output size. This is provably asymptotically optimal and significantly better than other R-tree variants, where a query may visit all {$ N / B $} leaves in the tree even when {$ T = 0 $}. We also present an extensive experimental study of the practical performance of the PR-tree using both real-life and synthetic data. This study shows that the PR-tree performs similarly to the best-known R-tree variants on real-life and relatively nicely distributed data, but outperforms them significantly on more extreme data.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "R-trees", } @Article{Gudmundsson:2008:ADO, author = "Joachim Gudmundsson and Christos Levcopoulos and Giri Narasimhan and Michiel Smid", title = "Approximate distance oracles for geometric spanners", journal = j-TALG, volume = "4", number = "1", pages = "10:1--10:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328921", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given an arbitrary real constant $ \varepsilon > 0 $, and a geometric graph {$G$} in {$d$}-dimensional Euclidean space with {$n$} points, {$ O(n) $} edges, and constant dilation, our main result is a data structure that answers {$ (1 + \varepsilon) $}-approximate shortest-path-length queries in constant time. The data structure can be constructed in {$ O(n \log n) $} time using {$ O(n \log n) $} space. This represents the first data structure that answers {$ (1 + \varepsilon) $}-approximate shortest-path queries in constant time, and hence functions as an approximate distance oracle. The data structure is also applied to several other problems. In particular, we also show that approximate shortest-path queries between vertices in a planar polygonal domain with ``rounded'' obstacles can be answered in constant time. Other applications include query versions of closest-pair problems, and the efficient computation of the approximate dilations of geometric graphs. Finally, we show how to extend the main result to answer {$ (1 + \varepsilon) $}-approximate shortest-path-length queries in constant time for geometric spanner graphs with {$ m = \omega (n) $} edges. The resulting data structure can be constructed in {$ O(m + n \log n) $} time using {$ O(n \log n) $} space.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithm; computational geometry; geometric graphs; Shortest paths; spanners", } @Article{Gandhi:2008:IBS, author = "Rajiv Gandhi and Magn{\'u}s M. Halld{\'o}rsson and Guy Kortsarz and Hadas Shachnai", title = "Improved bounds for scheduling conflicting jobs with minsum criteria", journal = j-TALG, volume = "4", number = "1", pages = "11:1--11:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328922", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among jobs are formed as an arbitrary conflict graph.\par Building on the framework of Queyranne and Sviridenko [2002b], we present a general technique for reducing the weighted sum of completion-times problem to the classical makespan minimization problem. Using this technique, we improve the best-known results for scheduling conflicting jobs with the min-sum objective, on several fundamental classes of graphs, including line graphs, $ (k + 1) $-claw-free graphs, and perfect graphs. In particular, we obtain the first constant-factor approximation ratio for nonpreemptive scheduling on interval graphs. We also improve the results of Kim [2003] for scheduling jobs on line graphs and for resource-constrained scheduling.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; coloring; linear programming; LP rounding; scheduling; sum multicoloring", } @Article{Guerraoui:2008:CMA, author = "Rachid Guerraoui and Ron R. Levy and Bastian Pochon and Jim Pugh", title = "The collective memory of amnesic processes", journal = j-TALG, volume = "4", number = "1", pages = "12:1--12:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328923", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article considers the problem of robustly emulating a shared atomic memory over a distributed message-passing system where processes can fail by crashing and possibly recover. We revisit the notion of atomicity in the crash-recovery context and introduce a generic algorithm that emulates an atomic memory. The algorithm is instantiated for various settings according to whether processes have access to local stable storage, and whether, in every execution of the algorithm, a sufficient number of processes are assumed not to crash. We establish the optimality of specific instances of our algorithm in terms of resilience, log complexity (number of stable storage accesses needed in every read or write operation), as well as time complexity (number of communication steps needed in every read or write operation). The article also discusses the impact of considering a multiwriter versus a single-writer memory, as well as the impact of weakening the consistency of the memory by providing safe or regular semantics instead of atomicity.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "\log complexity; Atomic registers; crash recovery; shared-memory emulation", } @Article{Karakostas:2008:FAS, author = "George Karakostas", title = "Faster approximation schemes for fractional multicommodity flow problems", journal = j-TALG, volume = "4", number = "1", pages = "13:1--13:17", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328924", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present fully polynomial approximation schemes for concurrent multicommodity flow problems that run in time of the minimum possible dependencies on the number of commodities $k$. We show that by modifying the algorithms by Garg and K{\"o}nemann [1998] and Fleischer [2000], we can reduce their running time on a graph with $n$ vertices and $m$ edges from {$ \tilde {O}(\varepsilon^{ - 2}(m^2 + k m)) $} to {$ \tilde {O}({\varepsilon^{ - 2m}}^2) $} for an {\em implicit\/} representation of the output, or {$ \tilde {O}(\varepsilon^{ - 2}(m^2 + k n)) $} for an {\em explicit\/} representation, where {$ \tilde {O}(f) $} denotes a quantity that is {$ O(f \log^{O(1)} m)$}. The implicit representation consists of a set of trees rooted at sources (there can be more than one tree per source), and with sinks as their leaves, together with flow values for the flow directed from the source to the sinks in a particular tree. Given this implicit representation, the approximate value of the concurrent flow is known, but if we want the explicit flow per commodity per edge, we would have to combine all these trees together, and the cost of doing so may be prohibitive. In case we want to calculate explicitly the solution flow, we modify our schemes so that they run in time polylogarithmic in {$ n k $} ({$n$} is the number of nodes in the network). This is within a polylogarithmic factor of the trivial lower bound of time {$ \Omega (n k) $} needed to explicitly write down a multicommodity flow of {$k$} commodities in a network of {$n$} nodes. Therefore our schemes are within a polylogarithmic factor of the minimum possible dependencies of the running time on the number of commodities {$k$}.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "fully-polynomial time approximation schemes; Multicommodity flows", } @Article{Lemire:2008:HBO, author = "Daniel Lemire and Owen Kaser", title = "Hierarchical bin buffering: {Online} local moments for dynamic external memory arrays", journal = j-TALG, volume = "4", number = "1", pages = "14:1--14:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328925", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a massive I/O array of size $n$, we want to compute the first {$N$} local moments, for some constant {$N$}. Our simpler algorithms partition the array into consecutive ranges called bins, and apply not only to local-moment queries, but also to algebraic queries. With {$N$} buffers of size {$ \sqrt {n} $}, time complexity drops to {$ O(\sqrt {n}) $}. A more sophisticated approach uses hierarchical buffering and has a logarithmic time complexity ({$ O(b \log b n) $}), when using {$N$} hierarchical buffers of size {$ n / b $}. Using overlapped bin buffering, we show that only one buffer is needed, as with wavelet-based algorithms, but using much less storage.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "hierarchical buffers; polynomial fitting; statistical queries; Very large arrays", } @Article{Anshelevich:2008:PDU, author = "Elliot Anshelevich and Lisa Zhang", title = "Path decomposition under a new cost measure with applications to optical network design", journal = j-TALG, volume = "4", number = "1", pages = "15:1--15:??", month = mar, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1328911.1328926", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:15 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a problem directly inspired by its application to DWDM (dense wavelength division multiplexing) network design. We are given a set of demands to be carried over a network. Our goal is to choose a route for each demand and to decompose the network into a collection of edge-disjoint simple paths. These paths are called optical line systems. The cost of routing one unit of demand is the number of line systems with which the demand route overlaps; our design objective is to minimize the total cost over all demands. This cost metric is motivated by the need to minimize O-E-O(optical-electrical-optical) conversions in optical transmission.\par For given line systems, it is easy to find the optimal demand routes. On the other hand, for given demand routes designing the optimal line systems can be NP-hard. We first present a 2-approximation for general network topologies. As optical networks often have low node degrees, we offer an algorithm that finds the optimal solution for the special case in which the node degree is at most 3. Our solution is based on a local greedy approach.\par If neither demand routes nor line systems are fixed, the situation becomes much harder. Even for a restricted scenario on a 3-regular Hamiltonian network, no efficient algorithm can guarantee a constant approximation better than 2. For general topologies, we offer a simple algorithm with an {$ O(\log K) $}- and an {$ O(\log n) $}-approximation, where {$K$} is the number of demands and {$n$} the number of nodes. This approximation ratio is almost tight. For rings, a common special topology, we offer a more complex 3/2-approximation algorithm.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; Optical network design; path decomposition", } @Article{Buchsbaum:2008:GE, author = "Adam L. Buchsbaum", title = "Guest editorial", journal = j-TALG, volume = "4", number = "2", pages = "16:1--16:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361193", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Blandford:2008:CDV, author = "Daniel K. Blandford and Guy E. Blelloch", title = "Compact dictionaries for variable-length keys and data with applications", journal = j-TALG, volume = "4", number = "2", pages = "17:1--17:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361194", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of maintaining a dynamic dictionary {$T$} of keys and associated data for which both the keys and data are bit strings that can vary in length from zero up to the length {$w$} of a machine word. We present a data structure for this variable-bit-length dictionary problem that supports constant time lookup and expected amortized constant-time insertion and deletion. It uses {$ O(m + 3 n - n \log 2 n) $} bits, where {$n$} is the number of elements in {$T$}, and {$m$} is the total number of bits across all strings in {$T$} (keys and data). Our dictionary uses an array {$ A[1 \ldots n] $} in which locations store variable-bit-length strings. We present a data structure for this variable-bit-length array problem that supports worst-case constant-time lookups and updates and uses {$ O(m + n) $} bits, where {$m$} is the total number of bits across all strings stored in {$A$}.\par The motivation for these structures is to support applications for which it is helpful to efficiently store short varying-length bit strings. We present several applications, including representations for semidynamic graphs, order queries on integers sets, cardinal trees with varying cardinality, and simplicial meshes of {$d$} dimensions. These results either generalize or simplify previous results.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Compression", } @Article{Kolluri:2008:PGM, author = "Ravikrishna Kolluri", title = "Provably good moving least squares", journal = j-TALG, volume = "4", number = "2", pages = "18:1--18:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361195", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We analyze a moving least squares (MLS) interpolation scheme for reconstructing a surface from point cloud data. The input is a sufficiently dense set of sample points that lie near a closed surface F with approximate surface normals. The output is a reconstructed surface passing near the sample points. For each sample point $s$ in the input, we define a linear point function that represents the local shape of the surface near $s$. These point functions are combined by a weighted average, yielding a three-dimensional function {$I$}. The reconstructed surface is implicitly defined as the zero set of {$I$}.\par We prove that the function {$I$} is a good approximation to the signed distance function of the sampled surface {$F$} and that the reconstructed surface is geometrically close to and isotopic to {$F$}. Our sampling requirements are derived from the local feature size function used in Delaunay-based surface reconstruction algorithms. Our analysis can handle noisy data provided the amount of noise in the input dataset is small compared to the feature size of {$F$}.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "implicit surfaces; interpolation; Reconstruction", } @Article{Fusy:2008:DOT, author = "{\'E}ric Fusy and Gilles Schaeffer and Dominique Poulalhon", title = "Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling", journal = j-TALG, volume = "4", number = "2", pages = "19:1--19:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361196", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a bijection between some quadrangular dissections of an hexagon and unrooted binary trees with interesting consequences for enumeration, mesh compression, and graph sampling. Our bijection yields an efficient uniform random sampler for 3-connected planar graphs, which turns out to be determinant for the quadratic complexity of the current best-known uniform random sampler for labelled planar graphs. It also provides an encoding for the set {$ P(n) $} of {$n$}-edge 3-connected planar graphs that matches the entropy bound {$ 1 / n \log 2 | P(n)| = 2 + o (1) $} bits per edge (bpe). This solves a theoretical problem recently raised in mesh compression as these graphs abstract the combinatorial part of meshes with spherical topology. We also achieve the optimal parametric rate {$ 1 / n \log 2 | P(n, i, j)| $} bpe for graphs of {$ P(n) $} with {$i$} vertices and {$j$} faces, matching in particular the optimal rate for triangulations. Our encoding relies on a linear time algorithm to compute an orientation associated with the minimal Schnyder wood of a 3-connected planar map. This algorithm is of independent interest, and it is, for instance, a key ingredient in a recent straight line drawing algorithm for 3-connected planar graphs.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Bijection; coding; counting; random generation", } @Article{VeghVegh:2008:PDA, author = "L{\'a}szl{\'o} A. V{\'e}ghV{\'e}gh and Andr{\'a}s A. Bencz{\'u}r", title = "Primal-dual approach for directed vertex connectivity augmentation and generalizations", journal = j-TALG, volume = "4", number = "2", pages = "20:1--20:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361197", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In their seminal paper, Frank and Jord{\'a}n [1995] show that a large class of optimization problems, including certain directed graph augmentation, fall into the class of covering supermodular functions over pairs of sets. They also give an algorithm for such problems, however, it relies on the ellipsoid method. Prior to our result, combinatorial algorithms existed only for the 0--1 valued problem. Our key result is a combinatorial algorithm for the general problem that includes directed vertex or S-T connectivity augmentation. The algorithm is based on Bencz{\'u}r's previous algorithm for the 0--1 valued case [Bencz{\'u}r 2003].\par Our algorithm uses a primal-dual scheme for finding covers of partially ordered sets that satisfy natural abstract properties as in Frank and Jord{\'a}n. For an initial (possibly greedy) cover, the algorithm searches for witnesses for the necessity of each element in the cover. If no two (weighted) witnesses have a common cover, the solution is optimal. As long as this is not the case, the witnesses are gradually exchanged for smaller ones. Each witness change defines an appropriate change in the solution; these changes are finally unwound in a shortest-path manner to obtain a solution of size one less.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "combinatorial algorithm; Vertex connectivity augmentation", } @Article{Sanders:2008:AAS, author = "Peter Sanders and David Steurer", title = "An asymptotic approximation scheme for multigraph edge coloring", journal = j-TALG, volume = "4", number = "2", pages = "21:1--21:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361198", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The edge coloring problem considers the assignment of colors from a minimum number of colors to edges of a graph such that no two edges with the same color are incident to the same node. We give polynomial time algorithms for approximate edge coloring of multigraphs, that is, parallel edges are allowed. The best previous algorithms achieve a fixed constant approximation factor plus a small additive offset. One of our algorithms achieves solution quality $ {\rm opt} + \sqrt {9 {\rm opt} / 2} $ and has execution time polynomial in the number of nodes and the logarithm of the maximum edge multiplicity.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "chromatic index; data migration; Edge coloring; multigraphs", } @Article{Chawla:2008:ENT, author = "Shuchi Chawla and Anupam Gupta and Harald R{\"a}cke", title = "Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut", journal = j-TALG, volume = "4", number = "2", pages = "22:1--22:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361199", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we study metrics of negative type, which are metrics {$ (V, d) $} such that {$ \sqrt {d} $} is an Euclidean metric; these metrics are thus also known as {$ \ell_2 $}-squared metrics. We show how to embed {$n$}-point negative-type metrics into Euclidean space $ \ell_2 $ with distortion {$ D = O(\log 3 / 4 n) $}. This embedding result, in turn, implies an {$ O(\log 3 / 4 k) $}-approximation algorithm for the Sparsest Cut problem with nonuniform demands. Another corollary we obtain is that {$n$}-point subsets of {$ \ell_1 $} embed into {$ \ell_2 $} with distortion {$ O(\log 3 / 4 n) $}.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; embedding; metrics; negative-type metric; sparsest cut", } @Article{Chuzhoy:2008:ASN, author = "Julia Chuzhoy and Anupam Gupta and Joseph (Seffi) Naor and Amitabh Sinha", title = "On the approximability of some network design problems", journal = j-TALG, volume = "4", number = "2", pages = "23:1--23:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361200", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider the following classical network design problem: a set of terminals {$ T = \{ t_i \} $} wishes to send traffic to a root {$r$} in an {$n$}-node graph {$ G = (V, E) $}. Each terminal {$ t_i $} sends {$ d_i $} units of traffic and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge {$e$} can only be allocated in integral multiples of some base capacity $ u_e $ and hence provisioning $ k {\times } u_e $ bandwidth on edge $e$ incurs a cost of $ \lceil k \rceil $ times the cost of that edge. The objective is a minimum-cost feasible solution.\par This is one of many network design problems widely studied where the bandwidth allocation is governed by side constraints: edges can only allow a subset of cables to be purchased on them or certain quality-of-service requirements may have to be met.\par In this work, we show that this problem and, in fact, several basic problems in this general network design framework cannot be approximated better than {$ \Omega (\log \log n) $} unless {$ {\rm NP} \subseteq {\rm DTIME}(n O(\log \log \log n)) $}, where {$ |V| = n $}. In particular, we show that this inapproximability threshold holds for (i) the Priority-Steiner Tree problem, (ii) the (single-sink) Cost-Distance problem, and (iii) the single-sink version of an even more fundamental problem, Fixed Charge Network Flow. Our results provide a further breakthrough in the understanding of the level of complexity of network design problems. These are the first nonconstant hardness results known for all these problems.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "cost-distance; fixed charge network flow; Hardness of approximation; network design; priority Steiner tree", } @Article{Immorlica:2008:LCM, author = "Nicole Immorlica and Mohammad Mahdian and Vahab S. Mirrokni", title = "Limitations of cross-monotonic cost-sharing schemes", journal = j-TALG, volume = "4", number = "2", pages = "24:1--24:??", month = may, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1361192.1361201", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Mon Jun 16 11:56:51 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A cost-sharing scheme is a set of rules defining how to share the cost of a service (often computed by solving a combinatorial optimization problem) among serviced customers. A cost-sharing scheme is cross-monotonic if it satisfies the property that everyone is better off when the set of people who receive the service expands. In this article, we develop a novel technique for proving upper bounds on the budget-balance factor of cross-monotonic cost-sharing schemes or the worst-case ratio of recovered cost to total cost. We apply this technique to games defined, based on several combinatorial optimization problems, including the problems of edge cover, vertex cover, set cover, and metric facility location and, in each case, derive tight or nearly-tight bounds. In particular, we show that for the facility location game, there is no cross-monotonic cost-sharing scheme that recovers more than a third of the total cost. This result, together with a recent 1/3-budget-balanced cross-monotonic cost-sharing scheme of P{\'a}l and Tardos [2003] closes the gap for the facility location game. For the vertex cover and set cover games, we show that no cross-monotonic cost-sharing scheme can recover more than a {$ O(n - 1 / 3) $} and {$ O(1 / n) $} fraction of the total cost, respectively. Finally, we study the implications of our results on the existence of group-strategyproof mechanisms. We show that every group-strategyproof mechanism corresponds to a cost-sharing scheme that satisfies a condition weaker than cross-monotonicity. Using this, we prove that group-strategyproof mechanisms satisfying additional properties give rise to cross-monotonic cost-sharing schemes and therefore our upper bounds hold.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Cross-monotonic cost-sharing schemes; group-strategyproof mechanism design; probabilistic method", } @Article{Dinitz:2008:OAS, author = "Yefim Dinitz and Shay Solomon", title = "Optimality of an algorithm solving the {Bottleneck Tower of Hanoi} problem", journal = j-TALG, volume = "4", number = "3", pages = "25:1--25:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367065", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the Bottleneck Tower of Hanoi puzzle posed by D. Wood in 1981. There, a relaxed placement rule allows a larger disk to be placed {\em higher\/} than a smaller one if their size difference is less than a pregiven value $k$. A shortest sequence of moves (optimal algorithm) transferring all the disks placed on some peg in decreasing order of size, to another peg in the same order is in question. In 1992, D. Poole suggested a natural disk-moving strategy for this problem, and computed the length of the shortest move sequence under its framework. However, other strategies were overlooked, so the lower bound/optimality question remained open. In 1998, Benditkis, Berend, and Safro proved the optimality of Poole's algorithm for the first nontrivial case $ k = 2 $. We prove Poole's algorithm to be optimal in the general case.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Optimality proofs; Tower of Hanoi", } @Article{Alonso:2008:DP, author = "Laurent Alonso and Edward M. Reingold", title = "Determining plurality", journal = j-TALG, volume = "4", number = "3", pages = "26:1--26:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367066", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set of $n$ elements, each of which is colored one of $c$ colors, we must determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We prove that $ (c - 1)(n - c) / 2 $ color comparisons are necessary in the worst case to determine the plurality color and give an algorithm requiring {$ (0.775 c + 5.9) n + O(c^2) $} color comparisons for {$ c \geq 9 $}.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithm analysis; majority problem; plurality problem", } @Article{Alonso:2008:ACL, author = "Laurent Alonso and Edward M. Reingold", title = "Average-case lower bounds for the plurality problem", journal = j-TALG, volume = "4", number = "3", pages = "27:1--27:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367067", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set of $n$ elements, each of which is colored one of $ c \geq 2 $ colors, we have to determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We derive lower bounds for the expected number of color comparisons when the $ c^n $ colorings are equally probable. We prove a general lower bound of {$ c / 3 n - O(\sqrt n) $} for {$ c \geq 2 $}; we prove the stronger particular bounds of {$ 7 / 6 n - O(\sqrt n) $} for {$ c = 3 $}, {$ 54 / 35 n - O(\sqrt n) $} for {$ c = 4 $}, {$ 607 / 315 n O(\sqrt n) $} for {$ c = 5 $}, {$ 1592 / 693 n - O(\sqrt n) $} for {$ c = 6 $}, {$ 7985 / 3003 n - O(\sqrt n) $} for {$ c = 7 $}, and {$ 19402 / 6435 n - O(\sqrt n) $} for {$ c = 8 $}.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithm analysis; majority problem; plurality problem", } @Article{Lu:2008:BPS, author = "Hsueh-I Lu and Chia-Chi Yeh", title = "Balanced parentheses strike back", journal = j-TALG, volume = "4", number = "3", pages = "28:1--28:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367068", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An {\em ordinal tree\/} is an arbitrary rooted tree where the children of each node are ordered. Succinct representations for ordinal trees with efficient query support have been extensively studied. The best previously known result is due to Geary et al. [2004b, pages 1--10]. The number of bits required by their representation for an $n$-node ordinal tree {$T$} is {$ 2 n + o(n) $}, whose first-order term is information-theoretically optimal. Their representation supports a large set of {$ O(1) $}-time queries on {$T$}. Based upon a balanced string of {$ 2 n $} parentheses, we give an improved {$ 2 n + o(n) $}-bit representation for {$T$}. Our improvement is two-fold: First, the set of {$ O(1) $}-time queries supported by our representation is a proper superset of that supported by the representation of Geary, Raman, and Raman. Second, it is also much easier for our representation to support new queries by simply adding new auxiliary strings.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Succinct data structures; XML document representation", } @Article{Roditty:2008:RSR, author = "Iam Roditty and Mikkel Thorup and Uri Zwick", title = "Roundtrip spanners and roundtrip routing in directed graphs", journal = j-TALG, volume = "4", number = "3", pages = "29:1--29:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367069", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce the notion of {\em roundtrip-spanners\/} of weighted {\em directed\/} graphs and describe efficient algorithms for their construction. We show that for every integer $ k \geq 1 $ and any $ \epsilon > 0 $, any directed graph on $n$ vertices with edge weights in the range {$ [1, W] $} has a {$ (2 k + \epsilon) $}-roundtrip-spanner with {$ O(\min (k^2 / \epsilon)) n^{1 + 1 / k} (\log (n W), (k / \epsilon)^2 n^{1 + 1 / k}, (\log n)^{2 - 1 / k}) $} edges. We then extend these constructions and obtain compact roundtrip routing schemes. For every integer {$ k \geq 1 $} and every {$ \epsilon > 0 $}, we describe a roundtrip routing scheme that has stretch {$ 4 k + \epsilon $}, and uses at each vertex a routing table of size {$ \tilde {O}((k^2 / \epsilon) n^{1 / k} \log (n W)) $}. We also show that any weighted directed graph with {\em arbitrary / \/} positive edge weights has a 3-roundtrip-spanner with {$ O(n^{3 / 2}) $} edges. This result is optimal. Finally, we present a stretch 3 roundtrip routing scheme that uses local routing tables of size {$ \tilde {O}(n^{1 / 2}) $}. This routing scheme is essentially optimal. The roundtrip-spanner constructions and the roundtrip routing schemes for directed graphs that we describe are only slightly worse than the best available spanners and routing schemes for undirected graphs. Our roundtrip routing schemes substantially improve previous results of Cowen and Wagner. Our results are obtained by combining ideas of Cohen, Cowen and Wagner, Thorup and Zwick, with some new ideas.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distances; roundtrip; Routing; shortest paths; spanners", } @Article{Gu:2008:OBD, author = "Qian-Ping Gu and Hisao Tamaki", title = "Optimal branch-decomposition of planar graphs in {$ O(n^3) $} time", journal = j-TALG, volume = "4", number = "3", pages = "30:1--30:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367070", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give an {$ O(n^3) $} time algorithm for constructing a minimum-width branch-decomposition of a given planar graph with {$n$} vertices. This is achieved through a refinement to the previously best known algorithm of Seymour and Thomas, which runs in {$ O(n^4) $} time.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Branch-decompositions; planar graphs", } @Article{Czumaj:2008:TEM, author = "Artur Czumaj and Christian Sohler", title = "Testing {Euclidean} minimum spanning trees in the plane", journal = j-TALG, volume = "4", number = "3", pages = "31:1--31:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367071", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a Euclidean graph {$G$} over a set {$P$} of {$n$} points in the plane, we are interested in verifying whether {$G$} is a Euclidean minimum spanning tree (EMST) of {$P$} or {$G$} differs from it in more than {$ \epsilon n $} edges. We assume that {$G$} is given in adjacency list representation and the point/vertex set {$P$} is given in an array. We present a property testing algorithm that accepts graph {$G$} if it is an EMST of {$P$} and that rejects with probability at least {$ 2 / 3 $} if {$G$} differs from every EMST of {$P$} in more than {$ \epsilon, n $} edges. Our algorithm runs in {$ O(\sqrt n / \epsilon \cdot \log^2 (n / \epsilon)) $} time and has a query complexity of {$ O(\sqrt n / \epsilon \cdot \log (n / \epsilon)) $}.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Euclidean minimum spanning tree; property testing; randomized algorithms", } @Article{Makinen:2008:DEC, author = "Veli M{\"a}kinen and Gonzalo Navarro", title = "Dynamic entropy-compressed sequences and full-text indexes", journal = j-TALG, volume = "4", number = "3", pages = "32:1--32:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367072", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give new solutions to the Searchable Partial Sums with Indels problem. Given a sequence of $n$ $k$-bit numbers, we present a structure taking $ k n + o(k n) $ bits of space, able of performing operations {\em sum}, {\em search}, {\em insert}, and {\em delete}, all in {$ O(\log n) $} worst-case time, for any {$ k = O(\log n) $}. This extends previous results by Hon et al. [2003c] achieving the same space and {$ O(\log n / \log \log n) $} time complexities for the queries, yet offering complexities for {\em insert\/} and {\em delete\/} that are amortized and worse than ours, and supported only for {$ k = O(1) $}. Our result matches an existing lower bound for large values of {$k$}.\par We also give new solutions to the Dynamic Sequence problem. Given a sequence of {$n$} symbols in the range {$ [1, \sigma] $} with binary zero-order entropy {$ H_0 $}, we present a dynamic data structure that requires {$ n_0 + o(n \log \sigma) $} bits of space, which is able of performing {\em rank\/} and {\em select}, as well as inserting and deleting symbols at arbitrary positions, in {$ O(\log n \log \sigma) $} time. Our result is the {\em first\/} entropy-bound dynamic data structure for {\em rank\/} and {\em select\/} over general sequences.\par In the case {$ \sigma = 2 $}, where both previous problems coincide, we improve the dynamic solution of Hon et al. [2003c] in that we compress the sequence. The only previous result with entropy-bound space for dynamic binary sequences is by Blandford and Blelloch [2004], which has the same complexities as our structure, but does not achieve constant 1 multiplying the entropy term in the space complexity.\par Finally, we present a new dynamic compressed full-text self-index, for a collection of texts over an alphabet of size {$ \sigma $}, of overall length {$n$} and $h$ th order empirical entropy {$ H_h $}. The index requires {$ n H_h + o(n \log \sigma) $} bits of space, for any {$ h \leq \alpha \log_\sigma n $} and constant {$0$}.\par An important result we prove in this paper is that the wavelet tree of the Burrows--Wheeler transform of a text, if compressed with a technique that achieves zero-order compression locally (e.g., Raman et al. [2002]), automatically achieves $h$ th order entropy space for any $h$. This unforeseen relation is essential for the results of the previous paragraph, but it also derives into significant simplifications on many existing static compressed full-text self-indexes that build on wavelet trees.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Compressed dynamic data structures; compressed text databases; entropy; partial sums; sequences", } @Article{Kowalski:2008:WAD, author = "Dariusz R. Kowalski and Alexander A. Shvartsman", title = "Writing-all deterministically and optimally using a nontrivial number of asynchronous processors", journal = j-TALG, volume = "4", number = "3", pages = "33:1--33:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367073", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The problem of performing $n$ tasks on $p$ asynchronous or undependable processors is a basic problem in distributed computing. This article considers an abstraction of this problem called {\em Write-All: using $p$ processors write 1's into all locations of an array of size n}. In this problem writing 1 abstracts the notion of performing a simple task. Despite substantial research, there is a dearth of efficient deterministic asynchronous algorithms for {\em Write-All/}. Efficiency of algorithms is measured in terms of {\em work\/} that accounts for all local steps performed by the processors in solving the problem. Thus, an optimal algorithm would have work {$ \Theta (n) $}, however it is known that optimality cannot be achieved when {$ p = \Omega (n) $}. The quest then is to obtain work-optimal solutions for this problem using a nontrivial, compared to {$n$}, number of processors {$p$}. The algorithm presented in this article has work complexity of {$ O(n + p^{2 + \epsilon }) $}, and it achieves work optimality for {$ p = O(n^{1 / (2 + \epsilon)}) $} for any {$ \epsilon > 0 $}, while the previous best result achieved optimality for {$ p \leq 4 \sqrt n / \log n $}. Additionally, the new result uses {\em only\/} the atomic read/write memory, without resorting to using the test-and-set primitive that was necessary in the previous solution.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Asynchrony; distributed algorithms; shared memory; work; Write-All", } @Article{Even:2008:ACR, author = "Guy Even and Retsef Levi and Dror Rawitz and Baruch Schieber and Shimon (Moni) Shahar and Maxim Sviridenko", title = "Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs", journal = j-TALG, volume = "4", number = "3", pages = "34:1--34:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367074", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the rectangle stabbing problem, we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. In this article, we study the capacitated version of this problem in which the input includes an integral capacity for each line. The capacity of a line bounds the number of rectangles that the line can cover. We consider two versions of this problem. In the first, one is allowed to use only a single copy of each line ({\em hard capacities\/}), and in the second, one is allowed to use multiple copies of every line, but the multiplicities are counted in the size (or weight) of the solution ({\em soft capacities\/}).\par We present an exact polynomial-time algorithm for the weighted one dimensional case with hard capacities that can be extended to the one dimensional weighted case with soft capacities. This algorithm is also extended to solve a certain capacitated multi-item {\em lot-sizing\/} inventory problem with joint set-up costs. For the case of $d$-dimensional rectangle stabbing with soft capacities, we present a $ 3 d $-approximation algorithm for the unweighted case. For $d$-dimensional rectangle stabbing problem with hard capacities, we present a bi-criteria algorithm that computes $ 4 d $-approximate solutions that use at most two copies of every line. Finally, we present hardness results for rectangle stabbing when the dimension is part of the input and for a two-dimensional weighted version with hard capacities.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; capacitated covering; lot sizing; rectangle stabbing", } @Article{Zhang:2008:CCP, author = "Cun-Quan Zhang and Yongbin Ou", title = "Clustering, community partition and disjoint spanning trees", journal = j-TALG, volume = "4", number = "3", pages = "35:1--35:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367075", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Clustering method is one of the most important tools in statistics. In a graph theory model, clustering is the process of finding all dense subgraphs. A mathematically well-defined measure for graph density is introduced in this article as follows. Let {$ G = (V, E) $} be a graph (or multi-graph) and {$H$} be a subgraph of {$G$}. The dynamic density of {$H$} is the greatest integer {$k$} such that {$ \min_\forall P \{ | E (H / P)| / | V (H / P)| - 1 \} > k $} where the minimum is taken over all possible partitions {$P$} of the vertex set of {$H$}, and {$ H / P $} is the graph obtained from {$H$} by contracting each part of {$P$} into a single vertex. A subgraph {$H$} of {$G$} is a level-{$k$} community if {$H$} is a maximal subgraph of {$G$} with dynamic density at least {$k$}. An algorithm is designed in this paper to detect all level-{$h$} communities of an input multi-graph {$G$}. The worst-case complexity of this algorithm is upper bounded by {$ O(|V(G)|^2 h^2) $}. This new method is one of few available clustering methods that are mathematically well-defined, supported by rigorous mathematical proof and able to achieve the optimization goal with polynomial complexity. As a byproduct, this algorithm also can be applied for finding edge-disjoint spanning trees of a multi-graph. The worst-case complexity is lower than all known algorithms for multi-graphs.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "clustering; community; dense subgraph; dynamic density; hierarchical clustering; polynomial algorithm; Spanning trees", } @Article{Yu:2008:IAM, author = "Hung-I. Yu and Tzu-Chin Lin and Biing-Feng Wang", title = "Improved algorithms for the minmax-regret 1-center and 1-median problems", journal = j-TALG, volume = "4", number = "3", pages = "36:1--36:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367076", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, efficient algorithms are presented for the minmax-regret 1-center and 1-median problems on a general graph and a tree with uncertain vertex weights. For the minmax-regret 1-center problem on a general graph, we improve the previous upper bound from {$ O(m n^2 \log n) $} to {$ O(m n \log n) $}. For the problem on a tree, we improve the upper bound from {$ O(n^2) $} to {$ O(n \log^2 n) $}. For the minmax-regret 1-median problem on a general graph, we improve the upper bound from {$ O(m n^2 \log n) $} to {$ O(m n^2 + n^3 \log n) $}. For the problem on a tree, we improve the upper bound from {$ O(n \log^2 n) $} to {$ O(n \log n) $}.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "centers; general graphs; Location theory; medians; minmax-regret optimization; trees", } @Article{Abraham:2008:CNI, author = "Ittai Abraham and Cyril Gavoille and Dahlia Malkhi and Noam Nisan and Mikkel Thorup", title = "Compact name-independent routing with minimum stretch", journal = j-TALG, volume = "4", number = "3", pages = "37:1--37:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367077", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a weighted undirected network with arbitrary node names, we present a compact routing scheme, using a {$ \tilde {O}(\sqrt n) $} space routing table at each node, and routing along paths of stretch 3, that is, at most thrice as long as the minimum cost paths. This is optimal in a very strong sense. It is known that no compact routing using {$ o(n) $} space per node can route with stretch below 3. Also, it is known that any stretch below 5 requires {$ \Omega (\sqrt n) $} space per node.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Compact routing", } @Article{Pruhs:2008:GBR, author = "Kirk Pruhs and Patchrawat Uthaisombut and Gerhard Woeginger", title = "Getting the best response for your erg", journal = j-TALG, volume = "4", number = "3", pages = "38:1--38:??", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1367064.1367078", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:06 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the speed scaling problem of minimizing the average response time of a collection of dynamically released jobs subject to a constraint {$A$} on energy used. We propose an algorithmic approach in which an energy optimal schedule is computed for a huge {$A$}, and then the energy optimal schedule is maintained as {$A$} decreases. We show that this approach yields an efficient algorithm for equi-work jobs. We note that the energy optimal schedule has the surprising feature that the job speeds are not monotone functions of the available energy. We then explain why this algorithmic approach is problematic for arbitrary work jobs. Finally, we explain how to use the algorithm for equi-work jobs to obtain an algorithm for arbitrary work jobs that is {$ O(1) $}-approximate with respect to average response time, given an additional factor of {$ (1 + \epsilon) $} energy.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "frequency scaling; power management; scheduling; Speed scaling; voltage scaling", } @Article{Ajwani:2008:AIT, author = "Deepak Ajwani and Tobias Friedrich and Ulrich Meyer", title = "An {$ O(n^{2.75}) $} algorithm for incremental topological ordering", journal = j-TALG, volume = "4", number = "4", pages = "39:1--39:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383370", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a simple algorithm which maintains the topological order of a directed acyclic graph (DAG) with $n$ nodes, under an online edge insertion sequence, in {$ O(n^{2.75}) $} time, independent of the number {$m$} of edges inserted. For dense DAGs, this is an improvement over the previous best result of {$ O(\min m^{3 / 2} \log n, m^{3 / 2} + n^2 \log n) $} by Katriel and Bodlaender [2006]. We also provide an empirical comparison of our algorithm with other algorithms for incremental topological sorting.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Dynamic algorithms; graphs; online algorithms; topological order", } @Article{Ibarra:2008:FDA, author = "Louis Ibarra", title = "Fully dynamic algorithms for chordal graphs and split graphs", journal = j-TALG, volume = "4", number = "4", pages = "40:1--40:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383371", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the first dynamic algorithm that maintains a clique tree representation of a chordal graph and supports the following operations: (1) query whether deleting or inserting an arbitrary edge preserves chordality; and (2) delete or insert an arbitrary edge, provided it preserves chordality. We give two implementations. In the first, each operation runs in {$ O(n) $} time, where {$n$} is the number of vertices. In the second, an insertion query runs in {$ O(\log^2 n) $} time, an insertion in {$ O(n) $} time, a deletion query in {$ O(n) $} time, and a deletion in {$ O(n \log n) $} time. We also present a data structure that allows a deletion query to run in {$ O(\sqrt m) $} time in either implementation, where {$m$} is the current number of edges. Updating this data structure after a deletion or insertion requires {$ O(m) $} time.\par We also present a very simple dynamic algorithm that supports each of the following operations in {$ O(1) $} time on a general graph: (1) query whether the graph is split, and (2) delete or insert an arbitrary edge.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "chordal graphs; clique trees; Dynamic graph algorithms; split graphs", } @Article{Korman:2008:DRS, author = "Amos Korman and David Peleg", title = "Dynamic routing schemes for graphs with low local density", journal = j-TALG, volume = "4", number = "4", pages = "41:1--41:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383372", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article studies approximate distributed routing schemes on dynamic communication networks. The work focuses on dynamic weighted general graphs where the vertices of the graph are fixed, but the weights of the edges may change. Our main contribution concerns bounding the cost of adapting to dynamic changes. The update efficiency of a routing scheme is measured by the time needed in order to update the routing scheme following a weight change. A naive dynamic routing scheme, which updates all vertices following a weight change, requires {$ \Omega (\hbox {\em Diam \/ }) $} time in order to perform the updates after every weight change, where {\em Diam\/} is the diameter of the underlying graph. In contrast, this article presents approximate dynamic routing schemes with average time complexity {$ \tilde {\Theta }(d) $} per topological change, where {$d$} is the local density parameter of the underlying graph. Following a weight change, our scheme never incurs more than {\em Diam\/} time; thus, our scheme is particularly efficient on graphs which have low local density and large diameter. The article also establishes upper and lower bounds on the size of the databases required by the scheme at each site.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distributed algorithms; dynamic networks; Routing schemes", } @Article{Cohen:2008:LGG, author = "Reuven Cohen and Pierre Fraigniaud and David Ilcinkas and Amos Korman and David Peleg", title = "Label-guided graph exploration by a finite automaton", journal = j-TALG, volume = "4", number = "4", pages = "42:1--42:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383373", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A finite automaton, simply referred to as a {\em robot}, has to explore a graph, that is, visit all the nodes of the graph. The robot has no a priori knowledge of the topology of the graph, nor of its size. It is known that for any $k$-state robot, there exists a graph of maximum degree 3 that the robot cannot explore. This article considers the effects of allowing the system designer to add short labels to the graph nodes in a preprocessing stage, for helping the exploration by the robot. We describe an exploration algorithm that, given appropriate 2-bit labels (in fact, only 3-valued labels), allows a robot to explore all graphs. Furthermore, we describe a suitable labeling algorithm for generating the required labels in linear time. We also show how to modify our labeling scheme so that a robot can explore all graphs of bounded degree, given appropriate 1-bit labels. In other words, although there is no robot able to explore all graphs of maximum degree 3, there is a robot {$R$}, and a way to color in black or white the nodes of any bounded-degree graph {$G$}, so that {$R$} can explore the colored graph {$G$}. Finally, we give impossibility results regarding graph exploration by a robot with no internal memory (i.e., a single-state automaton).", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Distributed algorithms; graph exploration; labeling schemes", } @Article{Suzuki:2008:DSP, author = "Akiko Suzuki and Takeshi Tokuyama", title = "Dense subgraph problems with output-density conditions", journal = j-TALG, volume = "4", number = "4", pages = "43:1--43:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383374", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the dense subgraph problem that extracts a subgraph, with a prescribed number of vertices, having the maximum number of edges (or total edge weight, in the weighted case) in a given graph. We give approximation algorithms with improved theoretical approximation ratios assuming that the density of the optimal output subgraph is high, where density is the ratio of number of edges (or sum of edge weights) to the number of edges in the clique on the same number of vertices. Moreover, we investigate the case where the input graph is bipartite and design a randomized pseudopolynomial time approximation scheme that can become a randomized PTAS, even if the size of the optimal output graph is comparatively small. This is a significant improvement in a theoretical sense, since no constant-ratio approximation algorithm was known previously if the output graph has o(n) vertices.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; Combinatorial optimization; dense subgraph; randomized algorithms", } @Article{Bar-Noy:2008:DCF, author = "Amotz Bar-Noy and Panagiotis Cheilaris and Shakhar Smorodinsky", title = "Deterministic conflict-free coloring for intervals: {From} offline to online", journal = j-TALG, volume = "4", number = "4", pages = "44:1--44:18", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383375", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate deterministic algorithms for a frequency assignment problem in cellular networks. The problem can be modeled as a special vertex coloring problem for hypergraphs: In every hyperedge there must exist a vertex with a color that occurs exactly once in the hyperedge (the conflict-free property). We concentrate on a special case of the problem, called conflict-free coloring for intervals. We introduce a hierarchy of four models for the aforesaid problem: (i) static, (ii) dynamic offline, (iii) dynamic online with absolute positions, and (iv) dynamic online with relative positions. In the dynamic offline model, we give a deterministic algorithm that uses at most $ \log_{3 / 2} n + 1 \approx 1.71 \log_2 n $ colors and show inputs that force any algorithm to use at least $ 3 \log_5 n + 1 \approx 1.29 \log_2 n $ colors. For the online absolute-positions model, we give a deterministic algorithm that uses at most $ 3 \lceil \log_3 n \rceil \approx 1.89 \log_2 n $ colors. To the best of our knowledge, this is the first deterministic online algorithm using {$ O(\log n) $} colors in a nontrivial online model. In the online relative-positions model, we resolve an open problem by showing a tight analysis on the number of colors used by the first-fit greedy online algorithm. We also consider conflict-free coloring only with respect to intervals that contain at least one of the two extreme points.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "cellular networks; coloring; conflict free; frequency assignment; Online algorithms", } @Article{Chandran:2008:IAO, author = "Nishanth Chandran and Ryan Moriarty and Rafail Ostrovsky and Omkant Pandey and Mohammad Ali Safari and Amit Sahai", title = "Improved algorithms for optimal embeddings", journal = j-TALG, volume = "4", number = "4", pages = "45:1--45:14", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383376", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the last decade, the notion of metric embeddings with small distortion has received wide attention in the literature, with applications in combinatorial optimization, discrete mathematics, and bio-informatics. The notion of embedding is, given two metric spaces on the same number of points, to find a bijection that minimizes maximum Lipschitz and bi-Lipschitz constants. One reason for the popularity of the notion is that algorithms designed for one metric space can be applied to a different one, given an embedding with small distortion. The better distortion, the better the effectiveness of the original algorithm applied to a new metric space.\par The goal recently studied by Kenyon et al. [2004] is to consider all possible embeddings between two {\em finite\/} metric spaces and to find the best possible one; that is, consider a single objective function over the space of all possible embeddings that minimizes the distortion. In this article we continue this important direction. In particular, using a theorem of Albert and Atkinson [2005], we are able to provide an algorithm to find the optimal bijection between two line metrics, provided that the optimal distortion is smaller than 13.602. This improves the previous bound of $ 3 + 2 \sqrt {2} $, solving an open question posed by Kenyon et al. [2004]. Further, we show an inherent limitation of algorithms using the ``forbidden pattern'' based dynamic programming approach, in that they cannot find optimal mapping if the optimal distortion is more than $ 7 + 4 \sqrt {3} (\simeq 13.928) $. Thus, our results are almost optimal for this method. We also show that previous techniques for general embeddings apply to a (slightly) more general class of metrics.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "dynamic programming; forbidden patterns; line embeddings; metric spaces; Optimal metric embeddings; shape matching", } @Article{Alon:2008:OEM, author = "Noga Alon and Mihai B{\~a}doiu and Erik D. Demaine and Martin Farach-Colton and Mohammadtaghi Hajiaghayi and Anastasios Sidiropoulos", title = "Ordinal embeddings of minimum relaxation: {General} properties, trees, and ultrametrics", journal = j-TALG, volume = "4", number = "4", pages = "46:1--46:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383377", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new notion of embedding, called {\em minimum-relaxation ordinal embedding}, parallel to the standard notion of minimum-distortion (metric) embedding. In an ordinal embedding, it is the relative order between pairs of distances, and not the distances themselves, that must be preserved as much as possible. The (multiplicative) relaxation of an ordinal embedding is the maximum ratio between two distances whose relative order is inverted by the embedding. We develop several worst-case bounds and approximation algorithms on ordinal embedding. In particular, we establish that ordinal embedding has many qualitative differences from metric embedding, and we capture the ordinal behavior of ultrametrics and shortest-path metrics of unweighted trees.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distortion; Metrics; ordinal embedding; relaxation", } @Article{Blaser:2008:NAA, author = "Markus Bl{\"a}ser", title = "A new approximation algorithm for the asymmetric {TSP} with triangle inequality", journal = j-TALG, volume = "4", number = "4", pages = "47:1--47:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383378", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a polynomial time factor $ 0.999 \cdot \log n $ approximation algorithm for the asymmetric traveling salesperson problem with triangle inequality.", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; cycle cover; traveling salesman problem; TSP", } @Article{Boyar:2008:RWO, author = "Joan Boyar and Paul Medvedev", title = "The relative worst order ratio applied to seat reservation", journal = j-TALG, volume = "4", number = "4", pages = "48:1--48:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383379", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The seat reservation problem is the problem of assigning passengers to seats on a train with $n$ seats and $k$ stations enroute in an online manner. The performance of algorithms for this problem is studied using the relative worst order ratio, a fairly new measure for the quality of online algorithms, which allows for direct comparisons between algorithms. This study has yielded new separations between algorithms. For example, for both variants of the problem considered, using the relative worst order ratio, First-Fit and Best-Fit are shown to be better than Worst-Fit.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Online; quality measure; relative worst order ratio; seat reservation", } @Article{Nieberg:2008:ASW, author = "Tim Nieberg and Johann Hurink and Walter Kern", title = "Approximation schemes for wireless networks", journal = j-TALG, volume = "4", number = "4", pages = "49:1--49:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383380", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Wireless networks are created by the communication links between a collection of radio transceivers. The nature of wireless transmissions does not lead to arbitrary undirected graphs but to structured graphs which we characterize by the polynomially bounded growth property. In contrast to many existing graph models for wireless networks, the property of polynomially bounded growth is defined independently of geometric data such as positional information.\par On such wireless networks, we present an approach that can be used to create polynomial-time approximation schemes for several optimization problems called the local neighborhood-based scheme. We apply this approach to the problems of seeking maximum (weight) independent sets and minimum dominating sets. These are two important problems in the area of wireless communication networks and are also used in many applications ranging from clustering to routing strategies. However, the approach is presented in a general fashion since it can be applied to other problems as well.\par The approach for the approximation schemes is robust in the sense that it accepts any undirected graph as input and either outputs a solution of desired quality or correctly asserts that the graph presented as input does not satisfy the structural assumption of a wireless network (an NP-hard problem).", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "bounded growth; maximum independent set; minimum dominating set; PTAS; Wireless ad-hoc networks", } @Article{Massberg:2008:AAF, author = "Jens Ma{\ss}berg and Jens Vygen", title = "Approximation algorithms for a facility location problem with service capacities", journal = j-TALG, volume = "4", number = "4", pages = "50:1--50:15", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383381", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the first constant-factor approximation algorithms for the following problem. Given a metric space {$ (V, c) $}, a finite set {$ d \subseteq V $} of terminals\slash customers with demands {$ d : d \rightarrow \mathbb {R}_+ $}, a facility opening cost {$ f \in \mathbb {R}_+ $} and a capacity {$ u \in \mathbb {R}_+ $}, find a partition {$ d = D_1 \dot {\cup } \cdots {} \dot {\cup } D_k $} and Steiner trees {$ T_i $} for {$ D_i (i = 1, \ldots {}, k) $} with {$ c(E(T_i)) + d(D_i) \leq u $} for {$ i = 1, \ldots {}, k $} such that {$ \sum_{i = 1}^k c(E(T_i)) + k f $} is minimum. This problem arises in VLSI design. It generalizes the bin-packing problem and the Steiner tree problem. In contrast to other network design and facility location problems, it has the additional feature of upper bounds on the service cost that each facility can handle. Among other results, we obtain a 4.1-approximation in polynomial time, a 4.5-approximation in cubic time, and a 5-approximation as fast as computing a minimum spanning tree on {$ (D, c) $}.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; facility location; network design; VLSI design", } @Article{Swamy:2008:FTF, author = "Chaitanya Swamy and David B. Shmoys", title = "Fault-tolerant facility location", journal = j-TALG, volume = "4", number = "4", pages = "51:1--51:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383382", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a fault-tolerant generalization of the classical uncapacitated facility location problem, where each client $j$ has a requirement that $ r_j $ {\em distinct\/} facilities serve it, instead of just one. We give a 2.076-approximation algorithm for this problem using LP rounding, which is currently the best-known performance guarantee. Our algorithm exploits primal and dual complementary slackness conditions and is based on {\em clustered randomized rounding}. A technical difficulty that we overcome is the presence of terms with negative coefficients in the dual objective function, which makes it difficult to bound the cost in terms of dual variables. For the case where all requirements are the same, we give a primal-dual 1.52-approximation algorithm.\par We also consider a fault-tolerant version of the $k$-median problem. In the metric $k$-median problem, we are given $n$ points in a metric space. We must select $k$ of these to be centers, and then assign each input point $j$ to the selected center that is closest to it. In the fault-tolerant version we want $j$ to be assigned to $ r_j $ distinct centers. The goal is to select the $k$ centers so as to minimize the sum of assignment costs. The primal-dual algorithm for fault-tolerant facility location with uniform requirements also yields a 4-approximation algorithm for the fault-tolerant $k$-median problem for this case. This the first constant-factor approximation algorithm for the uniform requirements case.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; facility location; k-median problem", } @Article{Fotakis:2008:ACG, author = "Dimitris Fotakis and Spyros Kontogiannis and Paul Spirakis", title = "Atomic congestion games among coalitions", journal = j-TALG, volume = "4", number = "4", pages = "52:1--52:??", month = aug, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1383369.1383383", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:03:43 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider algorithmic questions concerning the existence, tractability, and quality of Nash equilibria, in atomic congestion games among users participating in selfish coalitions.\par We introduce a coalitional congestion model among atomic players and demonstrate many interesting similarities with the noncooperative case. For example, there exists a potential function proving the existence of pure Nash equilibria (PNE) in the unrelated parallel links setting; in the network setting, the finite improvement property collapses as soon as we depart from linear delays, but there is an exact potential (and thus PNE) for linear delays. The price of anarchy on identical parallel links demonstrates a quite surprising threshold behavior: It persists on being asymptotically equal to that in the case of the noncooperative KP-model, unless the number of coalitions is {\em sublogarithmic}.\par We also show crucial differences, mainly concerning the hardness of algorithmic problems that are solved efficiently in the noncooperative case. Although we demonstrate convergence to robust PNE, we also prove the hardness of computing them. On the other hand, we propose a generalized fully mixed Nash equilibrium that can be efficiently constructed in most cases. Finally, we propose a natural improvement policy and prove its convergence in pseudopolynomial time to PNE which are robust against (even dynamically forming) coalitions of small size.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithmic game theory; congestion games; convergence to equilibria; price of anarchy", } @Article{Torng:2008:SOU, author = "Eric Torng and Jason McCullough", title = "{SRPT} optimally utilizes faster machines to minimize flow time", journal = j-TALG, volume = "5", number = "1", pages = "1:1--1:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435376", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We analyze the shortest remaining processing time (SRPT) algorithm with respect to the problem of scheduling $n$ jobs with release times on $m$ identical machines to minimize total flow time. It is known that SRPT is optimal if $ m = 1$ but that SRPT has a worst-case approximation ratio of $ \Theta (\min (\log n / m, \log \Delta)) $ for this problem, where $ \Delta $ is the ratio of the length of the longest job divided by the length of the shortest job. It has previously been shown that SRPT is able to use faster machines to produce a schedule {\em as good as\/} an optimal algorithm using slower machines. We now show that SRPT {\em optimally\/} uses these faster machines with respect to the worst-case approximation ratio. That is, if SRPT is given machines that are $ s \geq 2 - 1 / m $ times as fast as those used by an optimal algorithm, SRPT's flow time is at least $s$ {\em times smaller\/} than the flow time incurred by the optimal algorithm. Clearly, no algorithm can offer a better worst-case guarantee, and we show that existing algorithms with similar performance guarantees to SRPT without resource augmentation do not optimally use extra resources.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "flow time; parallel machines; resource augmentation; scheduling; SRPT", } @Article{Goldwasser:2008:ONS, author = "Michael H. Goldwasser and Mark Pedigo", title = "Online nonpreemptive scheduling of equal-length jobs on two identical machines", journal = j-TALG, volume = "5", number = "1", pages = "2:1--2:18", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435377", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the nonpreemptive scheduling of two identical machines for jobs with equal processing times yet arbitrary release dates and deadlines. Our objective is to maximize the number of jobs completed by their deadlines. Using standard nomenclature, this problem is denoted as {$ P 2 \mid p_j = p, 4_j \mid \sum {\bar {U}}_j $}. The problem is known to be polynomially solvable in an offline setting.\par In an online variant of the problem, a job's existence and parameters are revealed to the scheduler only upon that job's release date. We present an online deterministic algorithm for the problem and prove that it is {$ 3 / 2 $}-competitive. A simple lower bound shows that this is the optimal deterministic competitiveness.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Admission control; competitive analysis; scheduling", } @Article{Aiello:2008:CBM, author = "William Aiello and Alex Kesselman and Yishay Mansour", title = "Competitive buffer management for shared-memory switches", journal = j-TALG, volume = "5", number = "1", pages = "3:1--3:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435378", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider buffer management policies for shared memory switches. We study the case of overloads resulting in packet loss, where the constraint is the limited shared memory capacity. The goal of the buffer management policy is that of maximizing the number of packets transmitted. The problem is online in nature, and thus we use competitive analysis to measure the performance of the buffer management policies. Our main result is to show that the well-known preemptive Longest Queue Drop ({\em LQD\/}) policy is at most 2-competitive and at least $ \sqrt 2 $-competitive. We also demonstrate a general lower bound of $ 4 / 3 $ on the performance of any deterministic online policy. Finally, we consider some other popular non-preemptive policies including Complete Partition, Complete Sharing, Static Threshold and Dynamic Threshold and derive almost tight bounds on their performance.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Buffer management; competitive analysis; shared memory", } @Article{Agarwal:2008:KDD, author = "Pankaj K. Agarwal and Haim Kaplan and Micha Sharir", title = "Kinetic and dynamic data structures for closest pair and all nearest neighbors", journal = j-TALG, volume = "5", number = "1", pages = "4:1--4:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435379", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present simple, fully dynamic and kinetic data structures, which are variants of a dynamic two-dimensional range tree, for maintaining the closest pair and all nearest neighbors for a set of $n$ moving points in the plane; insertions and deletions of points are also allowed. If no insertions or deletions take place, the structure for the closest pair uses {$ O(n \log n) $} space, and processes {$ O(n^2 \beta_+ 2 (n) \log n) $} critical events, each in {$ O(\log^2 n) $} time. Here {$s$} is the maximum number of times where the distances between any two specific pairs of points can become equal, {$ \beta_s(q) = \lambda_s(q) / q $}, and {$ \lambda_s(q) $} is the maximum length of Davenport--Schinzel sequences of order $s$ on $q$ symbols. The dynamic version of the problem incurs a slight degradation in performance: If $ m \geq n $ insertions and deletions are performed, the structure still uses {$ O(n \log n) $} space, and processes {$ O(m n \beta_s + 2 (n) \log^3 n) $} events, each in {$ O(\log^3 n) $} time.\par Our kinetic data structure for all nearest neighbors uses {$ O(n \log^2 n) $} space, and processes {$ O(n^2 \beta^{2_s + 2}(n) \log^3 n) $} critical events. The expected time to process all events is {$ O(n^2 \beta_{s + 2}^2 (n) \log^4 n) $}, though processing a single event may take {$ \Theta (n) $} expected time in the worst case. If {$ m \geq n $} insertions and deletions are performed, then the expected number of events is {$ O(m n \beta^2_{s + 2}(n) \log^3 n) $} and processing them all takes {$ O(m n \beta^2_{s + 2} (n) \log^4 n) $}. An insertion or deletion takes {$ O(n) $} expected time.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "closest pair; computational geometry; Kinetic data structures; nearest neighbors", } @Article{Agarwal:2008:ACT, author = "Pankaj K. Agarwal and Micha Sharir and Emo Welzl", title = "Algorithms for center and {Tverberg} points", journal = j-TALG, volume = "5", number = "1", pages = "5:1--5:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435380", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set $s$ of $n$ points in {$ R^3 $}, a point {$x$} in {$ R^3 $} is called {\em center point of $S$ \/} if every closed halfspace whose bounding hyperplane passes through {$x$} contains at least {$ \lceil n / 4 \rceil $} points from {$S$}. We present a near-quadratic algorithm for computing the {\em center region}, that is the set of all center points, of a set of {$n$} points in {$ R^3 $}. This is nearly tight in the worst case since the center region can have {$ \Omega (n^2) $} complexity.\par We then consider sets {$s$} of {$ 3 n $} points in the plane which are the union of three disjoint sets consisting respectively of {$n$} red, $n$ blue, and $n$ green points. A point $x$ in {$ R^2 $} is called a {\em colored Tverberg point of $S$ \/} if there is a partition of {$s$} into {$n$} triples with one point of each color, so that {$x$} lies in all triangles spanned by these triples. We present a first polynomial-time algorithm for recognizing whether a given point is a colored Tverberg point of such a 3-colored set {$S$}.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Arrangements; center point; Tverberg point", } @Article{Grandoni:2008:DWV, author = "Fabrizio Grandoni and Jochen K{\"o}nemann and Alessandro Panconesi", title = "Distributed weighted vertex cover via maximal matchings", journal = j-TALG, volume = "5", number = "1", pages = "6:1--6:12", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435381", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider the problem of computing a minimum-weight vertex-cover in an $n$-node, weighted, undirected graph {$ G = (V, E) $}. We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of {$ O(\log n + \log \hat {W}) $} communication rounds, where {$ \hat {W} $} is the average vertex-weight. The previous best algorithm for this problem requires {$ O(\log n (\log n + \log \hat {W})) $} rounds and it is not fully distributed.\par For a maximal matching {$m$} in {$G$}, it is a well-known fact that any vertex-cover in {$G$} needs to have at least {$ |m| $} vertices. Our algorithm is based on a generalization of this combinatorial lower-bound to the weighted setting.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; distributed algorithms; maximal matching; vertex cover", } @Article{Vishwanathan:2008:HIA, author = "Sundar Vishwanathan", title = "On hard instances of approximate vertex cover", journal = j-TALG, volume = "5", number = "1", pages = "7:1--7:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435382", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that if there is a $ 2 - \epsilon $ approximation algorithm for vertex cover on graphs with vector chromatic number at most $ 2 + \delta $, then there is a $ 2 - f(\epsilon, \delta) $ approximation algorithm for vertex cover for all graphs.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; vertex cover", } @Article{Berend:2008:CDG, author = "Daniel Berend and Steven S. Skiena and Yochai Twitto", title = "Combinatorial dominance guarantees for problems with infeasible solutions", journal = j-TALG, volume = "5", number = "1", pages = "8:1--8:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435383", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The design and analysis of approximation algorithms for {\em NP\/}-hard problems is perhaps the most active research area in the theory of combinatorial algorithms. In this article, we study the notion of a {\em combinatorial dominance guarantee\/} as a way for assessing the performance of a given approximation algorithm. An $ f(n) $ dominance bound is a guarantee that the heuristic always returns a solution not worse than at least $ f(n) $ solutions. We give tight analysis of many heuristics, and establish novel and interesting dominance guarantees even for certain inapproximable problems and heuristic search algorithms. For example, we show that the maximal matching heuristic of VERTEX COVER offers a combinatorial dominance guarantee of $ 2^n - (1.839 + o(1))^n $. We also give inapproximability results for most of the problems we discuss.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "algorithms analysis; approximation algorithms; Computation complexity; dominance analysis", } @Article{Fomin:2008:CBM, author = "Fedor V. Fomin and Fabrizio Grandoni and Artem V. Pyatkin and Alexey A. Stepanov", title = "Combinatorial bounds via measure and conquer: {Bounding} minimal dominating sets and applications", journal = j-TALG, volume = "5", number = "1", pages = "9:1--9:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435384", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We provide an algorithm listing all minimal dominating sets of a graph on $n$ vertices in time {$ O(1.7159^n) $}. This result can be seen as an algorithmic proof of the fact that the number of minimal dominating sets in a graph on {$n$} vertices is at most {$ 1.7159^n $}, thus improving on the trivial {$ O(2^n / \sqrt n) $} bound. Our result makes use of the measure-and-conquer technique which was recently developed in the area of exact algorithms.\par Based on this result, we derive an {$ O(2.8718^n) $} algorithm for the domatic number problem.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "domatic number; Exact exponential algorithms; listing algorithms; measure and conquer; minimum dominating set; minimum set cover", } @Article{Oum:2008:ARW, author = "Sang-Il Oum", title = "Approximating rank-width and clique-width quickly", journal = j-TALG, volume = "5", number = "1", pages = "10:1--10:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435385", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Rank-width was defined by Oum and Seymour [2006] to investigate clique-width. They constructed an algorithm that either outputs a rank-decomposition of width at most $ f(k) $ for some function f or confirms that rank-width is larger than $k$ in time {$ O(|V|^9 \log |V|) $} for an input graph {$ G = (V, E) $} and a fixed {$k$}. We develop three separate algorithms of this kind with faster running time. We construct an {$ O(|V|^4) $}-time algorithm with {$ f(k) = 3 k + 1 $} by constructing a subroutine for the previous algorithm; we avoid generic algorithms minimizing submodular functions used by Oum and Seymour. Another one is an {$ O(|V|^3) $}-time algorithm with {$ f(k) = 24 k $}, achieved by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hlin{\^e}n{\'y} [2005]. Finally we construct an {$ O(|V|^3) $}-time algorithm with {$ f(k) = 3 k - 1 $} by combining the ideas of the two previously cited papers.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; branch-width; clique-width; matroids; rank-width", } @Article{Brandstadt:2008:SLT, author = "Andreas Brandst{\"a}dt and Van Bang Le and R. Sritharan", title = "Structure and linear-time recognition of 4-leaf powers", journal = j-TALG, volume = "5", number = "1", pages = "11:1--11:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435386", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A graph {$G$} is the {$k$}-{\em leaf power\/} of a tree {$T$} if its vertices are leaves of {$T$} such that two vertices are adjacent in {$G$} if and only if their distance in {$T$} is at most {$k$}. Then {$T$} is a {$k$}-{\em leaf root\/} of {$G$}. This notion was introduced and studied by Nishimura, Ragde, and Thilikos [2002], motivated by the search for underlying phylogenetic trees. Their results imply an {$ O(n^3) $}-time recognition algorithm for 4-leaf powers. Recently, Rautenbach [2006] as well as Dom et al. [2005] characterized 4-leaf powers without true twins in terms of forbidden subgraphs. We give new characterizations for 4-leaf powers and squares of trees by a complete structural analysis. As a consequence, we obtain a conceptually simple linear-time recognition of 4-leaf powers.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Graph powers; leaf powers; phylogenetic trees; squares of trees; trees", } @Article{Chen:2008:MCI, author = "Xin Chen and Lan Liu and Zheng Liu and Tao Jiang", title = "On the minimum common integer partition problem", journal = j-TALG, volume = "5", number = "1", pages = "12:1--12:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435387", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new combinatorial optimization problem in this article, called the {\em minimum common integer partition\/} (MCIP) problem, which was inspired by computational biology applications including ortholog assignment and DNA fingerprint assembly. A {\em partition\/} of a positive integer $n$ is a multiset of positive integers that add up to exactly $n$, and an {\em integer partition\/} of a multiset $s$ of integers is defined as the multiset union of partitions of integers in {$S$}. Given a sequence of multisets {$ s_1, s_2, \ldots, S_k $} of integers, where {$ k \geq 2 $}, we say that a multiset is a {\em common integer partition\/} if it is an integer partition of every multiset {$ S_i, 1 \leq i \leq k $}. The MCIP problem is thus defined as to find a common integer partition of {$ s_1, s_2, \ldots, S_k $} with the minimum cardinality, denoted as MCIP({$ s_1 $}, {$ S_2 $}, \ldots {}, {$ S_k $}). It is easy to see that the MCIP problem is NP-hard, since it generalizes the well-known subset sum problem. We can in fact show that it is APX-hard. We will also present a {$ 5 / 4 $}-approximation algorithm for the MCIP problem when {$ k = 2 $}, and a {$ 3 k (k - 1) / 3 k - 2 $}-approximation algorithm for $ k \geq 3 $.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithm; combinatorial optimization; computational biology; integer partition; NP-hard; Subset sum", } @Article{Azriel:2008:IFS, author = "Dany Azriel and Noam Solomon and Shay Solomon", title = "On an infinite family of solvable {Hanoi} graphs", journal = j-TALG, volume = "5", number = "1", pages = "13:1--13:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435388", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed graph {$G$} with two distinguished vertices, {$s$} and {$D$}, and allowing moves only along arcs of this graph. An optimal solution for such a graph {$G$} is an algorithm that completes the task of moving a tower of any given number of disks from {$s$} to {$d$} in a minimal number of disk moves.\par In this article we present an algorithm which solves the problem for two infinite families of graphs, and prove its optimality. To the best of our knowledge, this is the first optimality proof for an {\em infinite\/} family of graphs.\par Furthermore, we present a unified algorithm that solves the problem for a wider family of graphs and conjecture its optimality.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Optimality proofs; Tower of Hanoi", } @Article{Elmasry:2008:MPQ, author = "Amr Elmasry and Claus Jensen and Jyrki Katajainen", title = "Multipartite priority queues", journal = j-TALG, volume = "5", number = "1", pages = "14:1--14:??", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1435375.1435389", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:04:20 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a framework for reducing the number of element comparisons performed in priority-queue operations. In particular, we give a priority queue which guarantees the worst-case cost of {$ O(1) $} per minimum finding and insertion, and the worst-case cost of {$ O(\log n) $} with at most {$ \log n + O(1) $} element comparisons per deletion, improving the bound of {$ 2 \log n + O(1) $} known for binomial queues. Here, {$n$} denotes the number of elements stored in the data structure prior to the operation in question, and {$ \log n $} equals {$ \log_2 (\max \{ 2, n \}) $}. As an immediate application of the priority queue developed, we obtain a sorting algorithm that is optimally adaptive with respect to the inversion measure of disorder, and that sorts a sequence having $n$ elements and {$I$} inversions with at most {$ n \log (I / n) + O(n) $} element comparisons.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "constant factors; heaps; meticulous analysis; Priority queues", } @Article{Eppstein:2009:TBG, author = "David Eppstein", title = "Testing bipartiteness of geometric intersection graphs", journal = j-TALG, volume = "5", number = "2", pages = "15:1--15:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497291", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show how to test the bipartiteness of an intersection graph of $n$ line segments or simple polygons in the plane, or of an intersection graph of balls in $d$-dimensional Euclidean space, in time {$ O(n \log n) $}. More generally, we find subquadratic algorithms for connectivity and bipartiteness testing of intersection graphs of a broad class of geometric objects. Our algorithms for these problems return either a bipartition of the input or an odd cycle in its intersection graph. We also consider lower bounds for connectivity and {$k$}-colorability problems of geometric intersection graphs. For unit balls in {$d$} dimensions, connectivity testing has equivalent randomized complexity to construction of Euclidean minimum spanning trees, and for line segments in the plane connectivity testing has the same lower bounds as Hopcroft's point-line incidence testing problem; therefore, for these problems, connectivity is unlikely to be solved as efficiently as bipartiteness. For line segments or planar disks, testing {$k$}-colorability of intersection graphs for $k$ > 2 is NP-complete.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Bipartite graph; coin graph; disks; geometric thickness; graph coloring; Hopcroft's problem; intersection graph; line segments; minimum spanning tree", } @Article{Chen:2009:OCF, author = "Ke Chen and Haim Kaplan and Micha Sharir", title = "Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles", journal = j-TALG, volume = "5", number = "2", pages = "16:1--16:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497292", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present randomized algorithms for online conflict-free coloring (CF in short) of points in the plane, with respect to halfplanes, congruent disks, and nearly-equal axis-parallel rectangles. In all three cases, the coloring algorithms use {$ O(\log n) $} colors, with high probability.\par We also present a deterministic algorithm for online CF coloring of points in the plane with respect to nearly-equal axis-parallel rectangles, using {$ O(\log^3 n) $} colors. This is the first efficient (i.e., using {$ \polylog (n) $} colors) deterministic online CF coloring algorithm for this problem.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "coloring; Conflict free coloring; online algorithms", } @Article{Alonso:2009:ACA, author = "Laurent Alonso and Edward M. Reingold", title = "Average-case analysis of some plurality algorithms", journal = j-TALG, volume = "5", number = "2", pages = "17:1--17:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497293", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set of $n$ elements, each of which is colored one of $c$ colors, we must determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We focus on the expected number of color comparisons when the $ c^n $ colorings are equally probable. We analyze an obvious algorithm, showing that its expected performance is {$ c^2 + c - 2 / 2 c n - O(c^2) $}, with variance {$ \Theta (c^2 n) $}. We present and analyze an algorithm for the case {$ c = 3 $} colors whose average complexity on the {$ 3^n $} equally probable inputs is {$ 7083 / 5425 n + O(\sqrt n) = 1.3056 \ldots {} n + O(\sqrt n) $}, substantially better than the expected complexity {$ 5 / 3 n + O(1) = 1.6666 \ldots {} n + O(1) $} of the obvious algorithm. We describe a similar algorithm for {$ c = 4 $} colors whose average complexity on the {$ 4^n $} equally probable inputs is {$ 761311 / 402850 n + O(\log n) = 1.8898 \ldots {} n + O(\log n) $}, substantially better than the expected complexity {$ 9 / 4 n + O(1) = 2.25 n + O(1) $} of the obvious algorithm.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Algorithm analysis; majority problem; plurality problem", } @Article{Bar-Noy:2009:TMR, author = "Amotz Bar-Noy and Sudipto Guha and Yoav Katz and Joseph (Seffi) Naor and Baruch Schieber and Hadas Shachnai", title = "Throughput maximization of real-time scheduling with batching", journal = j-TALG, volume = "5", number = "2", pages = "18:1--18:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497294", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the following scheduling with batching problem that has many applications, for example, in multimedia-on-demand and manufacturing of integrated circuits. The input to the problem consists of $n$ jobs and $k$ parallel machines. Each job is associated with a set of time intervals in which it can be scheduled (given either explicitly or nonexplicitly), a weight, and a family. Each family is associated with a processing time. Jobs that belong to the same family can be batched and executed together on the same machine. The processing time of each batch is the processing time of the family of jobs it contains. The goal is to find a nonpreemptive schedule with batching that maximizes the weight of the scheduled jobs. We give constant factor ($4$ or $ 4 + \epsilon $ ) approximation algorithms for two variants of the problem, depending on the precise representation of the input. When the batch size is unbounded and each job is associated with a time window in which it can be processed, these approximation ratios reduce to $2$ and $ 2 + \epsilon $, respectively. We also give approximation algorithms for two special cases when all release times are the same.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "batching; local ratio technique; Scheduling", } @Article{Rabani:2009:BAT, author = "Yuval Rabani and Gabriel Scalosub", title = "Bicriteria approximation tradeoff for the node-cost budget problem", journal = j-TALG, volume = "5", number = "2", pages = "19:1--19:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497295", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider an optimization problem consisting of an undirected graph, with cost and profit functions defined on all vertices. The goal is to find a connected subset of vertices with maximum total profit, whose total cost does not exceed a given budget. The best result known prior to this work guaranteed a $ (2, O(\log n)) $ bicriteria approximation, that is, the solution's profit is at least a fraction of $ 1 / O(\log n) $ of an optimum solution respecting the budget, while its cost is at most twice the given budget. We improve these results and present a bicriteria tradeoff that, given any $ \epsilon \in (0, 1] $, guarantees a $ (1 + \epsilon, O(1 / \epsilon \log n)) $-approximation.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; bicriteria approximation", } @Article{Li:2009:PTA, author = "Guojun Li and Xiaotie Deng and Ying Xu", title = "A polynomial-time approximation scheme for embedding hypergraph in a cycle", journal = j-TALG, volume = "5", number = "2", pages = "20:1--20:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497296", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of embedding hyperedges of a hypergraph as paths in a cycle such that the maximum congestion, namely the maximum number of paths that use any single edge in a cycle, is minimized.\par The {\em minimum congestion hypergraph embedding in a cycle\/} problem is known to be NP-hard and its graph version, the {\em minimum congestion graph embedding in a cycle}, is solvable in polynomial-time. Furthermore, for the graph problem, a polynomial-time approximation scheme for the weighted version is known. For the hypergraph model, several approximation algorithms with a ratio of two have been previously published. A recent paper reduced the approximation ratio to 1.5. We present a polynomial-time approximation scheme in this article, settling the debate regarding whether the problem is polynomial-time approximable.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Hypergraph embedding; minimum congestion; NP-hard; polynomial-time approximation scheme", } @Article{Even:2009:AAA, author = "Guy Even and Jon Feldman and Guy Kortsarz and Zeev Nutov", title = "A 1.8 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2", journal = j-TALG, volume = "5", number = "2", pages = "21:1--21:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497297", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a 1.8-approximation algorithm for the following NP-hard problem: Given a connected graph {$ G = (V, E) $} and an edge set {$E$} on {$V$} disjoint to {$E$}, find a minimum-size subset of edges {$ F \subseteq E $} such that {$ (V, E \cup f) $} is 2-edge-connected. Our result improves and significantly simplifies the approximation algorithm with ratio {$ 1.875 + \epsilon $} of Nagamochi.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; connectivity; graphs", } @Article{Marko:2009:ADP, author = "Sharon Marko and Dana Ron", title = "Approximating the distance to properties in bounded-degree and general sparse graphs", journal = j-TALG, volume = "5", number = "2", pages = "22:1--22:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497298", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We address the problem of approximating the distance of bounded-degree and general sparse graphs from having some predetermined graph property $p$. That is, we are interested in sublinear algorithms for estimating the fraction of edge modifications (additions or deletions) that must be performed on a graph so that it obtains $p$. This fraction is taken with respect to a given upper bound $m$ on the number of edges. In particular, for graphs with degree bound $d$ over $n$ vertices, $ m = d n $. To perform such an approximation the algorithm may ask for the degree of any vertex of its choice, and may ask for the neighbors of any vertex.\par The problem of estimating the distance to having a property was first explicitly addressed by Parnas et al. [2006]. In the context of graphs this problem was studied by Fischer and Newman [2007] in the dense graphs model. In this model the fraction of edge modifications is taken with respect to $ n^2 $, and the algorithm may ask for the existence of an edge between any pair of vertices of its choice. Fischer and Newman showed that every graph property that has a testing algorithm in this model, with query complexity independent of the size of the graph, also has a distance approximation algorithm with query complexity that is independent of the size of graph.\par In this work we focus on bounded-degree and general sparse graphs, and give algorithms for all properties shown to have efficient testing algorithms by Goldreich and Ron [2002]. Specifically, these properties are $k$-edge connectivity, subgraph freeness (for constant-size subgraphs), being an Eulerian graph, and cycle freeness. A variant of our subgraph-freeness algorithm approximates the size of a minimum vertex cover of a graph in sublinear time. This approximation improves on a recent result of Parnas and Ron [2007].", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distance approximation; graph properties; property testing; Sublinear approximation algorithms", } @Article{Berry:2009:LTA, author = "Vincent Berry and Christophe Paul and Sylvain Guillemot and Fran{\c{c}}ois Nicolas", title = "Linear time 3-approximation for the {MAST} problem", journal = j-TALG, volume = "5", number = "2", pages = "23:1--23:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497299", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set of leaf-labeled trees with identical leaf sets, the well-known Maximum Agreement SubTree (MAST) problem consists in finding a subtree homeomorphically included in all input trees and with the largest number of leaves. MAST and its variant called Maximum Compatible Tree (MCT) are of particular interest in computational biology. This article presents a linear-time approximation algorithm to solve the complement version of MAST, namely identifying the smallest set of leaves to remove from input trees to obtain isomorphic trees. We also present an {$ O(n^2 + k n) $} algorithm to solve the complement version of MCT. For both problems, we thus achieve significantly lower running times than previously known algorithms. Fast running times are especially important in phylogenetics where large collections of trees are routinely produced by resampling procedures, such as the nonparametric bootstrap or Bayesian MCMC methods.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; maximum agreement subtree; maximum compatible subtree; phylogenetic tree", } @Article{Condon:2009:ADA, author = "Anne Condon and Amol Deshpande and Lisa Hellerstein and Ning Wu", title = "Algorithms for distributional and adversarial pipelined filter ordering problems", journal = j-TALG, volume = "5", number = "2", pages = "24:1--24:??", month = mar, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1497290.1497300", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Jul 14 19:05:00 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Pipelined filter ordering is a central problem in database query optimization. The problem is to determine the optimal order in which to apply a given set of commutative filters (predicates) to a set of elements (the tuples of a relation), so as to find, as efficiently as possible, the tuples that satisfy all of the filters. Optimization of pipelined filter ordering has recently received renewed attention in the context of environments such as the Web, continuous high-speed data streams, and sensor networks. Pipelined filter ordering problems are also studied in areas such as fault detection and machine learning under names such as learning with attribute costs, minimum-sum set cover, and satisfying search. We present algorithms for two natural extensions of the classical pipelined filter ordering problem: (1) a {\em distributional-type\/} problem where the filters run in parallel and the goal is to maximize throughput, and (2) an {\em adversarial-type\/} problem where the goal is to minimize the expected value of {\em multiplicative regret}. We present two related algorithms for solving (1), both running in time {$ O(n^2) $}, which improve on the {$ O(n 3 \log n) $} algorithm of Kodialam. We use techniques from our algorithms for (1) to obtain an algorithm for 1.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "flow algorithms; Pipelined filter ordering; query optimization; selection ordering", } @Article{Gabow:2009:FSI, author = "Harold Gabow", title = "Foreword to special issue on {SODA 2007}", journal = j-TALG, volume = "5", number = "3", pages = "25:1--25:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541886", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ruzic:2009:MDS, author = "Milan Ru{\v{z}}i{\'c}", title = "Making deterministic signatures quickly", journal = j-TALG, volume = "5", number = "3", pages = "26:1--26:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541887", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a new technique of universe reduction. Primary applications are the dictionary problem and the predecessor problem. We give several new results on static dictionaries in different computational models: the word RAM, the practical RAM, and the cache-oblivious model. All algorithms and data structures are deterministic and use linear space. Representative results are: a dictionary with a lookup time of {$ O(\log \log n) $} and construction time of {$ O(n) $} on sorted input on a word RAM, and a static predecessor structure for variable- and unbounded length binary strings that in the cache-oblivious model has a query performance of {$ O(| s | / B + \log | s |) $} I/Os, for query argument {$s$}.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Carr:2009:CCN, author = "Robert D. Carr and Goran Konjevod and Greg Little and Venkatesh Natarajan and Ojas Parekh", title = "Compacting cuts: a new linear formulation for minimum cut", journal = j-TALG, volume = "5", number = "3", pages = "27:1--27:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541888", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a graph (V, E), existing compact linear formulations for the minimum cut problem require {$ \Theta (|V| |E|) $} variables and constraints and can be interpreted as a composition of {$ |V| - 1 $} polyhedra for minimum {$s$}--{$t$} cuts in much the same way as early approaches to finding globally minimum cuts relied on {$ |V| - 1 $} calls to a minimum {$s$}--{$t$} cut algorithm. We present the first formulation to beat this bound, one that uses {$ O(|V|^2) $} variables and {$ O(|V|^3) $} constraints. An immediate consequence of our result is a compact linear relaxation with {$ O(|V|^2) $} constraints and {$ O(|V|^3) $} variables for enforcing global connectivity constraints. This relaxation is as strong as standard cut-based relaxations and has applications in solving traveling salesman problems by integer programming as well as finding approximate solutions for survivable network design problems using Jain's iterative rounding method. Another application is a polynomial-time verifiable certificate of size {$n$} for for the NP-complete problem of {$ l_1 $}-embeddability of a rational metric on an {$n$}-set (as opposed to a certificate of size $ n^2 $ known previously).", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Giora:2009:ODV, author = "Yoav Giora and Haim Kaplan", title = "{Optimal} dynamic vertical ray shooting in rectilinear planar subdivisions", journal = j-TALG, volume = "5", number = "3", pages = "28:1--28:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541889", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the dynamic vertical ray shooting problem against horizontal disjoint segments, that is, the task of maintaining a dynamic set {$S$} of {$n$} nonintersecting horizontal line segments in the plane under a query that reports the first segment in {$S$} intersecting a vertical ray from a query point. We develop a linear-size structure that supports queries, insertions, and deletion in {$ O(\log n) $} worst-case time. Our structure works in the comparison model on a random access machine.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2009:STS, author = "David Eppstein", title = "Squarepants in a tree: {Sum} of subtree clustering and hyperbolic pants decomposition", journal = j-TALG, volume = "5", number = "3", pages = "29:1--29:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541890", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We provide efficient constant-factor approximation algorithms for the problems of finding a hierarchical clustering of a point set in any metric space, minimizing the sum of minimimum spanning tree lengths within each cluster, and in the hyperbolic or Euclidean planes, minimizing the sum of cluster perimeters. Our algorithms for the hyperbolic and Euclidean planes can also be used to provide a pants decomposition, that is, a set of disjoint simple closed curves partitioning the plane minus the input points into subsets with exactly three boundary components, with approximately minimum total length. In the Euclidean case, these curves are squares; in the hyperbolic case, they combine our Euclidean square pants decomposition with our tree clustering method for general metric spaces.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2009:MM, author = "Erik D. Demaine and Mohammadtaghi Hajiaghayi and Hamid Mahini and Amin S. Sayedi-Roshkhar and Shayan Oveisgharan and Morteza Zadimoghaddam", title = "Minimizing movement", journal = j-TALG, volume = "5", number = "3", pages = "30:1--30:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541891", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the maximum or average movement. In particular, we consider the goals of achieving connectivity (undirected and directed), achieving connectivity between a given pair of vertices, achieving independence (a dispersion problem), and achieving a perfect matching (with applications to multicasting). This general family of movement problems encompasses an intriguing range of graph and geometric algorithms, with several real-world applications and a surprising range of approximability. In some cases, we obtain tight approximation and inapproximability results using direct techniques (without use of PCP), assuming just that P $ \neq $ NP.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borradaile:2009:ASS, author = "Glencora Borradaile and Philip Klein and Claire Mathieu", title = "An {$ {O}(n \log n) $} approximation scheme for {Steiner} tree in planar graphs", journal = j-TALG, volume = "5", number = "3", pages = "31:1--31:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541892", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Tue Mar 16 09:37:25 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borradaile:2009:LAS, author = "Glencora Borradaile and Philip Klein and Claire Mathieu", title = "An {$ O(n \log n) $} approximation scheme for {Steiner} tree in planar graphs", journal = j-TALG, volume = "5", number = "3", pages = "31:1--31:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541892", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a Polynomial-Time Approximation Scheme (PTAS) for the Steiner tree problem in planar graphs. The running time is {$ O(n \log n) $}.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Charikar:2009:NOA, author = "Moses Charikar and Konstantin Makarychev and Yury Makarychev", title = "Near-optimal algorithms for maximum constraint satisfaction problems", journal = j-TALG, volume = "5", number = "3", pages = "32:1--32:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541893", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we present two approximation algorithms for the maximum constraint satisfaction problem with $k$ variables in each constraint (MAX $k$-CSP). Given a $ (1 - \epsilon) $ satisfiable 2CSP our first algorithm finds an assignment of variables satisfying a {$ 1 - O(\sqrt \epsilon) $} fraction of all constraints. The best previously known result, due to Zwick, was {$ 1 - O(\epsilon^{1 / 3}) $}. The second algorithm finds a {$ c k / 2^k $} approximation for the MAX {$k$}-CSP problem (where {$ c > 0.44 $} is an absolute constant). This result improves the previously best known algorithm by Hast, which had an approximation guarantee of {$ \Omega (k / (2^k \log k)) $}. Both results are optimal assuming the unique games conjecture and are based on rounding natural semidefinite programming relaxations. We also believe that our algorithms and their analysis are simpler than those previously known.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andrews:2009:IFP, author = "Matthew Andrews", title = "Instability of {FIFO} in the permanent sessions model at arbitrarily small network loads", journal = j-TALG, volume = "5", number = "3", pages = "33:1--33:??", month = jul, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1541885.1541894", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:27 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that for any $ r > 0 $, there is a network of First-In-First-Out servers and a fixed set of sessions such that:\par --- The network load is $r$ with respect to the permanent sessions model with bounded arrivals.\par --- The network can be made unstable.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Golubchik:2009:AAD, author = "Leana Golubchik and Sanjeev Khanna and Samir Khuller and Ramakrishna Thurimella and An Zhu", title = "Approximation algorithms for data placement on parallel disks", journal = j-TALG, volume = "5", number = "4", pages = "34:1--34:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597037", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of {$M$} multimedia objects (data objects) that need to be assigned to a storage system consisting of {$N$} disks {$ d_1 $}, {$ d_2 $}, \ldots {}, {$ d_N $}. We are also given sets {$ U_1 $}, {$ U_2 $}, \ldots {}, {$ U_M $} such that {$ U_i $} is the set of clients seeking the {$i$} th data object. Each disk {$ d_j $} is characterized by two parameters, namely, its storage capacity {$ C_j $} which indicates the maximum number of data objects that may be assigned to it, and a load capacity {$ L_j $} which indicates the maximum number of clients that it can serve. The goal is to find a placement of data objects to disks and an assignment of clients to disks so as to maximize the total number of clients served, subject to the capacity constraints of the storage system. We study this data placement problem for two natural classes of storage systems, namely, homogeneous and uniform ratio. We show that an algorithm developed by Shachnai and Tamir [2000a] for data placement achieves the best possible absolute bound regarding the number of clients that can always be satisfied. We also show how to implement the algorithm so that it has a running time of {$ O((N + M) \log (N + M)) $}. In addition, we design a polynomial-time approximation scheme, solving an open problem posed in the same paper.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Guha:2009:SEE, author = "Sudipto Guha and Andrew McGregor and Suresh Venkatasubramanian", title = "Sublinear estimation of entropy and information distances", journal = j-TALG, volume = "5", number = "4", pages = "35:1--35:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597038", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In many data mining and machine learning problems, the data items that need to be clustered or classified are not arbitrary points in a high-dimensional space, but are distributions, that is, points on a high-dimensional simplex. For distributions, natural measures are not l$_p$ distances, but information-theoretic measures such as the Kullback--Leibler and Hellinger divergences. Similarly, quantities such as the entropy of a distribution are more natural than frequency moments. Efficient estimation of these quantities is a key component in algorithms for manipulating distributions. Since the datasets involved are typically massive, these algorithms need to have only sublinear complexity in order to be feasible in practice. We present a range of sublinear-time algorithms in various oracle models in which the algorithm accesses the data via an oracle that supports various queries. In particular, we answer a question posed by Batu et al. on testing whether two distributions are close in an information-theoretic sense given independent samples. We then present optimal algorithms for estimating various information-divergences and entropy with a more powerful oracle called the combined oracle that was also considered by Batu et al. Finally, we consider sublinear-space algorithms for these quantities in the data-stream model. In the course of doing so, we explore the relationship between the aforementioned oracle models and the data-stream model. This continues work initiated by Feigenbaum et al. An important additional component to the study is considering data streams that are ordered randomly rather than just those which are ordered adversarially.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Levin:2009:GMC, author = "Asaf Levin", title = "A generalized minimum cost $k$-clustering", journal = j-TALG, volume = "5", number = "4", pages = "36:1--36:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597039", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problems of set partitioning into $k$ clusters with minimum total cost and minimum of the maximum cost of a cluster. The cost function is given by an oracle, and we assume that it satisfies some natural structural constraints. That is, we assume that the cost function is monotone, the cost of a singleton is zero, and we assume that for all {$ S \cap S' \neq \oslash $} the following holds {$ c(S) + c(S') \geq c(S \cup S') $}. For the problem of minimizing the maximum cost of a cluster we present a {$ (2 k - 1) $}-approximation algorithm for {$ k \geq 3 $}, a 2-approximation algorithm for {$ k = 2 $}, and we also show a lower bound of $k$ on the performance guarantee of any polynomial-time algorithm. For the problem of minimizing the total cost of all the clusters, we present a 2-approximation algorithm for the case where $k$ is a fixed constant, a $ (4 k - 3) $-approximation where $k$ is unbounded, and we show a lower bound of $2$ on the approximation ratio of any polynomial-time algorithm. Our lower bounds do not depend on the common assumption that P $ \neq $ NP.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Farach-Colton:2009:BHO, author = "Martin Farach-Colton and Rohan J. Fernandes and Miguel A. Mosteiro", title = "Bootstrapping a hop-optimal network in the weak sensor model", journal = j-TALG, volume = "5", number = "4", pages = "37:1--37:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597040", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Sensor nodes are very weak computers that get distributed at random on a surface. Once deployed, they must wake up and form a radio network. Sensor network bootstrapping research thus has three parts: One must model the restrictions on sensor nodes; one must prove that the connectivity graph of the sensors has a subgraph that would make a good network; and one must give a distributed protocol for finding such a network subgraph that can be implemented on sensor nodes. Although many particular restrictions on sensor nodes are implicit or explicit in many papers, there remain many inconsistencies and ambiguities from paper to paper. The lack of a clear model means that solutions to the network bootstrapping problem in both the theory and systems literature all violate constraints on sensor nodes. For example, random geometric graph results on sensor networks predict the existence of subgraphs on the connectivity graph with good route-stretch, but these results do not address the degree of such a graph, and sensor networks must have constant degree. Furthermore, proposed protocols for actually finding such graphs require that nodes have too much memory, whereas others assume the existence of a contention-resolution mechanism. We present a formal Weak Sensor model that summarizes the literature on sensor node restrictions, taking the most restrictive choices when possible. We show that sensor connectivity graphs have low-degree subgraphs with good hop-stretch, as required by the Weak Sensor model. Finally, we give a Weak Sensor model-compatible protocol for finding such graphs. Ours is the first network initialization algorithm that is implementable on sensor nodes.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2009:AMI, author = "David Eppstein", title = "All maximal independent sets and dynamic dominance for sparse graphs", journal = j-TALG, volume = "5", number = "4", pages = "38:1--38:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597042", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per set generated; for minor-closed graph families, the time is {$ O(n) $} per set, and for more general sparse graph families we achieve subquadratic time per set. We also describe new data structures for maintaining a dynamic vertex set {$S$} in a sparse or minor-closed graph family, and querying the number of vertices not dominated by {$S$}; for minor-closed graph families the time per update is constant, while it is sublinear for any sparse graph family. We can also maintain a dynamic vertex set in an arbitrary {$m$}-edge graph and test the independence of the maintained set in time {$ O(\sqrt m) $} per update. We use the domination data structures as part of our enumeration algorithms.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Reed:2009:LTA, author = "Bruce Reed and David R. Wood", title = "A linear-time algorithm to find a separator in a graph excluding a minor", journal = j-TALG, volume = "5", number = "4", pages = "39:1--39:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597043", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$G$} be an {$n$}-vertex {$m$}-edge graph with weighted vertices. A pair of vertex sets {$ A, B \subseteq V(G) $} is a {$ 2 / 3 $}-separation of order {$ |A \cap B| $} if {$ A \cup B = V(G) $}, there is no edge between {$A$}--{$B$} and {$B$}--{$A$}, and both {$A$}--{$B$} and {$B$}--{$A$} have weight at most {$ 2 / 3 $} the total weight of {$G$}. Let {$ l \in Z^+ $} be fixed. Alon et al. [1990] presented an algorithm that in {$ O(n^{1 / 2m}) $} time, outputs either a {$ K_l $}-minor of {$G$}, or a separation of {$G$} of order {$ O(n^{1 / 2}) $}. Whether there is a {$ O(n + m) $}-time algorithm for this theorem was left as an open problem. In this article, we obtain a {$ O(n + m) $}-time algorithm at the expense of a {$ O(n^{2 / 3}) $} separator. Moreover, our algorithm exhibits a trade-off between time complexity and the order of the separator. In particular, for any given {$ \epsilon \in [0, 1 / 2] $}, our algorithm outputs either a {$ K_l $}-minor of {$G$}, or a separation of {$G$} with order {$ O(n^{(2 - \epsilon) / 3}) $} in {$ O(n^{1 + \epsilon } + m) $} time. As an application we give a fast approximation algorithm for finding an independent set in a graph with no {$ K_l $}-minor.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ito:2009:EIC, author = "Hiro Ito and Kazuo Iwama", title = "Enumeration of isolated cliques and pseudo-cliques", journal = j-TALG, volume = "5", number = "4", pages = "40:1--40:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597044", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider isolated cliques and isolated dense subgraphs. For a given graph {$G$}, a vertex subset {$S$} of size {$k$} (and also its induced subgraph {$ G(S) $}) is said to be {$c$}-isolated if {$G$} (S) is connected to its outside via less than {$ c k $} edges. The number {$c$} is sometimes called the isolation factor. The subgraph appears more isolated if the isolation factor is smaller. The main result in this work shows that for a fixed constant {$c$}, we can enumerate all $c$-isolated maximal cliques (including a maximum one, if any) in linear time. In more detail, we show that, for a given graph {$G$} of {$n$} vertices and {$m$} edges, and a positive real number {$c$}, all $c$-isolated maximal cliques can be enumerated in time {$ O(c^4 2^{2c} m) $}. From this, we can see that: (1) if {$c$} is a constant, all {$c$}-isolated maximal cliques can be enumerated in linear time, and (2) if {$ c = O(\log n) $}, all {$c$}-isolated maximal cliques can be enumerated in polynomial time. Moreover, we show that these bounds are tight. That is, if {$ f(n) $} is an increasing function not bounded by any constant, then there is a graph of {$n$} vertices and $m$ edges for which the number of $ f(n) $-isolated maximal cliques is superlinear in $ n + m $. Furthermore, if $ f(n) = \omega (\log n) $, there is a graph of $n$ vertices and $m$ edges for which the number of $ f(n) $-isolated maximal cliques is superpolynomial in $ n + m $. We next introduce the idea of pseudo-cliques. A pseudo-clique having an average degree $ \alpha $ and a minimum degree $ \beta $, denoted by {$ {\rm PC}(\alpha, \beta) $}, is a set {$ V' \subseteq V $} such that the subgraph induced by {$ V' $} has an average degree of at least {$ \alpha $} and a minimum degree of at least {$ \beta $}. This article investigates these, and obtains some cases that can be solved in polynomial time and some other cases that have a superpolynomial number of solutions. Especially, we show the following results, where {$k$} is the number of vertices of the isolated pseudo-cliques: (1) For any $ \epsilon > 0 $ there is a graph of $n$ vertices for which the number of $1$-isolated {$ {\rm PC}(k - (\log k)^{1 + \epsilon }, k / (\log k)^{1 + \epsilon }) $} is superpolynomial, and (2) there is a polynomial-time algorithm which enumerates all {$c$}-isolated {$ {\rm PC}(k - \log k, k / \log k) $}, for any constant {$c$}.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Karakostas:2009:BAR, author = "George Karakostas", title = "A better approximation ratio for the vertex cover problem", journal = j-TALG, volume = "5", number = "4", pages = "41:1--41:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597045", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We reduce the approximation factor for the vertex cover to {$ 2 - \Theta (1 / \sqrt {\log n}) $} (instead of the previous {$ 2 - \Theta (\ln \ln n / 2 \ln n) $} obtained by Bar-Yehuda and Even [1985] and Monien and Speckenmeyer [1985]). The improvement of the vanishing factor comes as an application of the recent results of Arora et al. [2004] that improved the approximation factor of the sparsest cut and balanced cut problems. In particular, we use the existence of two big and well-separated sets of nodes in the solution of the semidefinite relaxation for balanced cut, proven by Arora et al. [2004]. We observe that a solution of the semidefinite relaxation for vertex cover, when strengthened with the triangle inequalities, can be transformed into a solution of a balanced cut problem, and therefore the existence of big well-separated sets in the sense of Arora et al. [2004] translates into the existence of a big independent set.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Berend:2009:LAC, author = "Daniel Berend and Vladimir Braverman", title = "A linear algorithm for computing convex hulls for random lines", journal = j-TALG, volume = "5", number = "4", pages = "42:1--42:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597046", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Finding the convex hull of $n$ points in the plane requires {$ O(n \log n) $} time in general. In Devroye and Toussaint [1993] and Golin et al. [2002] the problem of computing the convex hull of the intersection points of {$n$} lines was considered, where the lines are chosen randomly according to two various models. In both models, linear-time algorithms were developed. Here we improve the results of Devroye and Toussaint [1993] by giving a universal algorithm for a wider range of distributions.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kao:2009:RFD, author = "Ming-Yang Kao and Manan Sanghi and Robert Schweller", title = "Randomized fast design of short {DNA} words", journal = j-TALG, volume = "5", number = "4", pages = "43:1--43:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597047", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA self-assembly and DNA computing. Previous work has extended results from coding theory to obtain bounds on code size for new biologically motivated constraints and has applied heuristic local search and genetic algorithm techniques for code design. This article proposes a natural optimization formulation of the DNA code design problem in which the goal is to design $n$ strings that satisfy a given set of constraints while minimizing the length of the strings. For multiple sets of constraints, we provide simple randomized algorithms that run in time polynomial in $n$ and any given constraint parameters, and output strings of length within a constant factor of the optimal with high probability. To the best of our knowledge, this work is the first to consider this type of optimization problem in the context of DNA code design.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fernandez-Baca:2009:PAU, author = "David Fern{\'a}ndez-Baca and Balaji Venkatachalam", title = "Parametric analysis for ungapped {Markov} models of evolution", journal = j-TALG, volume = "5", number = "4", pages = "44:1--44:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597048", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Efficient sensitivity analysis algorithms are presented for two problems arising in the study of Markov models of sequence evolution: ancestral reconstruction in evolutionary trees and local ungapped alignment under log-odds scoring. The algorithms generate complete descriptions of the optimum solutions for all possible values of the evolutionary distance. The running time for the parametric ancestral reconstruction problem under the Kimura 2-parameter model is {$ O(k n + k n^{2 / 3} \log k) $}, where {$n$} is the number of sequences and {$k$} is their length, assuming all edges have the same length. For the parametric gapless alignment problem under the Jukes-Cantor model, the running time is {$ O(m n + m n^{2 / 3} \log m) $}, where {$m$} and {$n$} are the sequence lengths and {$ n \leq m $}.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Scott:2009:PCS, author = "Alexander D. Scott and Gregory B. Sorkin", title = "{Polynomial} constraint satisfaction problems, graph bisection, and the {Ising} partition function", journal = j-TALG, volume = "5", number = "4", pages = "45:1--45:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597049", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials, PCSP has scores that are arbitrary multivariate formal polynomials, or indeed take values in an arbitrary ring. Although PCSP is much more general than CSP, remarkably, all (exact, exponential-time) algorithms we know of for 2-CSP (where each score depends on at most 2 variables) extend to 2-PCSP, at the expense of just a polynomial factor in running time. Specifically, we extend the reduction-based algorithm of Scott and Sorkin [2007]; the specialization of that approach to sparse random instances, where the algorithm runs in polynomial expected time; dynamic-programming algorithms based on tree decompositions; and the split-and-list matrix-multiplication algorithm of Williams [2004]. This gives the first polynomial-space exact algorithm more efficient than exhaustive enumeration for the well-studied problems of finding a maximum bisection of a graph, and calculating the partition function of an Ising model. It also yields the most efficient algorithm known for certain instances of counting and/or weighted Maximum Independent Set. Furthermore, PCSP solves both optimization and counting versions of a wide range of problems, including all CSPs, and thus enables samplers including uniform sampling of optimal solutions and Gibbs sampling of all solutions.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Nguyen:2009:LDL, author = "Phong Q. Nguyen and Damien Stehl{\'e}", title = "Low-dimensional lattice basis reduction revisited", journal = j-TALG, volume = "5", number = "4", pages = "46:1--46:??", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1597036.1597050", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:29 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Lattice reduction is a geometric generalization of the problem of computing greatest common divisors. Most of the interesting algorithmic problems related to lattice reduction are NP-hard as the lattice dimension increases. This article deals with the low-dimensional case. We study a greedy lattice basis reduction algorithm for the Euclidean norm, which is arguably the most natural lattice basis reduction algorithm because it is a straightforward generalization of an old two-dimensional algorithm of Lagrange, usually known as Gauss' algorithm, and which is very similar to Euclid's gcd algorithm. Our results are twofold. From a mathematical point of view, we show that up to dimension four, the output of the greedy algorithm is optimal: The output basis reaches all the successive minima of the lattice. However, as soon as the lattice dimension is strictly higher than four, the output basis may be arbitrarily bad as it may not even reach the first minimum. More importantly, from a computational point of view, we show that up to dimension four, the bit-complexity of the greedy algorithm is quadratic without fast integer arithmetic, just like Euclid's gcd algorithm. This was already proved by Semaev up to dimension three using rather technical means, but it was previously unknown whether or not the algorithm was still polynomial in dimension four. We propose two different analyzes: a global approach based on the geometry of the current basis when the length decrease stalls, and a local approach showing directly that a significant length decrease must occur every {$ O(1) $} consecutive steps. Our analyzes simplify Semaev's analysis in dimensions two and three, and unify the cases of dimensions two to four. Although the global approach is much simpler, we also present the local approach because it gives further information on the behavior of the algorithm.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Finocchi:2009:RD, author = "Irene Finocchi and Fabrizio Grandoni and Giuseppe F. Italiano", title = "Resilient dictionaries", journal = j-TALG, volume = "6", number = "1", pages = "1:1--1:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644016", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We address the problem of designing data structures in the presence of faults that may arbitrarily corrupt memory locations. More precisely, we assume that an adaptive adversary can arbitrarily overwrite the content of up to $ \delta $ memory locations, that corrupted locations cannot be detected, and that only {$ O(1) $} memory locations are safe. In this framework, we call a data structure resilient if it is able to operate correctly (at least) on the set of uncorrupted values. We present a resilient dictionary, implementing search, insert, and delete operations. Our dictionary has {$ O(\log n + \delta) $} expected amortized time per operation, and {$ O(n) $} space complexity, where {$n$} denotes the current number of keys in the dictionary. We also describe a deterministic resilient dictionary, with the same amortized cost per operation over a sequence of at least {$ \delta^\epsilon $} operations, where {$ \epsilon > 0 $} is an arbitrary constant. Finally, we show that any resilient comparison-based dictionary must take {$ \Omega (\log n + \delta) $} expected time per search. Our results are achieved by means of simple, new techniques which might be of independent interest for the design of other resilient algorithms.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2009:ODA, author = "Erik D. Demaine and Shay Mozes and Benjamin Rossman and Oren Weimann", title = "An optimal decomposition algorithm for tree edit distance", journal = j-TALG, volume = "6", number = "1", pages = "2:1--2:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644017", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The edit distance between two ordered rooted trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this article, we present a worst-case {$ O(n^3) $}-time algorithm for the problem when the two trees have size {$n$}, improving the previous best {$ O(n^3 \log n) $}-time algorithm. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems, together with a deeper understanding of the previous algorithms for the problem. We prove the optimality of our algorithm among the family of decomposition strategy algorithms-which also includes the previous fastest algorithms-by tightening the known lower bound of {$ \Omega (n^2 \log^2 n) $} to {$ \Omega (n^3) $}, matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds for decomposition strategy algorithms of {$ \Theta (n m^2 (1 + \log n / m)) $} when the two trees have sizes {$m$} and {$n$} and {$ m < n $}.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bille:2009:IAS, author = "Philip Bille and Rolf Fagerberg and Inge Li G{\o}rtz", title = "Improved approximate string matching and regular expression matching on {Ziv--Lempel} compressed texts", journal = j-TALG, volume = "6", number = "1", pages = "3:1--3:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644018", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv--Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Duch:2009:URK, author = "Amalia Duch and Conrado Mart{\'\i}nez", title = "Updating relaxed {$ {K} $}-d trees", journal = j-TALG, volume = "6", number = "1", pages = "4:1--4:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644019", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this work we present an in-depth study of randomized relaxed $k$--$d$ trees. It covers two fundamental aspects: the randomized algorithms that allow to preserve the random properties of relaxed $k$--$d$ trees and the mathematical analysis of the expected performance of these algorithms. In particular, we describe randomized update algorithms for $k$--$d$ trees based on the split and join algorithms of Duch et al. [1998]. We carry out an analysis of the expected cost of all these algorithms, using analytic combinatorics techniques. We show that the average cost of split and join is of the form {$ \zeta (K) \cdot n^{\phi (K)} + o(n^{\phi (K)}) $}, with {$ 1 \leq \phi (K) < 1.561552813 $}, and we give explicit formul{\ae} for both {$ \zeta (K) $} and {$ \phi (K) $}. These results on the average performance of split and join imply that the expected cost of an insertion or a deletion is {$ \Theta (n^{\phi (K) - 1}) $} when {$ K > 2 $} and {$ \Theta (\log n) $} for {$ K = 2 $}.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Nutov:2009:ACA, author = "Zeev Nutov", title = "Approximating connectivity augmentation problems", journal = j-TALG, volume = "6", number = "1", pages = "5:1--5:19", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644020", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$ G = (V, E) $} be an undirected graph and let {$ S \subseteq V $}. The {$S$}-connectivity {$ \lambda^S_G(u, v) $} of a node pair {$ (u, v) $} in {$G$} is the maximum number of {$ u v $}-paths that no two of them have an edge or a node in {$ S - \{ u, v \} $} in common. The corresponding Connectivity Augmentation (CA) problem is: given a graph {$ G = (V, E) $}, a node subset {$ S \subseteq V $}, and a nonnegative integer requirement function {$ r(u, v) $} on {$ V \times V $}, add a minimum size set F of new edges to {$G$} so that {$ \lambda^S_{G + F}(u, v) \geq r(u, v) $} for all {$ (u, v) \in V \times V $}. Three extensively studied particular cases are: the Edge-CA ({$ S = \oslash $}), the Node-CA ({$ S = V $}), and the Element-CA {$ r(u, v) = 0 $} whenever {$ u \in S $} or {$ v \in S $}. A polynomial-time algorithm for Edge-CA was developed by Frank. In this article we consider the Element-CA and the Node-CA, that are NP-hard even for {$ r(u, v) \in \{ 0, 2 \} $}. The best known ratios for these problems were: 2 for Element-CA and {$ O(r_{\rm max} \cdot \ln n) $} for Node-CA, where {$ r_{\rm max} = \max_{u,_v} \in V r(u, v) $} and {$ n = |V| $}. Our main result is a 7/4-approximation algorithm for the Element-CA, improving the previously best known 2-approximation. For Element-CA with {$ r(u, v) \in \{ 0, 1, 2 \} $} we give a {$ 3 / 2 $}-approximation algorithm. These approximation ratios are based on a new splitting-off theorem, which implies an improved lower bound on the number of edges needed to cover a skew-supermodular set function. For Node-CA we establish the following approximation threshold: Node-CA with {$ r(u, v) \in \{ 0, k \} $} cannot be approximated within {$ O(2^{\log^{1 - \epsilon } n}) $} for any fixed {$ \epsilon > 0 $}, unless NP {$ \subseteq $} DTIME({$ n^{\polylog (n)} $} ).", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demetrescu:2009:TSP, author = "Camil Demetrescu and Irene Finocchi and Andrea Ribichini", title = "Trading off space for passes in graph streaming problems", journal = j-TALG, volume = "6", number = "1", pages = "6:1--6:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644021", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Data stream processing has recently received increasing attention as a computational paradigm for dealing with massive data sets. Surprisingly, no algorithm with both sublinear space and passes is known for natural graph problems in classical read-only streaming. Motivated by technological factors of modern storage systems, some authors have recently started to investigate the computational power of less restrictive models where writing streams is allowed. In this article, we show that the use of intermediate temporary streams is powerful enough to provide effective space-passes tradeoffs for natural graph problems. In particular, for any space restriction of $s$ bits, we show that single-source shortest paths in directed graphs with small positive integer edge weights can be solved in {$ O((n \log^{3 / 2} n) / \sqrt s) $} passes. The result can be generalized to deal with multiple sources within the same bounds. This is the first known streaming algorithm for shortest paths in directed graphs. For undirected connectivity, we devise an {$ O((n \log n) / s) $} passes algorithm. Both problems require {$ \Omega (n / s) $} passes under the restrictions we consider. We also show that the model where intermediate temporary streams are allowed can be strictly more powerful than classical streaming for some problems, while maintaining all of its hardness for others.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pettie:2009:LDS, author = "Seth Pettie", title = "{Low} distortion spanners", journal = j-TALG, volume = "6", number = "1", pages = "7:1--7:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644022", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A spanner of an undirected unweighted graph is a subgraph that approximates the distance metric of the original graph with some specified accuracy. Specifically, we say {$ H \subseteq G $} is an {$f$}-spanner of {$G$} if any two vertices {$ u, v $} at distance {$d$} in {$G$} are at distance at most {$ f(d) $} in {$H$}. There is clearly some trade-off between the sparsity of {$H$} and the distortion function {$f$}, though the nature of the optimal trade-off is still poorly understood. In this article we present a simple, modular framework for constructing sparse spanners that is based on interchangeable components called connection schemes. By assembling connection schemes in different ways we can recreate the additive 2- and 6-spanners of Aingworth et al. [1999] and Baswana et al. [2009], and give spanners whose multiplicative distortion quickly tends toward 1. Our results rival the simplicity of all previous algorithms and provide substantial improvements (up to a doubly exponential reduction in edge density) over the comparable spanners of Elkin and Peleg [2004] and Thorup and Zwick [2006].", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mehlhorn:2009:MCB, author = "Kurt Mehlhorn and Dimitrios Michail", title = "Minimum cycle bases: {Faster} and simpler", journal = j-TALG, volume = "6", number = "1", pages = "8:1--8:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644023", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of computing exact or approximate minimum cycle bases of an undirected (or directed) graph {$G$} with {$m$} edges, {$n$} vertices and nonnegative edge weights. In this problem, a {$ \{ 0, 1 \} ( - 1, 0, 1) $} incidence vector is associated with each cycle and the vector space over {$ F_2 (Q) $} generated by these vectors is the cycle space of {$G$}. A set of cycles is called a cycle basis of {$G$} if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of {$G$}. Cycle bases of low weight are useful in a number of contexts, for example, the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. There exists a set of {$ \Theta (m n) $} cycles which is guaranteed to contain a minimum cycle basis. A minimum basis can be extracted by Gaussian elimination. The resulting algorithm [Horton 1987] was the first polynomial-time algorithm. Faster and more complicated algorithms have been found since then. We present a very simple method for extracting a minimum cycle basis from the candidate set with running time {$ O(m^2 n) $}, which improves the running time for sparse graphs. Furthermore, in the undirected case by using bit-packing we improve the running time also in the case of dense graphs. For undirected graphs we derive an {$ O(m^2 n / \log n + n^2 m) $} algorithm. For directed graphs we get an {$ O(m^3 n) $} deterministic and an {$ O(m^2 n) $} randomized algorithm. Our results improve the running times of both exact and approximate algorithms. Finally, we derive a smaller candidate set with size in {$ \Omega (m) \cap O(m n) $}.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gaspers:2009:ETA, author = "Serge Gaspers and Dieter Kratsch and Mathieu Liedloff and Ioan Todinca", title = "Exponential time algorithms for the minimum dominating set problem on some graph classes", journal = j-TALG, volume = "6", number = "1", pages = "9:1--9:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644024", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The minimum dominating set problem remains NP-hard when restricted to any of the following graph classes: $c$-dense graphs, chordal graphs, 4-chordal graphs, weakly chordal graphs, and circle graphs. Developing and using a general approach, for each of these graph classes we present an exponential time algorithm solving the minimum dominating set problem faster than the best known algorithm for general graphs. Our algorithms have the following running time: {$ O(1.4124^n) $} for chordal graphs, {$ O(1.4776^n) $} for weakly chordal graphs, {$ O(1.4845^n) $} for 4-chordal graphs, {$ O(1.4887^n) $} for circle graphs, and {$ O(1.2273^{(1 + \sqrt {1 - 2 c}) n}) $} for {$c$}-dense graphs.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2009:OTE, author = "Ho-Leung Chan and Joseph Wun-Tat Chan and Tak-Wah Lam and Lap-Kei Lee and Kin-Sum Mak and Prudence W. H. Wong", title = "Optimizing throughput and energy in online deadline scheduling", journal = j-TALG, volume = "6", number = "1", pages = "10:1--10:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644025", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article extends the study of online algorithms for energy-efficient deadline scheduling to the overloaded setting. Specifically, we consider a processor that can vary its speed between $0$ and a maximum speed {$T$} to minimize its energy usage (the rate is believed to be a cubic function of the speed). As the speed is upper bounded, the processor may be overloaded with jobs and no scheduling algorithms can guarantee to meet the deadlines of all jobs. An optimal schedule is expected to maximize the throughput, and furthermore, its energy usage should be the smallest among all schedules that achieve the maximum throughput. In designing a scheduling algorithm, one has to face the dilemma of selecting more jobs and being conservative in energy usage. If we ignore energy usage, the best possible online algorithm is 4-competitive on throughput [Koren and Shasha 1995]. On the other hand, existing work on energy-efficient scheduling focuses on a setting where the processor speed is unbounded and the concern is on minimizing the energy to complete all jobs; {$ O(1) $}-competitive online algorithms with respect to energy usage have been known [Yao et al. 1995; Bansal et al. 2007a; Li et al. 2006]. This article presents the first online algorithm for the more realistic setting where processor speed is bounded and the system may be overloaded; the algorithm is {$ O(1) $}-competitive on both throughput and energy usage. If the maximum speed of the online scheduler is relaxed slightly to {$ (1 + \epsilon) T $} for some {$ \epsilon > 0 $}, we can improve the competitive ratio on throughput to arbitrarily close to one, while maintaining {$ O(1) $}-competitiveness on energy usage.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alon:2009:ACM, author = "Noga Alon and Yossi Azar and Shai Gutner", title = "Admission control to minimize rejections and online set cover with repetitions", journal = j-TALG, volume = "6", number = "1", pages = "11:1--11:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644026", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the admission control problem in general networks. Communication requests arrive over time, and the online algorithm accepts or rejects each request while maintaining the capacity limitations of the network. The admission control problem has been usually analyzed as a benefit problem, where the goal is to devise an online algorithm that accepts the maximum number of requests possible. The problem with this objective function is that even algorithms with optimal competitive ratios may reject almost all of the requests, when it would have been possible to reject only a few. This could be inappropriate for settings in which rejections are intended to be rare events. In this article, we consider preemptive online algorithms whose goal is to minimize the number of rejected requests. Each request arrives together with the path it should be routed on. We show an {$ O(\log^2 (m c)) $}-competitive randomized algorithm for the weighted case, where {$m$} is the number of edges in the graph and {$c$} is the maximum edge capacity. For the unweighted case, we give an {$ O(\log m \log c) $}-competitive randomized algorithm. This settles an open question of Blum et al. [2001]. We note that allowing preemption and handling requests with given paths are essential for avoiding trivial lower bounds. The admission control problem is a generalization of the online set cover with repetitions problem, whose input is a family of {$m$} subsets of a ground set of {$n$} elements. Elements of the ground set are given to the online algorithm one by one, possibly requesting each element a multiple number of times. (If each element arrives at most once, this corresponds to the online set cover problem.) The algorithm must cover each element by different subsets, according to the number of times it has been requested. We give an {$ O(\log m \log n) $}-competitive randomized algorithm for the online set cover with repetitions problem. This matches a recent lower bound of {$ \Omega (\log m \log n) $} given by Korman [2005] (based on Feige [1998]) for the competitive ratio of any randomized polynomial time algorithm, under the BPP /= NP assumption. Given any constant {$ \epsilon > 0 $}, an {$ O(\log m \log n) $}-competitive deterministic bicriteria algorithm is shown that covers each element by at least {$ (1 - \epsilon) k $} sets, where {$k$} is the number of times the element is covered by the optimal solution.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hay:2009:JRM, author = "David Hay and Gabriel Scalosub", title = "Jitter regulation for multiple streams", journal = j-TALG, volume = "6", number = "1", pages = "12:1--12:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644027", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For widely used interactive communication, it is essential that traffic is kept as smooth as possible; the smoothness of the traffic is typically captured by its delay jitter, that is, the difference between the maximal and minimal end-to-end delays. The task of minimizing the jitter is done by jitter regulators that use a limited-size buffer in order to shape the traffic. In many real-life situations regulators must handle multiple streams simultaneously and provide low jitter on each of them separately. Moreover, communication links have limited capacity, and these may pose further restrictions on the choices made by the regulator. This article investigates the problem of minimizing jitter in such an environment, using a fixed-size buffer. We show that the offline version of the problem can be solved in polynomial time, by introducing an efficient offline algorithm that finds a release schedule with optimal jitter. When regulating {$M$} streams in the online setting, we take a competitive analysis point of view and note that, in the upcapacitated case, previous results in Mansour and Patt-Shamir [2001] can be extended to an online algorithm that uses a buffer of size {$ 2 \cdot M \cdot B $} and obtains the optimal jitter possible with a buffer of size {$B$} (and an offline algorithm). The question arises whether such a resource augmentation is essential. We answer this question in the affirmative, by proving a lower bound that is tight up to a factor of 2, thus showing that jitter regulation does not scale well as the number of streams increases unless the buffer is sized-up proportionally.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Becchetti:2009:LCA, author = "Luca Becchetti and Alberto Marchetti-Spaccamela and Andrea Vitaletti and Peter Korteweg and Martin Skutella and Leen Stougie", title = "Latency-constrained aggregation in sensor networks", journal = j-TALG, volume = "6", number = "1", pages = "13:1--13:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644028", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A sensor network consists of sensing devices which may exchange data through wireless communication; sensor networks are highly energy constrained since they are usually battery operated. Data aggregation is a possible way to save energy consumption: nodes may delay data in order to aggregate them into a single packet before forwarding them towards some central node (sink). However, many applications impose constraints on the maximum delay of data; this translates into latency constraints for data arriving at the sink. We study the problem of data aggregation to minimize maximum energy consumption under latency constraints on sensed data delivery, and we assume unique communication paths that form an intree rooted at the sink. We prove that the offline problem is strongly NP-hard and we design a 2-approximation algorithm. The latter uses a novel rounding technique. Almost all real-life sensor networks are managed online by simple distributed algorithms in the nodes. In this context we consider both the case in which sensor nodes are synchronized or not. We assess the performance of the algorithm by competitive analysis. We also provide lower bounds for the models we consider, in some cases showing optimality of the algorithms we propose. Most of our results also hold when minimizing the total energy consumption of all nodes.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cohen:2009:TDM, author = "Rami Cohen and Dror Rawitz and Danny Raz", title = "Time-dependent multi-scheduling of multicast", journal = j-TALG, volume = "6", number = "1", pages = "14:1--14:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644029", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Many network applications that need to distribute content and data to a large number of clients use a hybrid scheme in which one (or more) multicast channel is used in parallel to a unicast dissemination. This way the application can distribute data using one of its available multicast channels or by sending one or more unicast transmissions. In such a model the utilization of the multicast channels is critical for the overall performance of the system. We study the scheduling algorithm of the sender in such a model. We describe this scheduling problem as an optimization problem where the objective is to maximize the utilization of the multicast channel. Our model captures the fact that it may be beneficial to multicast an object more than once (e.g., page update). Thus, the benefit depends, among other things, on the last time the object was sent, which makes the problem much more complex than previous related scheduling problems. We show that our problem is NP-hard. Then, using the local ratio technique we obtain a 4-approximation algorithm for the case where the objects are of fixed size and a 10-approximation algorithm for the general case. We also consider a special case which may be of practical interest, and prove that a simple greedy algorithm is a 3-approximation algorithm in this case.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gamzu:2009:IOA, author = "Iftah Gamzu and Danny Segev", title = "Improved online algorithms for the sorting buffer problem on line metrics", journal = j-TALG, volume = "6", number = "1", pages = "15:1--15:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644030", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An instance of the sorting buffer problem consists of a metric space and a server, equipped with a finite-capacity buffer capable of holding a limited number of requests. An additional ingredient of the input is an online sequence of requests, each of which is characterized by a destination in the given metric space; whenever a request arrives, it must be stored in the sorting buffer. At any point in time, a currently pending request can be served by drawing it out of the buffer and moving the server to its corresponding destination. The objective is to serve all input requests in a way that minimizes the total distance traveled by the server. In this article, we focus our attention on instances of the problem in which the underlying metric is either an evenly-spaced line metric or a continuous line metric. Our main findings can be briefly summarized as follows. (1) We present a deterministic {$ O(\log n) $}-competitive algorithm for {$n$}-point evenly-spaced line metrics. This result improves on a randomized {$ O(\log^2 n) $}-competitive algorithm due to Khandekar and Pandit [2006b]. It also refutes their conjecture, stating that a deterministic strategy is unlikely to obtain a nontrivial competitive ratio. (2) We devise a deterministic {$ O(\log N \log \log N) $}-competitive algorithm for continuous line metrics, where {$N$} denotes the length of the input sequence. In this context, we introduce a novel discretization technique of independent interest. (3) We establish the first nontrivial lower bound for the evenly-spaced case, by proving that the competitive ratio of any deterministic algorithm is at least {$ 2 + \sqrt 3 / \sqrt 3 \approx 2.154 $}. This result settles, to some extent, an open question due to Khandekar and Pandit [2006b], who posed the task of attaining lower bounds on the achievable competitive ratio as a foundational objective for future research.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andreev:2009:SSL, author = "Konstantin Andreev and Charles Garrod and Daniel Golovin and Bruce Maggs and Adam Meyerson", title = "Simultaneous source location", journal = j-TALG, volume = "6", number = "1", pages = "16:1--16:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644031", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of simultaneous source location: selecting locations for sources in a capacitated graph such that a given set of demands can be satisfied simultaneously, with the goal of minimizing the number of locations chosen. For general directed and undirected graphs we give an {$ O(\log D) $}-approximation algorithm, where {$D$} is the sum of demands, and prove matching {$ \Omega (\log D) $} hardness results assuming P {$ \neq $} NP. For undirected trees, we give an exact algorithm and show how this can be combined with a result of R{\"a}cke to give a solution that exceeds edge capacities by at most {$ O(\log^2 n \log \log n) $}, where {$n$} is the number of nodes. For undirected graphs of bounded treewidth we show that the problem is still NP-hard, but we are able to give a PTAS with at most {$ (1 + \epsilon) $} violation of the capacities for arbitrarily small {$ \epsilon $}, or a $ (k + 1) $ approximation with exact capacities, where $k$ is the treewidth.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bein:2009:KYQ, author = "Wolfgang Bein and Mordecai J. Golin and Lawrence L. Larmore and Yan Zhang", title = "The {Knuth--Yao} quadrangle-inequality speedup is a consequence of total monotonicity", journal = j-TALG, volume = "6", number = "1", pages = "17:1--17:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644032", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "There exist several general techniques in the literature for speeding up naive implementations of dynamic programming. Two of the best known are the Knuth--Yao quadrangle inequality speedup and the SMAWK algorithm for finding the row-minima of totally monotone matrices. Although both of these techniques use a quadrangle inequality and seem similar, they are actually quite different and have been used differently in the literature. In this article we show that the Knuth--Yao technique is actually a direct consequence of total monotonicity. As well as providing new derivations of the Knuth--Yao result, this also permits to solve the Knuth--Yao problem directly using the SMAWK algorithm. Another consequence of this approach is a method for solving online versions of problems with the Knuth--Yao property. The online algorithms given here are asymptotically as fast as the best previously known static ones. For example, the Knuth--Yao technique speeds up the standard dynamic program for finding the optimal binary search tree of $n$ elements from {$ \Theta (n^3) $} down to {$ O(n^2) $}, and the results in this article allow construction of an optimal binary search tree in an online fashion (adding a node to the left or the right of the current nodes at each step) in {$ O(n) $} time per step.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hassin:2009:AMQ, author = "Refael Hassin and Asaf Levin and Maxim Sviridenko", title = "Approximating the minimum quadratic assignment problems", journal = j-TALG, volume = "6", number = "1", pages = "18:1--18:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644033", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the well-known minimum quadratic assignment problem. In this problem we are given two $ n \times n $ nonnegative symmetric matrices {$ A = (a_{ij}) $} and {$ B = (b_{ij}) $}. The objective is to compute a permutation {$ \pi $} of {$ V = \{ 1, \ldots {}, n \} $} so that {$ \Sigma i, j \in V_{i \neq j} a_{\pi (i), \pi (j)} b_{i, j} $} is minimized. We assume that {$A$} is a {$ 0 / 1 $} incidence matrix of a graph, and that {$B$} satisfies the triangle inequality. We analyze the approximability of this class of problems by providing polynomial bounded approximations for some special cases, and inapproximability results for other cases.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alagic:2009:QAS, author = "Gorjan Alagic and Cristopher Moore and Alexander Russell", title = "Quantum algorithms for {Simon}'s problem over nonabelian groups", journal = j-TALG, volume = "6", number = "1", pages = "19:1--19:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644034", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Daniel Simon's 1994 discovery of an efficient quantum algorithm for finding ``hidden shifts'' of Z$_2^n$ provided the first algebraic problem for which quantum computers are exponentially faster than their classical counterparts. In this article, we study the generalization of Simon's problem to arbitrary groups. Fixing a finite group {$G$}, this is the problem of recovering an involution {$ m = (m_1, \ldots {}, m_n) \in G^n $} from an oracle {$f$} with the property that {$ f(x \cdot y) = f(x) \leq y \in \{ 1, m \} $}. In the current parlance, this is the hidden subgroup problem (HSP) over groups of the form {$ G^n $}, where {$G$} is a nonabelian group of constant size, and where the hidden subgroup is either trivial or has order two. Although groups of the form {$ G^n $} have a simple product structure, they share important representation--theoretic properties with the symmetric groups {$ S_n $}, where a solution to the HSP would yield a quantum algorithm for Graph Isomorphism. In particular, solving their HSP with the so-called ``standard method'' requires highly entangled measurements on the tensor product of many coset states. In this article, we provide quantum algorithms with time complexity {2$^{o(\sqrt n)}$} that recover hidden involutions {$ m = (m_1, \ldots {}, m_n) \in G^n $} where, as in Simon's problem, each {$ m_i $} is either the identity or the conjugate of a known element {$m$} which satisfies {$ \kappa (m) = - \kappa (1) $} for some {$ \kappa \in G $}. Our approach combines the general idea behind Kuperberg's sieve for dihedral groups with the ``missing harmonic'' approach of Moore and Russell. These are the first nontrivial HSP algorithms for group families that require highly entangled multiregister Fourier sampling.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Babai:2009:CRC, author = "L{\'a}szl{\'o} Babai and Pedro F. Felzenszwalb", title = "Computing rank-convolutions with a mask", journal = j-TALG, volume = "6", number = "1", pages = "20:1--20:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644035", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Rank-convolutions have important applications in a variety of areas such as signal processing and computer vision. We define a mask as a function taking only values zero and infinity. Rank-convolutions with masks are of special interest to image processing. We show how to compute the rank-$k$ convolution of a function over an interval of length $n$ with an arbitrary mask of length $m$ in {$ O(n \sqrt m \log m) $} time. The result generalizes to the {$d$}-dimensional case. Previously no algorithm performing significantly better than the brute-force {$ O(n m) $} bound was known. Our algorithm seems to perform well in practice. We describe an implementation, illustrating its application to a problem in image processing. Already on relatively small images, our experiments show a significant speedup compared to brute force.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bruss:2009:IAI, author = "F. Thomas Bruss and Guy Louchard and Mark Daniel Ward", title = "Inverse auctions: {Injecting} unique minima into random sets", journal = j-TALG, volume = "6", number = "1", pages = "21:1--21:??", month = dec, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1644015.1644036", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:31 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider auctions in which the winning bid is the smallest bid that is unique. Only the upper-price limit is given. Neither the number of participants nor the distribution of the offers are known, so that the problem of placing a bid to win with maximum probability looks, a priori, ill-posed. Indeed, the essence of the problem is to inject a (final) minimum into a random subset (of unique offers) of a larger random set. We will see, however, that here no more than two external (and almost compelling) arguments make the problem meaningful. By appropriately modeling the relationship between the number of participants and the distribution of the bids, we can then maximize our chances of winning the auction and propose a computable algorithm for placing our bid.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Albers:2010:EN, author = "Susanne Albers", title = "Editorial {Note}", journal = j-TALG, volume = "6", number = "2", pages = "22:1--22:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721838", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mathieu:2010:FSI, author = "Claire Mathieu", title = "Foreword to special issue {SODA} 2009", journal = j-TALG, volume = "6", number = "2", pages = "23:1--23:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721839", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cabello:2010:FSC, author = "Sergio Cabello", title = "Finding shortest contractible and shortest separating cycles in embedded graphs", journal = j-TALG, volume = "6", number = "2", pages = "24:1--24:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721840", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a polynomial-time algorithm to find a shortest contractible cycle (i.e., a closed walk without repeated vertices) in a graph embedded in a surface. This answers a question posed by Hutchinson. In contrast, we show that finding a shortest contractible cycle through a given vertex is NP-hard. We also show that finding a shortest separating cycle in an embedded graph is NP-hard. This answers a question posed by Mohar and Thomassen.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "3-path condition; forbidden pairs; graphs on surfaces; topological graph theory", } @Article{Aspnes:2010:ASM, author = "James Aspnes and Keren Censor", title = "Approximate shared-memory counting despite a strong adversary", journal = j-TALG, volume = "6", number = "2", pages = "25:1--25:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721841", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A new randomized asynchronous shared-memory data structure is given for implementing an approximate counter that can be incremented once by each of $n$ processes in a model that allows up to $ n - 1 $ crash failures. For any fixed $ \epsilon $, the counter achieves a relative error of $ \delta $ with high probability, at the cost of {$ O(((1 / \delta) \log n)^{O(1 / \epsilon)}) $} register operations per increment and {$ O(n^{4 / 5 + \epsilon }((1 / \delta) \log n)^{O(1 / \epsilon)}) $} register operations per read. The counter combines randomized sampling for estimating large values with an expander for estimating small values. This is the first counter implementation that is sublinear the number of processes and works despite a strong adversary scheduler that can observe internal states of processes.\par An application of the improved counter is an improved protocol for solving randomized shared-memory consensus, which reduces the best previously known individual work complexity from {$ O(n \log n) $} to an optimal {$ O(n) $}, resolving one of the last remaining open problems concerning consensus in this model.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximate counting; consensus; Distributed computing; expanders; martingales", } @Article{Chan:2010:CBT, author = "Timothy M. Chan", title = "Comparison-based time-space lower bounds for selection", journal = j-TALG, volume = "6", number = "2", pages = "26:1--26:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721842", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We establish the first nontrivial lower bounds on time-space trade-offs for the selection problem. We prove that any comparison-based randomized algorithm for finding the median requires {$ \Omega (n \log \log_S n) $} expected time in the RAM model (or more generally in the comparison branching program model), if we have {$S$} bits of extra space besides the read-only input array. This bound is tight for all {$ S > \log n $}, and remains true even if the array is given in a random order. Our result thus answers a 16-year-old question of Munro and Raman [1996], and also complements recent lower bounds that are restricted to sequential access, as in the multipass streaming model [Chakrabarti et al. 2008b].\par We also prove that any comparison-based, deterministic, multipass streaming algorithm for finding the median requires {$ \Omega (n \log^*(n / s) + n \log_s n) $} worst-case time (in scanning plus comparisons), if we have {$s$} cells of space. This bound is also tight for all {$ s > \log^2 n $}. We get deterministic lower bounds for I/O-efficient algorithms as well.\par The proofs in this article are self-contained and do not rely on communication complexity techniques.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Adversary arguments; lower bounds; median finding; RAM; randomized algorithms; streaming algorithms; time--space trade-offs", } @Article{Goel:2010:PMU, author = "Ashish Goel and Michael Kapralov and Sanjeev Khanna", title = "Perfect matchings via uniform sampling in regular bipartite graphs", journal = j-TALG, volume = "6", number = "2", pages = "27:1--27:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721843", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first nontrivial algorithm, with running time {$ O(m n) $}, dates back to K{\"o}nig's work in 1916 (here {$ m = n d $} is the number of edges in the graph, {$ 2^n $} is the number of vertices, and {$d$} is the degree of each node). The currently most efficient algorithm takes time {$ O(m) $}, and is due to Cole et al. [2001]. We improve this running time to {$ O(\min \{ m, n^{2.5} \ln n / d \}) $}; this minimum can never be larger than {$ O(n^{1.75} \sqrt {\ln n}) $}. We obtain this improvement by proving a uniform sampling theorem: if we sample each edge in a {$d$}-regular bipartite graph independently with a probability {$ p = O(n \ln n / d^2) $} then the resulting graph has a perfect matching with high probability. The proof involves a decomposition of the graph into pieces which are guaranteed to have many perfect matchings but do not have any small cuts. We then establish a correspondence between potential witnesses to nonexistence of a matching (after sampling) in any piece and cuts of comparable size in that same piece. Karger's sampling theorem [1994a, 1994b] for preserving cuts in a graph can now be adapted to prove our uniform sampling theorem for preserving perfect matchings. Using the {$ O(m \sqrt n) $} algorithm (due to Hopcroft and Karp [1973]) for finding maximum matchings in bipartite graphs on the sampled graph then yields the stated running time. We also provide an infinite family of instances to show that our uniform sampling result is tight up to polylogarithmic factors (in fact, up to {$ l n^2 n $} ).", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Perfect matching; regular bipartite graphs", } @Article{Aminof:2010:RAO, author = "Benjamin Aminof and Orna Kupferman and Robby Lampert", title = "Reasoning about online algorithms with weighted automata", journal = j-TALG, volume = "6", number = "2", pages = "28:1--28:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721844", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe an automata-theoretic approach for the competitive analysis of {\em online algorithms}. Our approach is based on {\em weighted automata}, which assign to each input word a cost in {$ R^{\geq 0} $}. By relating the ``unbounded look ahead'' of optimal offline algorithms with nondeterminism, and relating the ``no look ahead'' of online algorithms with determinism, we are able to solve problems about the competitive ratio of online algorithms, and the memory they require, by reducing them to questions about {\em determinization\/} and {\em approximated determinization\/} of weighted automata.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Formal verification; online algorithms; weighted automata", } @Article{Marx:2010:AFH, author = "D{\'a}niel Marx", title = "Approximating fractional hypertree width", journal = j-TALG, volume = "6", number = "2", pages = "29:1--29:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721845", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Fractional hypertree width is a hypergraph measure similar to tree width and hypertree width. Its algorithmic importance comes from the fact that, as shown in previous work, Constraint Satisfaction Problems (CSP) and various problems in database theory are polynomial-time solvable if the input contains a bounded-width fractional hypertree decomposition of the hypergraph of the constraints. In this article, we show that for every fixed $ w \geq 1 $, there is a polynomial-time algorithm that, given a hypergraph {$H$} with fractional hypertree width at most {$w$}, computes a fractional hypertree decomposition of width {$ O(w^3) $} for {$H$}. This means that polynomial-time algorithms relying on bounded-width fractional hypertree decompositions no longer need to be given a decomposition explicitly in the input, since an appropriate decomposition can be computed in polynomial time. Therefore, if {$H$} is a class of hypergraphs with bounded fractional hypertree width, then a CSP restricted to instances whose structure is in {$H$} is polynomial-time solvable. This makes bounded fractional hypertree width the most general known hypergraph property that makes CSP, Boolean conjunctive queries, and conjunctive query containment polynomial-time solvable.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "constraint satisfaction; fractional hypertree width; Treewidth", } @Article{Klein:2010:SPD, author = "Philip N. Klein and Shay Mozes and Oren Weimann", title = "Shortest paths in directed planar graphs with negative lengths: a linear-space {$ O(n \log^2 n) $}-time algorithm", journal = j-TALG, volume = "6", number = "2", pages = "30:1--30:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721846", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give an {$ O(n \log^2 n) $}-time, linear-space algorithm that, given a directed planar graph with positive and negative arc-lengths, and given a node {$s$}, finds the distances from {$s$} to all nodes.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Monge; Planar graphs; replacement paths; shortest paths", } @Article{Panagiotou:2010:MBS, author = "Konstantinos Panagiotou and Angelika Steger", title = "Maximal biconnected subgraphs of random planar graphs", journal = j-TALG, volume = "6", number = "2", pages = "31:1--31:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721847", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$C$} be a class of labeled connected graphs, and let {$ C_n $} be a graph drawn uniformly at random from graphs in {$C$} that contain exactly {$n$} vertices. Denote by {$ b(\ell; C_n) $} the number of blocks (i.e., maximal biconnected subgraphs) of {$ C_n $} that contain exactly {$ \ell $} vertices, and let {$ l b(C_n) $} be the number of vertices in a largest block of {$ C_n $}. We show that under certain general assumptions on {$C$}, {$ C_n $} belongs with high probability to one of the following categories:\par (1) {$ l b(C_n) \sim c n $}, for some explicitly given {$ c = c(C) $}, and the second largest block is of order {$ n^\alpha $}, where {$ 1 > \alpha = \alpha (C) $}, or\par (2) {$ l b(C_n) = O(\log n) $}, that is, all blocks contain at most logarithmically many vertices.\par Moreover, in both cases we show that the quantity {$ b(\ell; C_n) $} is concentrated for all {$ \ell $} and we determine its expected value. As a corollary we obtain that the class of planar graphs belongs to category {$1$}. In contrast to that, outerplanar and series-parallel graphs belong to category {$1$}.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Graphs with constraints; planar graphs; random structures", } @Article{Thomasse:2010:KFV, author = "St{\'e}phan Thomass{\'e}", title = "A $ 4 k^2 $ kernel for feedback vertex set", journal = j-TALG, volume = "6", number = "2", pages = "32:1--32:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721848", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:49:22 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We prove that given an undirected graph {$G$} on {$n$} vertices and an integer {$k$}, one can compute, in polynomial time in {$n$}, a graph {$ G \prime $} with at most {$ 4 k^2 $} vertices and an integer {$ k \prime $} such that {$G$} has a feedback vertex set of size at most {$ k \iff G \prime $} has a feedback vertex set of size at most {$ k \prime $}. This result improves a previous {$ O(k^{11}) $} kernel of Burrage et al., and a more recent cubic kernel of Bodlaender. This problem was communicated by Fellows.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "feedback vertex set; fixed parameter tractability; Kernelization; matching", } @Article{Thomasse:2010:KKF, author = "St{\'e}phan Thomass{\'e}", title = "A $ 4 k^2 $ kernel for feedback vertex set", journal = j-TALG, volume = "6", number = "2", pages = "32:1--32:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721848", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We prove that given an undirected graph {$G$} on {$n$} vertices and an integer {$k$}, one can compute, in polynomial time in {$n$}, a graph {$ G' $} with at most {$ 4 k^2 $} vertices and an integer {$ k' $} such that {$G$} has a feedback vertex set of size at most {$k$} iff {$ G' $} has a feedback vertex set of size at most {$ k' $}. This result improves a previous {$ O(k^{11}) $} kernel of Burrage et al., and a more recent cubic kernel of Bodlaender. This problem was communicated by Fellows.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Madani:2010:DDM, author = "Omid Madani and Mikkel Thorup and Uri Zwick", title = "Discounted deterministic {Markov} decision processes and discounted all-pairs shortest paths", journal = j-TALG, volume = "6", number = "2", pages = "33:1--33:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721849", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present algorithms for finding optimal strategies for discounted, infinite-horizon, Determinsitc Markov Decision Processes (DMDPs). Our fastest algorithm has a worst-case running time of {$ O(m n) $}, improving the recent bound of {$ O(m n^2) $} obtained by Andersson and Vorbyov [2006]. We also present a randomized {$ O(m^{1 / 2} n^2) $}-time algorithm for finding Discounted All-Pairs Shortest Paths (DAPSP), improving an {$ O(m n^2) $}-time algorithm that can be obtained using ideas of Papadimitriou and Tsitsiklis [1987].", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Markov decision processes; minimum mean weight cycles; shortest paths", } @Article{Shalita:2010:EAG, author = "Alon Shalita and Uri Zwick", title = "Efficient algorithms for the 2-gathering problem", journal = j-TALG, volume = "6", number = "2", pages = "34:1--34:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721850", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Pebbles are placed on some vertices of a directed graph. Is it possible to move each pebble along at most one edge of the graph so that in the final configuration no pebble is left on its own? We give an {$ O(m n) $}-time algorithm for solving this problem, which we call the {\em 2-gathering\/} problem, where {$n$} is the number of vertices and {$m$} is the number of edges of the graph. If such a 2-gathering is not possible, the algorithm finds a solution that minimizes the number of solitary pebbles. The 2-gathering problem forms a nontrivial generalization of the nonbipartite matching problem and it is solved by extending the augmenting paths technique used to solve matching problems.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "2-gatherings; augmenting paths; nonbipartite matchings", } @Article{Bansal:2010:DPI, author = "Nikhil Bansal and Ning Chen and Neva Cherniavsky and Atri Rurda and Baruch Schieber and Maxim Sviridenko", title = "Dynamic pricing for impatient bidders", journal = j-TALG, volume = "6", number = "2", pages = "35:1--35:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721851", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the following problem related to pricing over time. Assume there is a collection of bidders, each of whom is interested in buying a copy of an item of which there is an unlimited supply. Every bidder is associated with a time interval over which the bidder will consider buying a copy of the item, and a maximum value the bidder is willing to pay for the item. On every time unit, the seller sets a price for the item. The seller's goal is to set the prices so as to maximize revenue from the sale of copies of items over the time period.\par In the first model considered, we assume that all bidders are {\em impatient}, that is, bidders buy the item at the first time unit within their bid interval that they can afford the price. To the best of our knowledge, this is the first work that considers this model. In the offline setting, we assume that the seller knows the bids of all the bidders in advance. In the online setting we assume that at each time unit the seller only knows the values of the bids that have arrived before or at that time unit. We give a polynomial time offline algorithm and prove upper and lower bounds on the competitiveness of deterministic and randomized online algorithms, compared with the optimal offline solution. The gap between the upper and lower bounds is quadratic.\par We also consider the {\em envy-free\/} model in which bidders are sold the item at the minimum price during their bid interval, as long as it is not over their limit value. We prove tight bounds on the competitiveness of deterministic online algorithms for this model, and upper and lower bounds on the competitiveness of randomized algorithms with quadratic gap. The lower bounds for the randomized case in both models use a novel general technique.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Digital goods; online algorithms; pricing", } @Article{Azar:2010:TUF, author = "Yossi Azar and Iftah Gamzu and Shai Gutner", title = "Truthful unsplittable flow for large capacity networks", journal = j-TALG, volume = "6", number = "2", pages = "36:1--36:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721852", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The {\em unsplittable flow problem\/} is one of the most extensively studied optimization problems in the field of networking. An instance of it consists of an edge capacitated graph and a set of connection requests, each of which is associated with source and target vertices, a demand, and a value. The objective is to route a maximum value subset of requests subject to the edge capacities. It is a well known fact that as the capacities of the edges are larger with respect to the maximal demand among the requests, the problem can be approximated better. In particular, it is known that for sufficiently large capacities, the integrality gap of the corresponding integer linear program becomes $ 1 + \epsilon $, which can be matched by an algorithm that utilizes the randomized rounding technique.\par In this article, we focus our attention on the large capacities unsplittable flow problem in a game theoretic setting. In this setting, there are selfish agents, which control some of the requests characteristics, and may be dishonest about them. It is worth noting that in game theoretic settings many standard techniques, such as randomized rounding, violate certain monotonicity properties, which are imperative for truthfulness, and therefore cannot be employed. In light of this state of affairs, we design a monotone deterministic algorithm, which is based on a primal-dual machinery, which attains an approximation ratio of $ e / (e - 1) $, up to a disparity of $ \epsilon $ away. This implies an improvement on the current best truthful mechanism, as well as an improvement on the current best combinatorial algorithm for the problem under consideration. Surprisingly, we demonstrate that any algorithm in the family of reasonable iterative path minimizing algorithms, cannot yield a better approximation ratio. Consequently, it follows that in order to achieve a monotone PTAS, if that exists, one would have to exert different techniques. We also consider the large capacities {\em single-minded multi-unit combinatorial auction problem}. This problem is closely related to the unsplittable flow problem since one can formulate it as a special case of the integer linear program of the unsplittable flow problem. Accordingly, we obtain a comparable performance guarantee by refining the algorithm suggested for the unsplittable flow problem.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; combinatorial and multi-unit auctions; Mechanism design; primal-dual method", } @Article{Svitkina:2010:FLH, author = "Zoya Svitkina and {\'E}va Tardos", title = "Facility location with hierarchical facility costs", journal = j-TALG, volume = "6", number = "2", pages = "37:1--37:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721853", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a facility location problem with submodular facility cost functions, and give an {$ O(\log n) $} approximation algorithm for it. Then we focus on a special case of submodular costs, called hierarchical facility costs, and give a {$ (4.237 + \epsilon) $}-approximation algorithm using local search. The hierarchical facility costs model multilevel service installation. Shmoys et al. [2004] gave a constant factor approximation algorithm for a two-level version of the problem. Here we consider a multilevel problem, and give a constant factor approximation algorithm, independent of the number of levels, for the case of identical costs on all facilities.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithm; facility location; local search; submodular function", } @Article{Christodoulou:2010:MDF, author = "George Christodoulou and Elias Koutsoupias and Annam{\'a}ria Kov{\'a}cs", title = "Mechanism design for fractional scheduling on unrelated machines", journal = j-TALG, volume = "6", number = "2", pages = "38:1--38:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721854", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Scheduling on unrelated machines is one of the most general and classical variants of the task scheduling problem. Fractional scheduling is the LP-relaxation of the problem, which is polynomially solvable in the nonstrategic setting, and is a useful tool to design deterministic and randomized approximation algorithms.\par The mechanism design version of the scheduling problem was introduced by Nisan and Ronen. In this article, we consider the mechanism design version of the fractional variant of this problem. We give lower bounds for any fractional truthful mechanism. Our lower bounds also hold for any (randomized) mechanism for the integral case. In the positive direction, we propose a truthful mechanism that achieves approximation 3/2 for 2 machines, matching the lower bound. This is the first new tight bound on the approximation ratio of this problem, after the tight bound of 2, for 2 machines, obtained by Nisan and Ronen. For $n$ machines, our mechanism achieves an approximation ratio of $ n + 1 / 2 $.\par Motivated by the fact that all the known deterministic and randomized mechanisms for the problem assign each task independently from the others, we focus on an interesting subclass of allocation algorithms, the {\em task-independent\/} algorithms. We give a lower bound of $ n + 1 / 2 $, that holds for every (not only monotone) allocation algorithm that takes independent decisions. Under this consideration, our truthful independent mechanism is the best that we can hope from this family of algorithms.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "scheduling; Truthful mechanisms; unrelated machines", } @Article{Korman:2010:LSV, author = "Amos Korman", title = "Labeling schemes for vertex connectivity", journal = j-TALG, volume = "6", number = "2", pages = "39:1--39:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721855", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article studies labeling schemes for the vertex connectivity function on general graphs. We consider the problem of assigning short labels to the nodes of any $n$-node graph is such a way that given the labels of any two nodes $u$ and $v$, one can decide whether $u$ and $v$ are $k$-vertex connected in {$G$}, that is, whether there exist {$k$} vertex disjoint paths connecting {$u$} and {$v$}. This article establishes an upper bound of $ k^2 \log n $ on the number of bits used in a label. The best previous upper bound for the label size of such a labeling scheme is $ 2^k \log n $.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Graph algorithms; labeling schemes; vertex-connectivity", } @Article{Butman:2010:OPM, author = "Ayelet Butman and Danny Hermelin and Moshe Lewenstein and Dror Rawitz", title = "Optimization problems in multiple-interval graphs", journal = j-TALG, volume = "6", number = "2", pages = "40:1--40:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721856", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more then one interval associated with it. We initiate the study of optimization problems in multiple-interval graphs by considering three classical problems: Minimum Vertex Cover, Minimum Dominating Set, and Maximum Clique. We describe applications for each one of these problems, and then proceed to discuss approximation algorithms for them.\par Our results can be summarized as follows: Let $t$ be the number of intervals associated with each vertex in a given multiple-interval graph. For Minimum Vertex Cover, we give a $ (2 - 1 / t) $-approximation algorithm which also works when a $t$-interval representation of our given graph is absent. Following this, we give a $ t^2 $-approximation algorithm for Minimum Dominating Set which adapts well to more general variants of the problem. We then proceed to prove that Maximum Clique is NP-hard already for 3-interval graphs, and provide a $ t^2 - (t + 1) / 2 $-approximation algorithm for general values of $ t \geq 2 $, using bounds proven for the so-called transversal number of $t$-interval families.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "$t$-interval graphs; Approximation algorithms; maximum clique; minimum dominating set; minimum vertex cover; multiple-interval graphs", } @Article{Gupta:2010:DRF, author = "Anupam Gupta and Mohammadtaghi Hajiaghayi and Viswanath Nagarajan and R. Ravi", title = "Dial a {Ride} from $k$-forest", journal = j-TALG, volume = "6", number = "2", pages = "41:1--41:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721857", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:49:22 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The {\em $k$-forest problem\/} is a common generalization of both the $k$-MST and the {\em dense-$k$-subgraph\/} problems. Formally, given a metric space on $n$ vertices {$V$}, with {$m$} demand pairs {$ \subseteq V \times V $} and a ``target'' {$ k \leq m $}, the goal is to find a minimum cost subgraph that connects {\em at least\/} {$k$} pairs. In this paper, we give an {$ O(m i n \{ \sqrt n \cdot \log k, \sqrt k \}) $}-approximation algorithm for {$k$}-forest, improving on the previous best ratio of {$ O(m i n \{ n^{2 / 3}, \sqrt m \log n \}) $} by Segev and Segev.\par We then apply our algorithm for {$k$}-forest to obtain approximation algorithms for several {\em Dial-a-Ride\/} problems. The basic Dial-a-Ride problem is the following: given an {$n$} point metric space with {$m$} objects each with its own source and destination, and a vehicle capable of carrying {\em at most\/} $k$ objects at any time, find the minimum length tour that uses this vehicle to move each object from its source to destination. We want that the tour be {\em non-preemptive\/}: that is, each object, once picked up at its source, is dropped only at its destination. We prove that an $ \alpha $-approximation algorithm for the $k$-forest problem implies an {$ O(\alpha \cdot \log^2 n) $}-approximation algorithm for Dial-a-Ride. Using our results for {$k$}-forest, we get an {$ O(m i n \{ \sqrt n, \sqrt k \} \cdot \log^2 n) $}-approximation algorithm for Dial-a-Ride. The only previous result known for Dial-a-Ride was an {$ O(\sqrt k \log n) $}-approximation by Charikar and Raghavachari; our results give a different proof of a similar approximation guarantee --- in fact, when the vehicle capacity {$k$} is large, we give a slight improvement on their results. The reduction from Dial-a-Ride to the {$k$}-forest problem is fairly robust, and allows us to obtain approximation algorithms (with the same guarantee) for some interesting generalizations of Dial-a-Ride.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; network design; vehicle routing", } @Article{Gupta:2010:DRK, author = "Anupam Gupta and Mohammadtaghi Hajiaghayi and Viswanath Nagarajan and R. Ravi", title = "Dial a {Ride} from $k$-forest", journal = j-TALG, volume = "6", number = "2", pages = "41:1--41:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721857", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The $k$-forest problem is a common generalization of both the $k$-MST and the dense-$k$-subgraph problems. Formally, given a metric space on $n$ vertices {$V$}, with {$m$} demand pairs {$ \subseteq V \times V $} and a ``target'' {$ k \leq m $}, the goal is to find a minimum cost subgraph that connects at least {$k$} pairs. In this paper, we give an {$ O(m i n{\sqrt n \cdot \log k, \sqrt k}) $}-approximation algorithm for {$k$}-forest, improving on the previous best ratio of {$ O(m i n \{ n^{2 / 3}, \sqrt m \} \log n) $} by Segev and Segev. We then apply our algorithm for {$k$}-forest to obtain approximation algorithms for several Dial-a-Ride problems. The basic Dial-a-Ride problem is the following: given an {$n$} point metric space with {$m$} objects each with its own source and destination, and a vehicle capable of carrying at most $k$ objects at any time, find the minimum length tour that uses this vehicle to move each object from its source to destination. We want that the tour be non-preemptive: that is, each object, once picked up at its source, is dropped only at its destination. We prove that an $ \alpha $-approximation algorithm for the $k$-forest problem implies an {$ O(\alpha \cdot \log^2 n) $}-approximation algorithm for Dial-a-Ride. Using our results for {$k$}-forest, we get an {$ O(\min \{ \sqrt n, \sqrt k \} \cdot \log^2 n) $}-approximation algorithm for Dial-a-Ride. The only previous result known for Dial-a-Ride was an {$ O(\sqrt k \log n) $}-approximation by Charikar and Raghavachari; our results give a different proof of a similar approximation guarantee-in fact, when the vehicle capacity {$k$} is large, we give a slight improvement on their results. The reduction from Dial-a-Ride to the {$k$}-forest problem is fairly robust, and allows us to obtain approximation algorithms (with the same guarantee) for some interesting generalizations of Dial-a-Ride.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bobier:2010:FAG, author = "Bruce Bobier and Joe Sawada", title = "A fast algorithm to generate open meandric systems and meanders", journal = j-TALG, volume = "6", number = "2", pages = "42:1--42:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721858", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An open meandric system is a planar configuration of acyclic curves crossing an infinite horizontal line in the plane such that the curves may extend in both horizontal directions. We present a fast, recursive algorithm to exhaustively generate open meandric systems with $n$ crossings. We then illustrate how to modify the algorithm to generate unidirectional open meandric systems (the curves extend only to the right) and nonisomorphic open meandric systems where equivalence is taken under horizontal reflection. Each algorithm can be modified to generate systems with exactly $k$ curves. In the unidirectional case when $ k = 1 $, we can apply a minor modification along with some additional optimization steps to yield the first fast and simple algorithm to generate open meanders.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "CAT algorithm; meander; open meandric system", } @Article{Ergun:2010:PTS, author = "Funda Ergun and S. Muthukrishnan and Cenk Sahinalp", title = "Periodicity testing with sublinear samples and space", journal = j-TALG, volume = "6", number = "2", pages = "43:1--43:??", month = mar, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1721837.1721859", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:34 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this work, we are interested in periodic trends in long data streams in the presence of computational constraints. To this end; we present algorithms for discovering periodic trends in the combinatorial property testing model in a data stream {$S$} of length {$n$} using {$ o(n) $} samples and space.\par In accordance with the property testing model, we first explore the notion of being ``close'' to periodic by defining three different notions of self-distance through relaxing different notions of exact periodicity. An input {$S$} is then called approximately periodic if it exhibits a small self-distance (with respect to any one self-distance defined). We show that even though the different definitions of exact periodicity are equivalent, the resulting definitions of self-distance and approximate periodicity are not; we also show that these self-distances are constant approximations of each other. Afterwards, we present algorithms which distinguish between the two cases where {$S$} is exactly periodic and {$S$} is far from periodic with only a constant probability of error.\par Our algorithms sample only {$ O(\sqrt n \log^2 n) $} (or {$ O(\sqrt n \log^4 n) $}, depending on the self-distance) positions and use as much space. They can also find, using {$ o(n) $} samples and space, the largest/smallest period, and/or all of the approximate periods of {$S$}. These algorithms can also be viewed as working on streaming inputs where each data item is seen once and in order, storing only a sublinear ({$ O(\sqrt n \log^2 n) $} or {$ O(\sqrt n \log^4 n) $}) size sample from which periodicities are identified.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Combinatorial property testing; periodicity", } @Article{Vassilevska:2010:FHS, author = "Virginia Vassilevska and Ryan Williams and Raphael Yuster", title = "Finding heaviest {$H$}-subgraphs in real weighted graphs, with applications", journal = j-TALG, volume = "6", number = "3", pages = "44:1--44:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798597", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a graph {$G$} with real weights assigned to the vertices (edges), the MAX {$H$}-SUBGRAPH problem is to find an {$H$}-subgraph of {$G$} with maximum total weight, if one exists. Our main results are new strongly polynomial algorithms for the MAX {$H$}-SUBGRAPH problem. Some of our algorithms are based, in part, on fast matrix multiplication.\par For vertex-weighted graphs with {$n$} vertices we solve a more general problem: the {\em all pairs\/} MAX {$H$}-SUBGRAPH problem, where the task is to find for every pair of vertices {$ u, v $}, a maximum {$H$}-subgraph containing both {$u$} and {$v$}, if one exists. We obtain an {$ O(n^t(\omega, h)) $}-time algorithm for the {\em all pairs\/} MAX {$H$}-SUBGRAPH problem in the case where {$H$} is a fixed graph with {$h$} vertices and {$ \omega $}.\par We also present improved algorithms for the MAX {$H$}-SUBGRAPH problem in the edge-weighted case. In particular, we obtain an {$ O(m^{2 - 1 / k \log n}) $}-time algorithm for the heaviest cycle of length 2 {$k$} or {$ 2 k - 1 $} in a graph with {$m$} edges and an {$ O(n^3 / \log n) $}-time randomized algorithm for finding the heaviest cycle of any fixed length.\par Our methods also yield efficient algorithms for several related problems that are faster than any previously existing algorithms. For example, we show how to find chromatic {$H$}-subgraphs in edge-colored graphs, and how to compute the most significant bits of the distance product of two real matrices, in truly subcubic time.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "H-subgraph; matrix multiplication; weighted graph", } @Article{Ruskey:2010:EUC, author = "Frank Ruskey and Aaron Williams", title = "An explicit universal cycle for the $ (n - 1) $-permutations of an $n$-set", journal = j-TALG, volume = "6", number = "3", pages = "45:1--45:12", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798598", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show how to construct an {\em explicit\/} Hamilton cycle in the directed Cayley graph {$ \vec {\rm Cay}(\sigma_n, \sigma_{n - 1} : S_n) $}, where {$ \sigma_k $} is the rotation {$ (1 2 \cdots k) $}. The existence of such cycles was shown by Jackson [1996] but the proof only shows that a certain directed graph is Eulerian, and Knuth [2005] asks for an explicit construction. We show that a simple recursion describes our Hamilton cycle and that the cycle can be generated by an iterative algorithm that uses {$ O(n) $} space. Moreover, the algorithm produces each successive edge of the cycle in constant time; such algorithms are said to be {\em loopless}. Finally, our Hamilton cycle can be used to construct an explicit universal cycle for the {$ (n - 1) $}-permutations of a {$n$}-set, or as the basis of an efficient algorithm for generating every {$n$}-permutation of an $n$-set within a circular array or linked list.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "loopless algorithm; Universal cycle", } @Article{Drescher:2010:AAM, author = "Matthew Drescher and Adrian Vetta", title = "An approximation algorithm for the maximum leaf spanning arborescence problem", journal = j-TALG, volume = "6", number = "3", pages = "46:1--46:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798599", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present an {$ O(\sqrt {{\rm opt}}) $}-approximation algorithm for the maximum leaf spanning arborescence problem, where opt is the number of leaves in an optimal spanning arborescence. The result is based upon an {$ O(1) $}-approximation algorithm for a special class of directed graphs called willows. Incorporating the method for willow graphs as a subroutine in a local improvement algorithm gives the bound for general directed graphs.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation Algorithms; arborescence; directed graphs; maximum leaf", } @Article{Naor:2010:DCA, author = "Joseph (Seffi) Naor and Roy Schwartz", title = "The directed circular arrangement problem", journal = j-TALG, volume = "6", number = "3", pages = "47:1--47:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798600", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of embedding a directed graph onto evenly spaced points on a circle while minimizing the total weighted edge length. We present the first poly-logarithmic approximation factor algorithm for this problem which yields an approximation factor of {$ O(\log n \log \log n) $}, thus improving the previous {$ \tilde {O}(\sqrt n) $} approximation factor. In order to achieve this, we introduce a new problem which we call the {\em directed penalized linear arrangement}. This problem generalizes both the directed feedback edge set problem and the directed linear arrangement problem. We present an {$ O(\log n \log \log n) $}-approximation factor algorithm for this newly defined problem. Our solution uses two distinct directed metrics (``right'' and ``left'') which together yield a lower bound on the value of an optimal solution. In addition, we define a sequence of new directed spreading metrics that are used for applying the algorithm recursively on smaller subgraphs. The new spreading metrics allow us to define an asymmetric region growing procedure that accounts simultaneously for both incoming and outgoing edges. To the best of our knowledge, this is the first time that a region growing procedure is defined in directed graphs that allows for such an accounting.", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "region growing; scheduling; Spreading metrics", } @Article{Azar:2010:DEC, author = "Yossi Azar and Shay Kutten and Boaz Patt-Shamir", title = "Distributed error confinement", journal = j-TALG, volume = "6", number = "3", pages = "48:1--48:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798601", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study error confinement in distributed applications, which can be viewed as an extreme case of various fault locality notions studied in the past. Error confinement means that to the external observer, only nodes that were directly hit by a fault may deviate from their specified correct behavior, and only temporarily. The externally observable behavior of all other nodes must remain impeccable, even though their internal state may be affected. Error confinement is impossible if an adversary is allowed to inflict arbitrary transient faults on the system, since the faults might completely wipe out input values. We introduce a new fault-tolerance measure we call {\em agility}, which quantifies the fault tolerance of an algorithm that disseminates information against state corrupting faults.\par We then propose broadcast algorithms that guarantee error confinement with optimal agility to within a constant factor in synchronous networks. These algorithms can serve as building blocks in more general reactive systems. Previous results in exploring locality in reactive systems were not error confined, or allowed a wide range of behaviors to be considered correct. Our results also include a new technique that can be used to analyze the ``cow path'' problem.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Distributed algorithms; persistence; self-stabilization; voting", } @Article{Aggarwal:2010:AAC, author = "Gagan Aggarwal and Rina Panigrahy and Tom{\'a}s Feder and Dilys Thomas and Krishnaram Kenthapadi and Samir Khuller and An Zhu", title = "Achieving anonymity via clustering", journal = j-TALG, volume = "6", number = "3", pages = "49:1--49:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798602", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of deidentifying records is to remove identifying fields such as social security number, name, etc. However, recent research has shown that a large fraction of the U.S. population can be identified using nonkey attributes (called quasi-identifiers) such as date of birth, gender, and zip code. The $k$-anonymity model protects privacy via requiring that nonkey attributes that leak information are suppressed or generalized so that, for every record in the modified table, there are at least $k$-1 other records having exactly the same values for quasi-identifiers. We propose a new method for anonymizing data records, where quasi-identifiers of data records are first clustered and then cluster centers are published. To ensure privacy of the data records, we impose the constraint that each cluster must contain no fewer than a prespecified number of data records. This technique is more general since we have a much larger choice for cluster centers than $k$-anonymity. In many cases, it lets us release a lot more information without compromising privacy. We also provide constant factor approximation algorithms to come up with such a clustering. This is the first set of algorithms for the anonymization problem where the performance is independent of the anonymity parameter $k$. We further observe that a few outlier points can significantly increase the cost of anonymization. Hence, we extend our algorithms to allow an $ \epsilon $ fraction of points to remain unclustered, that is, deleted from the anonymized publication. Thus, by not releasing a small fraction of the database records, we can ensure that the data published for analysis has less distortion and hence is more useful. Our approximation algorithms for new clustering objectives are of independent interest and could be applicable in other clustering scenarios as well.", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "anonymity; approximation algorithms; clustering; Privacy", } @Article{Gordon:2010:CWT, author = "Eyal Gordon and Adi Ros{\'e}n", title = "Competitive weighted throughput analysis of greedy protocols on {DAGs}", journal = j-TALG, volume = "6", number = "3", pages = "50:1--50:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798603", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The combination of the buffer sizes of routers deployed in the Internet, and the Internet traffic itself, leads routinely to the dropping of packets. Motivated by this, we are interested in the problem of maximizing the throughput of protocols that control packet networks. Moreover, we are interested in a setting where different packets have different priorities (or weights), thus taking into account Quality-of-Service considerations.\par We first extend the Competitive Network Throughput (CNT) model introduced by Aiello et al. [2003] to the weighted packets case. We analyze the performance of online, local-control protocols by their competitive ratio, in the face of arbitrary traffic, using as a measure the total weight of the packets that arrive to their destinations, rather than being dropped en-route. We prove that on Directed Acyclic Graphs (DAGs), any greedy protocol is competitive, with competitive ratio independent of the weights of the packets. Here we mean by a ``greedy protocol'' a protocol that not only does not leave a resource idle unnecessarily, but also prefers packets with higher weight over those with lower weight. We give two independent upper bounds on the competitive ratio of general greedy protocols on DAGs. We further give lower bounds that show that our upper bounds cannot be improved (other than constant factors) in the general case. Both our upper and lower bounds apply also to the unweighted case, and they improve the results given in Aiello et al. [2003] for that case. We thus give tight (up to constant factors) upper and lower bounds for both the unweighted and weighted cases.\par In the course of proving our upper bounds we prove a lemma that gives upper bounds on the delivery times of packets by any greedy protocol on general DAGs (without buffer size considerations). We believe that this lemma may be of independent interest and may find additional applications.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Buffer management; competitive analysis; competitive network throughput; online algorithms", } @Article{Chakrabarti:2010:NOA, author = "Amit Chakrabarti and Graham Cormode and Andrew Mcgregor", title = "A near-optimal algorithm for estimating the entropy of a stream", journal = j-TALG, volume = "6", number = "3", pages = "51:1--51:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798604", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a simple algorithm for approximating the empirical entropy of a stream of $m$ values up to a multiplicative factor of $ (1 + \epsilon) $ using a single pass, {$ O(\epsilon^{ - 2} \log (\delta^{ - 1}) \log m) $} words of space, and {$ O(\log \epsilon^{ - 1} + \log \log \delta^{ - 1} + \log \log m) $} processing time per item in the stream. Our algorithm is based upon a novel extension of a method introduced by Alon et al. [1999]. This improves over previous work on this problem. We show a space lower bound of {$ \Omega (\epsilon^{ - 2} / \log^2 (\epsilon^{ - 1})) $}, demonstrating that our algorithm is near-optimal in terms of its dependency on {$ \epsilon $}.\par We show that generalizing to multiplicative-approximation of the {$k$} th-order entropy requires close to linear space for {$ k \geq 1 $}. In contrast we show that additive-approximation is possible in a single pass using only poly-logarithmic space. Lastly, we show how to compute a multiplicative approximation to the entropy of a random walk on an undirected graph.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; Data streams; entropy", } @Article{Fattal:2010:ADM, author = "Shahar Fattal and Dana Ron", title = "Approximating the distance to monotonicity in high dimensions", journal = j-TALG, volume = "6", number = "3", pages = "52:1--52:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798605", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we study the problem of approximating the distance of a function {$ f : [n]^d \rightarrow R $} to monotonicity where {$ [n] = \{ 1, \ldots, n \} $} and {$R$} is some fully ordered range. Namely, we are interested in randomized sublinear algorithms that approximate the Hamming distance between a given function and the closest monotone function. We allow both an additive error, parameterized by {$ \delta $}, and a multiplicative error.\par Previous work on distance approximation to monotonicity focused on the one-dimensional case and the only explicit extension to higher dimensions was with a multiplicative approximation factor exponential in the dimension {\em d}. Building on Goldreich et al. [2000] and Dodis et al. [1999], in which there are better implicit results for the case {$ n = 2 $}, we describe a reduction from the case of functions over the {$d$}-dimensional hypercube $ [n]^d $ to the case of functions over the $k$-dimensional hypercube $ [n]^k $, where $ 1 \leq k \leq d $. The quality of estimation that this reduction provides is linear in $ \lceil d / k \rceil $ and logarithmic in the size of the range {$ |R| $} (if the range is infinite or just very large, then {$ \log |R| $} can be replaced by {$ d \log n $}). Using this reduction and a known distance approximation algorithm for the one-dimensional case, we obtain a distance approximation algorithm for functions over the {$d$}-dimensional hypercube, with any range {$R$}, which has a multiplicative approximation factor of {$ O(d \log |R) $}.\par For the case of a binary range, we present algorithms for distance approximation to monotonicity of functions over one dimension, two dimensions, and the {$k$}-dimensional hypercube (for any {$ k \geq 1 $} ). Applying these algorithms and the reduction described before, we obtain a variety of distance approximation algorithms for Boolean functions over the {$d$}-dimensional hypercube which suggest a trade-off between quality of estimation and efficiency of computation. In particular, the multiplicative error ranges between {$ O(d) $} and {$ O(1) $}.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "distance approximation; monotonicity; property testing; Sublinear approximation algorithms", } @Article{Martinez:2010:ASS, author = "Conrado Mart{\'\i}nez and Daniel Panario and Alfredo Viola", title = "Adaptive sampling strategies for quickselects", journal = j-TALG, volume = "6", number = "3", pages = "53:1--53:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798606", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Quickselect with median-of-3 is largely used in practice and its behavior is fairly well understood. However, the following natural adaptive variant, which we call {\em proportion-from-3}, had not been previously analyzed: ``choose as pivot the smallest of the sample if the relative rank of the sought element is below 1/3, the largest if the relative rank is above 2/3, and the median if the relative rank is between 1/3 and 2/3.'' We first analyze the average number of comparisons made when using proportion-from-2 and then for proportion-from-3. We also analyze $ \nu $-find, a generalization of proportion-from-3 with interval breakpoints at $ \nu $ and $ 1 - \nu $. We show that there exists an optimal value of $ \nu $ and we also provide the range of values of $ \nu $ where $ \nu $-find outperforms median-of-3. Then, we consider the average total cost of these strategies, which takes into account the cost of both comparisons and exchanges. Our results strongly suggest that a suitable implementation of $ \nu $-find could be the method of choice in a practical setting. We also study the behavior of proportion-from-$s$ with $ s > 3 $ and in particular we show that proportion-from-$s$-like strategies are optimal when $ s \rightarrow \infty $.", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Analytic combinatorics; average-case analysis; divide-and-conquer; Find; quickselect; sampling; selection", } @Article{Alon:2010:BFP, author = "Noga Alon and Shai Gutner", title = "Balanced families of perfect hash functions and their applications", journal = j-TALG, volume = "6", number = "3", pages = "54:1--54:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798607", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The construction of perfect hash functions is a well-studied topic. In this article, this concept is generalized with the following definition. We say that a family of functions from $ [n] $ to $ [k] $ is a $ \delta $-balanced $ (n, k) $-family of perfect hash functions if for every {$ S \subseteq [n] $}, {$ |S| = k $}, the number of functions that are {$1$}-{$1$} on {$S$} is between {$ T / \delta $} and {$ \delta T $} for some constant {$ T > 0 $}. The standard definition of a family of perfect hash functions requires that there will be at least one function that is {$1$}-{$1$} on {$S$}, for each {$S$} of size {$k$}. In the new notion of balanced families, we require the number of {$1$}-{$1$} functions to be almost the same (taking $ \delta $ to be close to $1$ ) for every such {$S$}. Our main result is that for any constant {$ \delta > 1 $}, a {$ \delta $}-balanced {$ (n, k) $}-family of perfect hash functions of size {$ 2^{O(k \log \log k)} \log n $} can be constructed in time {$ 2^{O(k \log \log k)} n \log n $}. Using the technique of color-coding we can apply our explicit constructions to devise approximation algorithms for various counting problems in graphs. In particular, we exhibit a deterministic polynomial-time algorithm for approximating both the number of simple paths of length {$k$} and the number of simple cycles of size {$k$} for any {$ k \leq O(\log n / \log \log \log n) $} in a graph with {$n$} vertices. The approximation is up to any fixed desirable relative error.", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximate counting of subgraphs; color-coding; perfect hashing", } @Article{Coppersmith:2010:OWN, author = "Don Coppersmith and Lisa K. Fleischer and Atri Rurda", title = "Ordering by weighted number of wins gives a good ranking for weighted tournaments", journal = j-TALG, volume = "6", number = "3", pages = "55:1--55:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798608", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the following simple algorithm for feedback arc set problem in weighted tournaments: order the vertices by their weighted indegrees. We show that this algorithm has an approximation guarantee of 5 if the weights satisfy {\em probability constraints\/} (for any pair of vertices $u$ and $v$, $ w_{uv} + w_{vu} = 1 $ ). Special cases of the feedback arc set problem in such weighted tournaments include the feedback arc set problem in unweighted tournaments and rank aggregation. To complement the upper bound, for any constant $ \epsilon > 0 $, we exhibit an infinite family of (unweighted) tournaments for which the aforesaid algorithm ({\em irrespective\/} of how ties are broken) has an approximation ratio of $ 5 - \epsilon $.", acknowledgement = ack-nhfb, articleno = "55", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "Approximation algorithms; Borda's method; feedback arc set problem; rank aggregation; tournaments", } @Article{Gonzalez-Gutierrez:2010:ACT, author = "Arturo Gonzalez-Gutierrez and Teofilo F. Gonzalez", title = "Approximating corridors and tours via restriction and relaxation techniques", journal = j-TALG, volume = "6", number = "3", pages = "56:1--56:??", month = jun, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1798596.1798609", ISSN = "1549-6325 (print), 1549-6333 (electronic)", bibdate = "Sat Aug 14 15:50:18 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a rectangular boundary partitioned into rectangles, the Minimum-Length Corridor (MLC-R) problem consists of finding a corridor of least total length. A corridor is a set of connected line segments, each of which must lie along the line segments that form the rectangular boundary and/or the boundary of the rectangles, and must include at least one point from the boundary of every rectangle and from the rectangular boundary. The MLC-R problem is known to be NP-hard. We present the first polynomial-time constant ratio approximation algorithm for the MLC-R and MLC$_k$ problems. The MLC$_k$ problem is a generalization of the MLC-R problem where the rectangles are rectilinear $c$-gons, for $ c \leq k $ and $k$ is a constant. We also present the first polynomial-time constant ratio approximation algorithm for the Group Traveling Salesperson Problem (GTSP) for a rectangular boundary partitioned into rectilinear $c$-gons as in the MLC$_k$ problem. Our algorithms are based on the restriction and relaxation approximation techniques.", acknowledgement = ack-nhfb, articleno = "56", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", keywords = "approximation algorithms; complexity; computational geometry; Corridors; restriction and relaxation techniques", } @Article{Alber:2010:EN, author = "Susanne Alber", title = "Editorial note", journal = j-TALG, volume = "6", number = "4", pages = "57:1--57:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824778", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "57", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hajiaghayi:2010:FSI, author = "Mohammad T. Hajiaghayi and Shang-Hua Teng", title = "Foreword to special issue on {SODA 2008}", journal = j-TALG, volume = "6", number = "4", pages = "58:1--58:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824793", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "58", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ackermann:2010:CMN, author = "Marcel R. Ackermann and Johannes Bl{\"o}mer and Christian Sohler", title = "Clustering for metric and nonmetric distance measures", journal = j-TALG, volume = "6", number = "4", pages = "59:1--59:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824779", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study a generalization of the $k$-median problem with respect to an arbitrary dissimilarity measure $D$. Given a finite set $P$ of size $n$, our goal is to find a set $C$ of size $k$ such that the sum of errors $ D(P, C) = \sum_{p \in P} \min_{c \in C} D(p, c)$ is minimized. The main result in this article can be stated as follows: There exists a $ (1 + \epsilon)$-approximation algorithm for the $k$-median problem with respect to $D$, if the 1-median problem can be approximated within a factor of $ (1 + \epsilon)$ by taking a random sample of constant size and solving the 1-median problem on the sample exactly. This algorithm requires time $ n 2^O(m k \log (m k / \epsilon))$, where $m$ is a constant that depends only on $ \epsilon $ and $D$. Using this characterization, we obtain the first linear time $ (1 + \epsilon)$-approximation algorithms for the $k$-median problem in an arbitrary metric space with bounded doubling dimension, for the Kullback--Leibler divergence (relative entropy), for the Itakura-Saito divergence, for Mahalanobis distances, and for some special cases of Bregman divergences. Moreover, we obtain previously known results for the Euclidean $k$-median problem and the Euclidean $k$-means problem in a simplified manner. Our results are based on a new analysis of an algorithm of Kumar et al. [2004].", acknowledgement = ack-nhfb, articleno = "59", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andersen:2010:LAF, author = "Reid Andersen", title = "A local algorithm for finding dense subgraphs", journal = j-TALG, volume = "6", number = "4", pages = "60:1--60:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824780", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a local algorithm for finding subgraphs with high density, according to a measure of density introduced by Kannan and Vinay [1999]. The algorithm takes as input a bipartite graph $G$, a starting vertex $v$, and a parameter $k$, and outputs an induced subgraph of $G$. It is local in the sense that it does not examine the entire input graph; instead, it adaptively explores a region of the graph near the starting vertex. The running time of the algorithm is bounded by $ O(\Delta k^2)$, which depends on the maximum degree $ \Delta $, but is otherwise independent of the graph. We prove the following approximation guarantee: for any subgraph $S$ with $ k'$ vertices and density $ \theta $, there exists a set $ S' \subseteq S$ for which the algorithm outputs a subgraph with density $ \Omega (\theta / \log \Delta)$ whenever $ v \in S'$ and $ k \geq k'$. We prove that $ S'$ contains at least half of the edges in $S$.", acknowledgement = ack-nhfb, articleno = "60", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cabello:2010:FOT, author = "Sergio Cabello and Matt Devos and Jeff Erickson and Bojan Mohar", title = "Finding one tight cycle", journal = j-TALG, volume = "6", number = "4", pages = "61:1--61:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824781", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A cycle on a combinatorial surface is tight if it as short as possible in its (free) homotopy class. We describe an algorithm to compute a single tight, noncontractible, essentially simple cycle on a given orientable combinatorial surface in $ O(n \log n) $ time. The only method previously known for this problem was to compute the globally shortest noncontractible or nonseparating cycle in $ O (\min \{ g^3, n, n \log n \}) $ time, where $g$ is the genus of the surface. As a consequence, we can compute the shortest cycle freely homotopic to a chosen boundary cycle in $ O (n \log n)$ time, a tight octagonal decomposition in $ O (g n \log n)$ time, and a shortest contractible cycle enclosing a nonempty set of faces in $ O (n \log^2 n)$ time.", acknowledgement = ack-nhfb, articleno = "61", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2010:BSP, author = "Timothy M. Chan", title = "On the bichromatic $k$-set problem", journal = j-TALG, volume = "6", number = "4", pages = "62:1--62:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824782", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study a generalization of the k -median problem with respect to an arbitrary dissimilarity measure D. Given a finite set P of size n, our goal is to find a set C of size k such that the sum of errors $ D(P, C) = \sum_{p \in P} \min_{c \in C} D(p, c) $ is minimized. The main result in this article can be stated as follows: There exists a $ (1 + \epsilon)$-approximation algorithm for the k median problem with respect to $D$, if the 1-median problem can be approximated within a factor of $ (1 + \epsilon)$ by taking a random sample of constant size and solving the 1-median problem on the sample exactly. This algorithm requires time $ n 2^O (m k \log (m k / \epsilon))$, where $m$ is a constant that depends only on $ \epsilon $ and $D$. Using this characterization, we obtain the first linear time $ (1 + \epsilon)$-approximation algorithms for the $k$ median problem in an arbitrary metric space with bounded doubling dimension, for the Kullback--Leibler divergence (relative entropy), for the Itakura-Saito divergence, for Mahalanobis distances, and for some special cases of Bregman divergences. Moreover, we obtain previously known results for the Euclidean $k$ median problem and the Euclidean $k$-means problem in a simplified manner. Our results are based on a new analysis of an algorithm of Kumar et al. [2004].", acknowledgement = ack-nhfb, articleno = "62", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Clarkson:2010:CSG, author = "Kenneth L. Clarkson", title = "Coresets, sparse greedy approximation, and the {Frank--Wolfe} algorithm", journal = j-TALG, volume = "6", number = "4", pages = "63:1--63:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824783", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The problem of maximizing a concave function $ f(x) $ in the unit simplex $ \Delta $ can be solved approximately by a simple greedy algorithm. For given $k$, the algorithm can find a point $ x_{(k)}$ on a $k$-dimensional face of $ \Delta $, such that $ f(x_{(k)}) \geq f(x_*) - O(1 / k)$. Here $ f(x_*)$ is the maximum value of $f$ in $ \Delta $, and the constant factor depends on $f$. This algorithm and analysis were known before, and related to problems of statistics and machine learning, such as boosting, regression, and density mixture estimation. In other work, coming from computational geometry, the existence of $ \epsilon $-coresets was shown for the minimum enclosing ball problem by means of a simple greedy algorithm. Similar greedy algorithms, which are special cases of the Frank-0Wolfe algorithm, were described for other enclosure problems. Here these results are tied together, stronger convergence results are reviewed, and several coreset bounds are generalized or strengthened.", acknowledgement = ack-nhfb, articleno = "63", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Emek:2010:NLT, author = "Yuval Emek and David Peleg and Liam Roditty", title = "A near-linear-time algorithm for computing replacement paths in planar directed graphs", journal = j-TALG, volume = "6", number = "4", pages = "64:1--64:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824784", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let $ G = (V(G), E(G)) $ be a directed graph with nonnegative edge lengths and let $P$ be a shortest path from $s$ to $t$ in $G$. In the replacement paths problem we are required to compute for every edge $e$ in $P$, the length of a shortest path from $s$ to $t$ that avoids $e$. The fastest known algorithm for solving the problem in weighted directed graphs is the trivial one: each edge in $P$ is removed from the graph in its turn and the distance from $s$ to $t$ in the modified graph is computed. The running time of this algorithm is $ O(m n + n^2 \log n)$, where $ n = | V(G) |$ and $ m = | E(G) |$. The replacement paths problem is strongly motivated by two different applications. First, the fastest algorithm to compute the $k$ simple shortest paths from $s$ to $t$ in directed graphs [Yen 1971; Lawler 1972] repeatedly computes the replacement paths from $s$ to $t$. Its running time is $ O(k n (m + n \log n))$. Second, the computation of Vickrey pricing of edges in distributed networks can be reduced to the replacement paths problem. An open question raised by Nisan and Ronen [2001] asks whether it is possible to compute the Vickrey pricing faster than the trivial algorithm described in the previous paragraph. In this article we present a near-linear time algorithm for computing replacement paths in weighted planar directed graphs. In particular, the algorithm computes the lengths of the replacement paths in $ O (n \log^3 n)$ time (recall that in planar graphs $ m = O(n)$). This result immediately improves the running time of the two applications mentioned before by almost a linear factor. Our algorithm is obtained by combining several new ideas with a data structure of Klein [2005] that supports multisource shortest paths queries in planar directed graphs in logarithmic time. Our algorithm can be adapted to address the variant of the problem in which one is interested in the replacement path itself (rather than the length of the path). In that case the algorithm is executed in a preprocessing stage constructing a data structure that supports replacement path queries in time $ {\tilde O}(h)$, where $h$ is the number of hops in the replacement path. In addition, we can handle the variant in which vertices should be avoided instead of edges.", acknowledgement = ack-nhfb, articleno = "64", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Faigle:2010:TPG, author = "Ulrich Faigle and Britta Peis", title = "Two-phase greedy algorithms for some classes of combinatorial linear programs", journal = j-TALG, volume = "6", number = "4", pages = "65:1--65:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824785", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present greedy algorithms for some classes of combinatorial packing and cover problems within the general formal framework of Hoffman and Schwartz' lattice polyhedra. Our algorithms compute in a first phase Monge solutions for the associated dual cover and packing problems and then proceed to construct greedy solutions for the primal problems in a second phase. We show optimality of the algorithms under certain sub- and supermodular assumptions and monotone constraints. For supermodular lattice polyhedra with submodular constraints, our algorithms offer the farthest reaching generalization of Edmonds' polymatroid greedy algorithm currently known.", acknowledgement = ack-nhfb, articleno = "65", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Feldman:2010:DSS, author = "Jon Feldman and S. Muthukrishnan and Anastasios Sidiropoulos and Cliff Stein and Zoya Svitkina", title = "On distributing symmetric streaming computations", journal = j-TALG, volume = "6", number = "4", pages = "66:1--66:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824786", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A common approach for dealing with large datasets is to stream over the input in one pass, and perform computations using sublinear resources. For truly massive datasets, however, even making a single pass over the data is prohibitive. Therefore, streaming computations must be distributed over many machines. In practice, obtaining significant speedups using distributed computation has numerous challenges including synchronization, load balancing, overcoming processor failures, and data distribution. Successful systems in practice such as Google's MapReduce and Apache's Hadoop address these problems by only allowing a certain class of highly distributable tasks defined by local computations that can be applied in any order to the input. The fundamental question that arises is: How does the class of computational tasks supported by these systems differ from the class for which streaming solutions exist? We introduce a simple algorithmic model for massive, unordered, distributed (mud) computation, as implemented by these systems. We show that in principle, mud algorithms are equivalent in power to symmetric streaming algorithms. More precisely, we show that any symmetric (order-invariant) function that can be computed by a streaming algorithm can also be computed by a mud algorithm, with comparable space and communication complexity. Our simulation uses Savitch's theorem and therefore has superpolynomial time complexity. We extend our simulation result to some natural classes of approximate and randomized streaming algorithms. We also give negative results, using communication complexity arguments to prove that extensions to private randomness, promise problems, and indeterminate functions are impossible. We also introduce an extension of the mud model to multiple keys and multiple rounds.", acknowledgement = ack-nhfb, articleno = "66", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Oudot:2010:GDT, author = "Steve Y. Oudot and Leonidas J. Guibas and Jie Gao and Yue Wang", title = "Geodesic {Delaunay} triangulations in bounded planar domains", journal = j-TALG, volume = "6", number = "4", pages = "67:1--67:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824787", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new feature size for bounded domains in the plane endowed with an intrinsic metric. Given a point $x$ in a domain $X$, the systolic feature size of $X$ at $x$ measures half the length of the shortest loop through $x$ that is not null-homotopic in $X$. The resort to an intrinsic metric makes the systolic feature size rather insensitive to the local geometry of the domain, in contrast with its predecessors (local feature size, weak feature size, homology feature size). This reduces the number of samples required to capture the topology of $X$, provided that a reliable approximation to the intrinsic metric of $X$ is available. Under sufficient sampling conditions involving the systolic feature size, we show that the geodesic Delaunay triangulation $ D_x(L)$ of a finite sampling $L$ is homotopy equivalent to $X$. Under similar conditions, $ D_x(L)$ is sandwiched between the geodesic witness complex $ C^W_X (L)$ and a relaxed version $ C^W_{X, \nu }(L)$. In the conference version of the article, we took advantage of this fact and proved that the homology of $ D_x(L)$ (and hence the one of $X$) can be retrieved by computing the persistent homology between $ C^W_X(L)$ and $ C^W_{X, \nu }(L)$. Here, we investigate further and show that the homology of $X$ can also be recovered from the persistent homology associated with inclusions of type $ C^W_{X, \nu }(L) \hookrightarrow C^W_{X, \nu '} (L)$, under some conditions on the parameters $ \nu \leq \nu '$. Similar results are obtained for Vietoris--Rips complexes in the intrinsic metric. The proofs draw some connections with recent advances on the front of homology inference from point cloud data, but also with several well-known concepts of Riemannian (and even metric) geometry. On the algorithmic front, we propose algorithms for estimating the systolic feature size of a bounded planar domain $X$, selecting a landmark set of sufficient density, and computing the homology of $X$ using geodesic witness complexes or Rips complexes.", acknowledgement = ack-nhfb, articleno = "67", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kapron:2010:FAB, author = "Bruce M. Kapron and David Kempe and Valerie King and Jared Saia and Vishal Sanwalani", title = "Fast asynchronous {Byzantine} agreement and leader election with full information", journal = j-TALG, volume = "6", number = "4", pages = "68:1--68:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824788", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We resolve two long-standing open problems in distributed computation by describing polylogarithmic protocols for Byzantine agreement and leader election in the asynchronous full information model with a nonadaptive malicious adversary. All past protocols for asynchronous Byzantine agreement had been exponential, and no protocol for asynchronous leader election had been known. Our protocols tolerate up to $ (1 / 3 - \epsilon) \cdot n $ faulty processors, for any positive constant $ \epsilon $. They are Monte Carlo, succeeding with probability $ 1 - o(1) $ for Byzantine agreement, and constant probability for leader election. A key technical contribution of our article is a new approach for emulating Feige's lightest bin protocol, even with adversarial message scheduling.", acknowledgement = ack-nhfb, articleno = "68", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Svitkina:2010:LBF, author = "Zoya Svitkina", title = "Lower-bounded facility location", journal = j-TALG, volume = "6", number = "4", pages = "69:1--69:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824789", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the lower-bounded facility location problem which generalizes the classical uncapacitated facility location problem in that it comes with lower bound constraints for the number of clients assigned to a facility in the case that this facility is opened. This problem was introduced independently in the papers by Karger and Minkoff [2000] and by Guha et al. [2000], both of which give bicriteria approximation algorithms for it. These bicriteria algorithms come within a constant factor of the optimal solution cost, but they also violate the lower bound constraints by a constant factor. Our result in this article is the first true approximation algorithm for the lower-bounded facility location problem which respects the lower bound constraints and achieves a constant approximation ratio for the objective function. The main technical idea for the design of the algorithm is a reduction to the capacitated facility location problem, which has known constant-factor approximation algorithms.", acknowledgement = ack-nhfb, articleno = "69", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Williams:2010:NPW, author = "Virginia Vassilevska Williams", title = "Nondecreasing paths in a weighted graph or: How to optimally read a train schedule", journal = j-TALG, volume = "6", number = "4", pages = "70:1--70:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824790", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A travel booking office has timetables giving arrival and departure times for all scheduled trains, including their origins and destinations. A customer presents a starting station and demands a route with perhaps several train connections taking him to his destination as early as possible. The booking office must find the best route for its customers. This problem was first considered in the theory of algorithms by Minty [1958], who reduced it to a problem on directed edge-weighted graphs: find a path from a given source to a given target such that the consecutive weights on the path are nondecreasing and the last weight on the path is minimized. Minty gave the first algorithm for the single-source version of the problem, in which one finds minimum last weight nondecreasing paths from the source to every other vertex. In this article we give the first linear -time algorithm for this problem in the word-RAM model of computation. We also define an all-pairs version for the problem and give a strongly polynomial truly subcubic algorithm for it. Finally, we discuss an extension of the problem in which one also has prices on trip segments and one wishes to find a cheapest valid itinerary.", acknowledgement = ack-nhfb, articleno = "70", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2010:HDU, author = "Pankaj K. Agarwal and Sariel Har-Peled and Micha Sharir and Yusu Wang", title = "{Hausdorff} distance under translation for points and balls", journal = j-TALG, volume = "6", number = "4", pages = "71:1--71:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824791", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the shape matching problem under the Hausdorff distance and its variants. In the first part of the article, we consider two sets $A$, $B$ of balls in $ R^d$, $ d = 2, 3$, and wish to find a translation t that minimizes the Hausdorff distance between $ A + t$, the set of all balls in $A$ shifted by $t$, and $B$. We consider several variants of this problem. First, we extend the notion of Hausdorff distance from sets of points to sets of balls, so that each ball has to be matched with the nearest ball in the other set. We also consider the problem in the standard setting, by computing the Hausdorff distance between the unions of the two sets (as point sets). Second, we consider either all possible translations $t$ (as is the standard approach), or consider only translations that keep the balls of $ A + t$ disjoint from those of $B$. We propose several exact and approximation algorithms for these problems. In the second part of the article, we note that the Hausdorff distance is sensitive to outliers, and thus consider two variants that are more robust: the root-mean-square (rms) and the summed Hausdorff distance. We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in $ R^d$. In order to obtain a fast algorithm for the summed Hausdorff distance, we propose a deterministic efficient dynamic data structure for maintaining an $ \epsilon $-approximation of the 1-median of a set of points in $ R^d$, under insertions and deletions.", acknowledgement = ack-nhfb, articleno = "71", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Carlsson:2010:FEC, author = "John Gunnar Carlsson and Benjamin Armbruster and Yinyu Ye", title = "Finding equitable convex partitions of points in a polygon efficiently", journal = j-TALG, volume = "6", number = "4", pages = "72:1--72:??", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1824777.1824792", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Previous work has developed algorithms for finding an equitable convex partition that partitions the plane into n convex pieces each containing an equal number of red and blue points. Motivated by a vehicle routing heuristic, we look at a related problem where each piece must contain one point and an equal fraction of the area of some convex polygon. We first show how algorithms for solving the older problem lead to approximate solutions for this new equitable convex partition problem. Then we demonstrate a new algorithm that finds an exact solution to our problem in $ O (N n \log N) $ time or operations, where n is the number of points, m the number of vertices or edges of the polygon, and $ N \colon = n + m $ the sum.", acknowledgement = ack-nhfb, articleno = "72", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Rutter:2010:CLM, author = "Ignaz Rutter and Alexander Wolff", title = "Computing large matchings fast", journal = j-TALG, volume = "7", number = "1", pages = "1:1--1:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868238", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/string-matching.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we present algorithms for computing large matchings in 3-regular graphs, graphs with maximum degree 3, and 3-connected planar graphs. The algorithms give a guarantee on the size of the computed matching and take linear or slightly superlinear time. Thus they are faster than the best-known algorithm for computing maximum matchings in general graphs, which runs in $ O(\sqrt {n m}) $ time, where $n$ denotes the number of vertices and $m$ the number of edges of the given graph. For the classes of 3-regular graphs and graphs with maximum degree 3, the bounds we achieve are known to be best possible. We also investigate graphs with block trees of bounded degree, where the $d$-block tree is the adjacency graph of the $d$-connected components of the given graph. In 3-regular graphs and 3-connected planar graphs with bounded-degree 2- and 4-block trees, respectively, we show how to compute maximum matchings in slightly superlinear time.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Iwama:2010:AAS, author = "Kazuo Iwama and Shuichi Miyazaki and Hiroki Yanagisawa", title = "Approximation algorithms for the sex-equal stable marriage problem", journal = j-TALG, volume = "7", number = "1", pages = "2:1--2:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868239", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The stable marriage problem is a classical matching problem introduced by Gale and Shapley. It is known that for any instance, there exists a solution, and there is a polynomial time algorithm to find one. However, the matching obtained by this algorithm is man-optimal, that is, the matching is favorable for men but unfavorable for women, (or, if we exchange the roles of men and women, the resulting matching is woman-optimal). The sex-equal stable marriage problem, posed by Gusfield and Irving, seeks a stable matching ``fair'' for both genders. Specifically it seeks a stable matching with the property that the sum of the men's scores is as close as possible to that of the women's. This problem is known to be strongly NP-hard. In this paper, we give a polynomial time algorithm for finding a near optimal solution for the sex-equal stable marriage problem. Furthermore, we consider the problem of optimizing an additional criterion: among stable matchings that are near optimal in terms of the sex-equality, find a minimum egalitarian stable matching. We show that this problem is strongly NP-hard, and give a polynomial time algorithm whose approximation ratio is less than two.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Djidjev:2010:FAC, author = "Hristo N. Djidjev", title = "A faster algorithm for computing the girth of planar and bounded genus graphs", journal = j-TALG, volume = "7", number = "1", pages = "3:1--3:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868240", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The girth of a graph $G$ is the length of a shortest cycle of $G$. In this article we design an $ O(n^{5 / 4} \log n)$ algorithm for finding the girth of an undirected $n$-vertex planar graph, the first $ o(n^2)$ algorithm for this problem. We also extend our results for the class of graphs embedded into an orientable surface of small genus. Our approach uses several techniques such as graph partitioning, hammock decomposition, graph covering, and dynamic shortest-path computation. We discuss extensions and generalizations of our result.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baier:2010:LBC, author = "Georg Baier and Thomas Erlebach and Alexander Hall and Ekkehard K{\"o}hler and Petr Kolman and Ondrej Pangr{\'a}c and Heiko Schilling and Martin Skutella", title = "Length-bounded cuts and flows", journal = j-TALG, volume = "7", number = "1", pages = "4:1--4:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868241", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a given number $L$, an $L$-length-bounded edge-cut (node-cut, respectively) in a graph $G$ with source $s$ and sink $t$ is a set $C$ of edges (nodes, respectively) such that no $s$--$t$-path of length at most $L$ remains in the graph after removing the edges (nodes, respectively) in $C$. An $L$-length-bounded flow is a flow that can be decomposed into flow paths of length at most $L$. In contrast to classical flow theory, we describe instances for which the minimum $L$-length-bounded edge-cut (node-cut, respectively) is $ \Theta (n^{2 / 3})$-times $ (\Theta (\sqrt {n}))$-times, respectively larger than the maximum $L$ length-bounded flow, where n denotes the number of nodes; this is the worst case. We show that the minimum length-bounded cut problem is NP -hard to approximate within a factor of $ 1.1377$ for $ L \geq 5$ in the case of node-cuts and for $ L \geq 4$ in the case of edge-cuts. We also describe algorithms with approximation ratio $ O(\min \{ L, n / L \}) \subseteq O (\sqrt {n})$ in the node case and $ O (\min \{ L, n^2 / L^2, \sqrt {m} \}) \subseteq O(n^{2 / 3})$ in the edge case, where $m$ denotes the number of edges. Concerning $L$ length-bounded flows, we show that in graphs with unit-capacities and general edge lengths it is NP complete to decide whether there is a fractional length-bounded flow of a given value. We analyze the structure of optimal solutions and present further complexity results.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baswana:2010:ASS, author = "Surender Baswana and Telikepalli Kavitha and Kurt Mehlhorn and Seth Pettie", title = "Additive spanners and $ (\alpha, \beta)$-spanners", journal = j-TALG, volume = "7", number = "1", pages = "5:1--5:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868242", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An $ (\alpha, \beta)$-spanner of an unweighted graph $G$ is a subgraph $H$ that distorts distances in $G$ up to a multiplicative factor of $ \alpha $ and an additive term $ \beta $. It is well known that any graph contains a (multiplicative) $ (2 k - 1, 0)$-spanner of size $ O (n^{1 + 1 / k})$ and an (additive) $ (1, 2)$-spanner of size $ O (n^{3 / 2})$. However no other additive spanners are known to exist. In this article we develop a couple of new techniques for constructing $ (\alpha, \beta)$-spanners. Our first result is an additive (1,6)-spanner of size $ O (n^{4 / 3})$. The construction algorithm can be understood as an economical agent that assigns costs and values to paths in the graph, purchasing affordable paths and ignoring expensive ones, which are intuitively well approximated by paths already purchased. We show that this path buying algorithm can be parameterized in different ways to yield other sparseness-distortion tradeoffs. Our second result addresses the problem of which $ (\alpha, \beta)$-spanners can be computed efficiently, ideally in linear time. We show that, for any $k$, a $ (k, k - 1)$-spanner with size $ O (k n^{1 + 1 / k})$ can be found in linear time, and, further, that in a distributed network the algorithm terminates in a constant number of rounds. Previous spanner constructions with similar performance had roughly twice the multiplicative distortion.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Flammini:2010:BSP, author = "Michele Flammini and Gaia Nicosia", title = "On the bicriteria $k$-server problem", journal = j-TALG, volume = "7", number = "1", pages = "6:1--6:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868244", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we consider multicriteria formulations of classical online problems in which an algorithm must simultaneously perform well with respect to two different cost measures. Every strategy for serving a sequence of requests is characterized by a pair of costs and therefore there can be many different minimal or optimal incomparable solutions. The adversary is assumed to choose from one of these minimal strategies and the performance of the algorithm is measured with respect to the costs the adversary pays servicing the sequence according to its determined choice of strategy. We consider a parametric family of functions which includes all the possible selections for such strategies. Then, starting from a simple general method that combines any multicriteria instance into a single-criterion one, we provide a universal multicriteria algorithm that can be applied to different online problems. In the multicriteria k-server formulation with two different edge weightings, for each function class, such a universal algorithm achieves competitive ratios that are only an O (log W) multiplicative factor away from the corresponding determined lower bounds, where W is the maximum ratio between the two weights associated to each edge. We then extend our results to two specific functions, for which nearly optimal competitive algorithms are obtained by exploiting more knowledge of the selection properties. Finally, we show how to apply our framework to other multicriteria online problems sharing similar properties.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Epstein:2010:OUC, author = "Leah Epstein and Rob {Van Stee}", title = "On the online unit clustering problem", journal = j-TALG, volume = "7", number = "1", pages = "7:1--7:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868245", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We continue the study of the online unit clustering problem, introduced by Chan and Zarrabi-Zadeh ( Workshop on Approximation and Online Algorithms 2006, LNCS 4368, p. 121--131. Springer, 2006). We design a deterministic algorithm with a competitive ratio of 7/4 for the one-dimensional case. This is the first deterministic algorithm that beats the bound of 2. It also has a better competitive ratio than the previous randomized algorithms. Moreover, we provide the first non-trivial deterministic lower bound, improve the randomized lower bound, and prove the first lower bounds for higher dimensions.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gao:2010:CLH, author = "Jie Gao and Michael Langberg and Leonard J. Schulman", title = "Clustering lines in high-dimensional space: Classification of incomplete data", journal = j-TALG, volume = "7", number = "1", pages = "8:1--8:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868246", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A set of k balls B$_1$, \ldots{}, B$_k$ in a Euclidean space is said to cover a collection of lines if every line intersects some ball. We consider the k --- center problem for lines in high-dimensional space: Given a set of n lines $^l$ = { l$_1$,\ldots{}, l$_n$ in R$^d$, find k balls of minimum radius which cover l. We present a 2-approximation algorithm for the cases k = 2, 3 of this problem, having running time quasi-linear in the number of lines and the dimension of the ambient space. Our result for 3-clustering is strongly based on a new result in discrete geometry that may be of independent interest: a Helly-type theorem for collections of axis-parallel ``crosses'' in the plane. The family of crosses does not have finite Helly number in the usual sense. Our Helly theorem is of a new type: it depends on $ \epsilon $-contracting the sets. In statistical practice, data is often incompletely specified; we consider lines as the most elementary case of incompletely specified data points. Clustering of data is a key primitive in nonparametric statistics. Our results provide a way of performing this primitive on incomplete data, as well as imputing the missing values.}", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cook:2010:GFD, author = "Atlas F. {Cook IV} and Carola Wenk", title = "Geodesic {Fr{\'e}chet} distance inside a simple polygon", journal = j-TALG, volume = "7", number = "1", pages = "9:1--9:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868247", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present an alternative to parametric search that applies to both the nongeodesic and geodesic Fr{\'e}chet optimization problems. This randomized approach is based on a variant of red-blue intersections and is appealing due to its elegance and practical efficiency when compared to parametric search. We introduce the first algorithm to compute the geodesic Fr{\'e}chet distance between two polygonal curves A and B inside a simple bounding polygon P. The geodesic Fr{\'e}chet decision problem is solved almost as fast as its nongeodesic sibling in $ O (N^2 \log k) $ time and $ O (k + N) $ space after $ O(k) $ preprocessing, where $N$ is the larger of the complexities of $A$ and $B$ and $k$ is the complexity of $P$. The geodesic Fr{\'e}chet optimization problem is solved by a randomized approach in $ O (k + N^2 \log k N \log N)$ expected time and $ O (k + N^2)$ space. This runtime is only a logarithmic factor larger than the standard nongeodesic Fr{\'e}chet algorithm [Alt and Godau 1995]. Results are also presented for the geodesic Fr{\'e}chet distance in a polygonal domain with obstacles and the geodesic Hausdorff distance for sets of points or sets of line segments inside a simple polygon P.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ferragina:2010:CPI, author = "Paolo Ferragina and Rossano Venturini", title = "The compressed permuterm index", journal = j-TALG, volume = "7", number = "1", pages = "10:1--10:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868248", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Permuterm index [Garfield 1976] is a time-efficient and elegant solution to the string dictionary problem in which pattern queries may possibly include one wild-card symbol (called Tolerant Retrieval problem). Unfortunately the Permuterm index is space inefficient because it quadruples the dictionary size. In this article we propose the Compressed Permuterm Index which solves the Tolerant Retrieval problem in time proportional to the length of the searched pattern, and space close to the $k$ th order empirical entropy of the indexed dictionary. We also design a dynamic version of this index that allows to efficiently manage insertion in, and deletion from, the dictionary of individual strings. The result is based on a simple variant of the Burrows--Wheeler Transform, defined on a dictionary of strings of variable length, that allows to efficiently solve the Tolerant Retrieval problem via known (dynamic) compressed indexes [Navarro and M{\"a}kinen 2007]. We will complement our theoretical study with a significant set of experiments that show that the Compressed Permuterm Index supports fast queries within a space occupancy that is close to the one achievable by compressing the string dictionary via gzip or bzip. This improves known approaches based on Front-Coding [Witten et al. 1999] by more than 50\% in absolute space occupancy, still guaranteeing comparable query time.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2010:EBU, author = "Pankaj K. Agarwal and Lars Arge and Ke Yi", title = "{I/O}-efficient batched union--find and its applications to terrain analysis", journal = j-TALG, volume = "7", number = "1", pages = "11:1--11:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868249", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we present an I/O-efficient algorithm for the batched (off-line) version of the union-find problem. Given any sequence of $N$ union and find operations, where each union operation joins two distinct sets, our algorithm uses $ O (\SORT (N)) = O (\frac N B \log_{M / B} \frac N B)$ I/Os, where $M$ is the memory size and $B$ is the disk block size. This bound is asymptotically optimal in the worst case. If there are union operations that join a set with itself, our algorithm uses $ O (\SORT (N) + \MST (N))$ I/Os, where $ \MST (N)$ is the number of I/Os needed to compute the minimum spanning tree of a graph with N edges. We also describe a simple and practical $ O (\SORT (N) \log (\frac N M))$-I/O algorithm for this problem, which we have implemented. We are interested in the union-find problem because of its applications in terrain analysis. A terrain can be abstracted as a height function defined over $ R^2$, and many problems that deal with such functions require a union-find data structure. With the emergence of modern mapping technologies, huge amount of elevation data is being generated that is too large to fit in memory, thus I/O-efficient algorithms are needed to process this data efficiently. In this article, we study two terrain-analysis problems that benefit from a union-find data structure: (i) computing topological persistence and (ii) constructing the contour tree. We give the first $ O(\SORT (N))$-I/O algorithms for these two problems, assuming that the input terrain is represented as a triangular mesh with $N$ vertices.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Goel:2010:HPE, author = "Ashish Goel and Sudipto Guha and Kamesh Munagala", title = "How to probe for an extreme value", journal = j-TALG, volume = "7", number = "1", pages = "12:1--12:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868250", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In several systems applications, parameters such as load are known only with some associated uncertainty, which is specified, or modeled, as a distribution over values. The performance of the system optimization and monitoring schemes can be improved by spending resources such as time or bandwidth in observing or resolving the values of these parameters. In a resource-constrained situation, deciding which parameters to observe in order to best optimize the expected system performance (or in general, optimize the expected value of a certain objective function) itself becomes an interesting optimization problem. In this article, we initiate the study of such problems that we term ``model-driven optimization''. In particular, we study the problem of optimizing the minimum value in the presence of observable distributions. We show that this problem is NP-Hard, and present greedy algorithms with good performance bounds. The proof of the performance bounds are via novel sub-modularity arguments and connections to covering integer programs.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Caragiannis:2010:TLA, author = "Ioannis Caragiannis and Christos Kaklamanis and Panagiotis Kanellopoulos", title = "Taxes for linear atomic congestion games", journal = j-TALG, volume = "7", number = "1", pages = "13:1--13:??", month = nov, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1868237.1868251", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 1 15:37:27 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study congestion games where players aim to access a set of resources. Each player has a set of possible strategies and each resource has a function associating the latency it incurs to the players using it. Players are non--cooperative and each wishes to follow a strategy that minimizes her own latency with no regard to the global optimum. Previous work has studied the impact of this selfish behavior on system performance. In this article, we study the question of how much the performance can be improved if players are forced to pay taxes for using resources. Our objective is to extend the original game so that selfish behavior does not deteriorate performance. We consider atomic congestion games with linear latency functions and present both negative and positive results. Our negative results show that optimal system performance cannot be achieved even in very simple games. On the positive side, we show that there are ways to assign taxes that can improve the performance of linear congestion games by forcing players to follow strategies where the total latency suffered is within a factor of 2 of the minimum possible; this result is shown to be tight. Furthermore, even in cases where in the absence of taxes the system behavior may be very poor, we show that the total disutility of players (latency plus taxes) is not much larger than the optimal total latency. Besides existential results, we show how to compute taxes in time polynomial in the size of the game by solving convex quadratic programs. Similar questions have been extensively studied in the model of non-atomic congestion games. To the best of our knowledge, this is the first study of the efficiency of taxes in atomic congestion games.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Georgiadis:2011:DSM, author = "Loukas Georgiadis and Haim Kaplan and Nira Shafrir and Robert E. Tarjan and Renato F. Werneck", title = "Data structures for mergeable trees", journal = j-TALG, volume = "7", number = "2", pages = "14:1--14:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921660", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Motivated by an application in computational geometry, we consider a novel variant of the problem of efficiently maintaining a forest of dynamic rooted trees. This variant includes an operation that merges two tree paths. In contrast to the standard problem, in which a single operation can only add or delete one arc, one merge can add and delete up to a linear number of arcs. In spite of this, we develop three different methods that need only polylogarithmic time per operation. The first method extends a solution of Farach and Thorup [1998] for the special case of paths. Each merge takes {$ O(\log^2 n) $} amortized time on an {$n$}-node forest and each standard dynamic tree operation takes {$ O(\log n) $} time; the latter bound is amortized, worst case, or randomized depending on the underlying data structure. For the special case that occurs in the motivating application, in which arbitrary arc deletions (cuts) do not occur, we give a method that takes {$ O(\log n) $} time per operation, including merging. This is best possible in a model of computation with an {$ \Omega (n \log n) $} lower bound for sorting {$n$} numbers, since such sorting can be done in {$ O(n) $} tree operations. For the even-more-special case in which there are no cuts and no parent queries, we give a method that uses standard dynamic trees as a black box: each mergeable tree operation becomes a constant number of standard dynamic tree operations. This third method can also be used in the motivating application, but only by changing the algorithm in the application. Each of our three methods needs different analytical tools and reveals different properties of dynamic trees.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chakaravarthy:2011:DTE, author = "Venkatesan T. Chakaravarthy and Vinayaka Pandit and Sambuddha Roy and Pranjal Awasthi and Mukesh K. Mohania", title = "Decision trees for entity identification: {Approximation} algorithms and hardness results", journal = j-TALG, volume = "7", number = "2", pages = "15:1--15:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921661", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of constructing decision trees for entity identification from a given relational table. The input is a table containing information about a set of entities over a fixed set of attributes and a probability distribution over the set of entities that specifies the likelihood of the occurrence of each entity. The goal is to construct a decision tree that identifies each entity unambiguously by testing the attribute values such that the average number of tests is minimized. This classical problem finds such diverse applications as efficient fault detection, species identification in biology, and efficient diagnosis in the field of medicine. Prior work mainly deals with the special case where the input table is binary and the probability distribution over the set of entities is uniform. We study the general problem involving arbitrary input tables and arbitrary probability distributions over the set of entities. We consider a natural greedy algorithm and prove an approximation guarantee of {$ O(r_K \cdot \log N) $}, where {$N$} is the number of entities and {$K$} is the maximum number of distinct values of an attribute. The value {$ r_K $} is a suitably defined Ramsey number, which is at most {$ \log K $}. We show that it is NP-hard to approximate the problem within a factor of {$ \Omega (\log N) $}, even for binary tables (i.e., {$ K = 2 $}). Thus, for the case of binary tables, our approximation algorithm is optimal up to constant factors (since {$ r_2 = 2 $}). In addition, our analysis indicates a possible way of resolving a Ramsey-theoretic conjecture by Erd{\H{o}}s.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jacobs:2011:CFA, author = "Tobias Jacobs", title = "Constant factor approximations for the hotlink assignment problem", journal = j-TALG, volume = "7", number = "2", pages = "16:1--16:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921662", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The concept of hotlink assignment aims at reducing the navigation effort for the users of a Web directory or similar structure by inserting a limited number of additional hyperlinks called hotlinks. The $k$-hotlink assignment problem denotes the task of adding at most $k$ outgoing hotlinks to each page of a tree-like site, minimizing the path length, that is, the expected number of ``clicks'' necessary for the user to reach her destination page. Another common formulation of this problem is to maximize the gain, that is, the path length reduction achieved by the assignment. In this work we analyze the natural greedy strategy, proving that it reaches the optimal gain up to the constant factor of 2. Considering the gain, we also prove the existence of a PTAS. Finally, we give a polynomial-time 2-approximation for the 1-hotlink assignment problem, which constitutes the first constant factor approximation in terms of the path length. The algorithms' performance analyses are made possible by a set of three new basic operations for the transformation of hotlink assignments.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ambuhl:2011:TEL, author = "Christoph Amb{\"u}hl and Leszek Gasieniec and Andrzej Pelc and Tomasz Radzik and Xiaohui Zhang", title = "Tree exploration with logarithmic memory", journal = j-TALG, volume = "7", number = "2", pages = "17:1--17:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921663", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the task of network exploration by a mobile agent (robot) with small memory. The agent has to traverse all nodes and edges of a network (represented as an undirected connected graph), and return to the starting node. Nodes of the network are unlabeled and edge ports are locally labeled at each node. The agent has no a priori knowledge of the topology of the network or of its size, and cannot mark nodes in any way. Under such weak assumptions, cycles in the network may prevent feasibility of exploration, hence we restrict attention to trees. We present an algorithm to accomplish tree exploration (with return) using {$ O(\log n) $}-bit memory for all {$n$}-node trees. This strengthens the result from Diks et al. [2004], where {$ O(\log^2 n) $}-bit memory was used for tree exploration, and matches the lower bound on memory size proved there. We also extend our {$ O(\log n) $}-bit memory traversal mechanism to a weaker model in which ports at each node are ordered in circular manner, however, the explicit values of port numbers are not available.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chekuri:2011:SCP, author = "Chandra Chekuri and Guy Even and Anupam Gupta and Danny Segev", title = "Set connectivity problems in undirected graphs and the directed {Steiner} network problem", journal = j-TALG, volume = "7", number = "2", pages = "18:1--18:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921664", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the generalized connectivity problem, we are given an edge-weighted graph {$ G = (V, E) $} and a collection {$ D = \{ (S_1, T_1), \ldots {}, (S_k, T_k) \} $} of distinct demands each demand {$ (S_i, T_i) $} is a pair of disjoint vertex subsets. We say that a subgraph {$F$} of {$G$} connects a demand {$ (S_i, T_i) $} when it contains a path with one endpoint in {$ S_i $} and the other in {$ T_i $}. The goal is to identify a minimum weight subgraph that connects all demands in D. Alon et al. (SODA '04) introduced this problem to study online network formation settings and showed that it captures some well-studied problems such as Steiner forest, facility location with nonmetric costs, tree multicast, and group Steiner tree. Obtaining a nontrivial approximation ratio for generalized connectivity was left as an open problem. We describe the first poly-logarithmic approximation algorithm for generalized connectivity that has a performance guarantee of {$ O(\log^2 n \log^2 k) $}. Here, {$n$} is the number of vertices in {$G$} and {$k$} is the number of demands. We also prove that the cut-covering relaxation of this problem has an {$ O(\log^3 n \log^2 k) $} integrality gap. Building upon the results for generalized connectivity, we obtain improved approximation algorithms for two problems that contain generalized connectivity as a special case. For the directed Steiner network problem, we obtain an {$ O(k^{1 / 2 + \epsilon }) $} approximation which improves on the currently best performance guarantee of {$ \tilde {O}(k^{2 / 3}) $} due to Charikar et al. (SODA '98). For the set connector problem, recently introduced by Fukunaga and Nagamochi (IPCO '07), we present a poly-logarithmic approximation; this result improves on the previously known ratio which can be {$ \Omega (n) $} in the worst case.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{DeVerdiere:2011:SVD, author = "{\'E}ric Colin {De Verdi{\`e}re} and Alexander Schrijver", title = "Shortest vertex-disjoint two-face paths in planar graphs", journal = j-TALG, volume = "7", number = "2", pages = "19:1--19:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921665", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$G$} be a directed planar graph of complexity {$n$}, each arc having a nonnegative length. Let {$s$} and {$t$} be two distinct faces of {$G$} let {$ s_1, \ldots {}, s_k $} be vertices incident with {$s$} let {$ t_1, \ldots {}, t_k $} be vertices incident with $t$. We give an algorithm to compute $k$ pairwise vertex-disjoint paths connecting the pairs $ (s_i, t_i) $ in {$G$}, with minimal total length, in {$ O(k n \log n) $} time.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2011:SFD, author = "Michael Elkin", title = "Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners", journal = j-TALG, volume = "7", number = "2", pages = "20:1--20:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921666", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a streaming algorithm for constructing sparse spanners and show that our algorithm significantly outperforms the state-of-the-art algorithm for this task (due to Feigenbaum et al.). Specifically, the processing time per edge of our algorithm is {$ O(1) $}, and it is drastically smaller than that of the algorithm of Feigenbaum et al., and all other efficiency parameters of our algorithm are no greater (and some of them are strictly smaller) than the respective parameters of the state-of-the-art algorithm. We also devise a fully dynamic centralized algorithm maintaining sparse spanners. This algorithm has incremental update time of {$ O(1) $}, and a nontrivial decremental update time. To our knowledge, this is the first fully dynamic centralized algorithm for maintaining sparse spanners that provides nontrivial bounds on both incremental and decremental update time for a wide range of stretch parameter {$t$}.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cormode:2011:ADF, author = "Graham Cormode and S. Muthukrishnan and Ke Yi", title = "Algorithms for distributed functional monitoring", journal = j-TALG, volume = "7", number = "2", pages = "21:1--21:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921667", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider the following problem: We have $k$ players each receiving a stream of items, and communicating with a central coordinator. Let the multiset of items received by player $i$ up until time $t$ be {$ A_i(t) $}. The coordinator's task is to monitor a given function {$f$} computed over the union of the inputs {$ \cup_i A_i(t) $}, continuously at all times {$t$}. The goal is to minimize the number of bits communicated between the players and the coordinator. Of interest is the approximate version where the coordinator outputs {$1$} if {$ f \geq \tau $} and $0$ if $ f \leq (1 - \epsilon) \tau $. This defines the $ (k, f, \tau, \epsilon) $ distributed functional monitoring problem. Functional monitoring problems are fundamental in distributed systems, in particular sensor networks, where we must minimize communication; they also connect to the well-studied streaming model and communication complexity. Yet few formal bounds are known for functional monitoring. We give upper and lower bounds for the $ (k, f, \tau, \epsilon) $ problem for some of the basic $f$'s. In particular, we study the frequency moments F$_p$ for $ p = 0, 1, 2 $. For {$ F_0 $} and {$ F_1 $}, we obtain monitoring algorithms with cost almost the same as algorithms that compute the function for a single instance of time. However, for {$ F_2 $} the monitoring problem seems to be much harder than computing the function for a single time instance. We give a carefully constructed multiround algorithm that uses ``sketch summaries'' at multiple levels of details and solves the {$ (k, F_2, \tau, \epsilon) $} problem with communication {$ \tilde {O} (k^2 / \epsilon + k^{3 / 2} / \epsilon^3) $}. Our algorithmic techniques are likely to be useful for other functional monitoring problems as well.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Halldorsson:2011:SEC, author = "Magn{\'u}s M. Halld{\'o}rsson and Guy Kortsarz and Maxim Sviridenko", title = "Sum edge coloring of multigraphs via configuration {LP}", journal = j-TALG, volume = "7", number = "2", pages = "22:1--22:21", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921668", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the scheduling of biprocessor jobs under sum objective (BPSMSM). Given a collection of unit-length jobs where each job requires the use of two processors, find a schedule such that no two jobs involving the same processor run concurrently. The objective is to minimize the sum of the completion times of the jobs. Equivalently, we would like to find a sum edge coloring of a given multigraph, that is, a partition of its edge set into matchings {$ M_1 $}, \ldots {}, {$ M_t $} minimizing {$ \Sigma_{i = 1}^t i |M_i| $}.\par This problem is APX-hard, even in the case of bipartite graphs [Marx 2009]. This special case is closely related to the classic open shop scheduling problem. We give a 1.8298-approximation algorithm for BPSMSM improving the previously best ratio known of 2 [Bar-Noy et al. 1998]. The algorithm combines a configuration LP with greedy methods, using nonstandard randomized rounding on the LP fractions. We also give an efficient combinatorial 1.8886-approximation algorithm for the case of simple graphs, which gives an improved {$ 1.79568 + O(\log \bar {d} / \bar {d}) $}-approximation in graphs of large average degree {$ \bar {d} $}.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ben-Aroya:2011:CAF, author = "Avraham Ben-Aroya and Sivan Toledo", title = "Competitive analysis of flash memory algorithms", journal = j-TALG, volume = "7", number = "2", pages = "23:1--23:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921669", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Flash memories are widely used in computer systems ranging from embedded systems to workstations and servers to digital cameras and mobile phones. The memory cells of flash devices can only endure a limited number of write cycles, usually between 10,000 and 1,000,000. Furthermore, cells containing data must be erased before they can store new data, and erasure operations erase large blocks of memory, not individual cells. To maximize the endurance of the device (the amount of useful data that can be written to it before one of its cells wears out), flash-based systems move data around in an attempt to reduce the total number of erasures and to level the wear of the different erase blocks. This data movement introduces an interesting online problem called the wear-leveling problem. Wear-leveling algorithms have been used at least since 1993, but they have never been mathematically analyzed. In this article we analyze the two main wear-leveling problems. We show that a simple randomized algorithm for one of them is essentially optimal both in the competitive sense and in the absolute sense (our competitive result relies on an analysis of a nearly-optimal offline algorithm). We show that deterministic algorithms cannot achieve comparable endurance. We also analyze a more difficult problem and show that offline algorithms for it can improve upon naive approaches, but that online algorithms essentially cannot.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aumann:2011:FWP, author = "Yonatan Aumann and Moshe Lewenstein and Noa Lewenstein and Dekel Tsur", title = "Finding witnesses by peeling", journal = j-TALG, volume = "7", number = "2", pages = "24:1--24:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921670", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the $k$-matches problem, we are given a pattern and a text, and for each text location, the desired output consists of all aligned matching characters if there are $k$ or fewer of them, and any $k$ aligned matching characters if there are more than $k$ of them. This problem is one of several string matching problems that seek not only to find where the pattern matches the text under different ``match'' definitions, but also to provide witnesses to the match. Other such problems include $k$-aligned ones, $k$-witnesses, and $k$-mismatches. In addition, the solutions to several other string matching problems rely on the efficient solutions of the witness finding problems. In this article we provide a general method for solving such witness finding problems efficiently. We do so by casting the problem as a generalization of group testing, which we then solve by a process we call peeling. Using this general framework we obtain improved results for all of the problems mentioned. We also show that our method also solves a couple of problems outside the pattern matching domain.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Choi:2011:CPM, author = "Yongwook Choi and Wojciech Szpankowski", title = "Constrained pattern matching", journal = j-TALG, volume = "7", number = "2", pages = "25:1--25:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921671", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Constrained sequences are strings satisfying certain additional structural restrictions (e.g., some patterns are forbidden). They find applications in communication, digital recording, and biology. In this article, we restrict our attention to the so-called $ (d, k) $ constrained binary sequences in which any run of zeros must be of length at least $d$ and at most $k$, where $ 0 \leq d < k $. In many applications, one needs to know the number of occurrences of a given pattern $w$ in such sequences, for which we coin the term constrained pattern matching. For a given word $w$, we first estimate the mean and the variance of the number of occurrences of $w$ in a $ (d, k) $ sequence generated by a memoryless source. Then we present the central limit theorem and large deviations results. As a by-product, we enumerate asymptotically the number of $ (d, k) $ sequences with exactly $r$ occurrences of $w$, and compute Shannon entropy of $ (d, k) $ sequences with a given number of occurrences of $w$. We also apply our results to detect under- and overrepresented patterns in neuronal data (spike trains), which satisfy structural constraints that match the framework of $ (d, k) $ binary sequences. Throughout this article we use techniques of analytic combinatorics such as combinatorial calculus, generating functions, and complex asymptotics.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fu:2011:DAH, author = "Bin Fu and Ming-Yang Kao and Lusheng Wang", title = "Discovering almost any hidden motif from multiple sequences", journal = j-TALG, volume = "7", number = "2", pages = "26:1--26:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921672", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study a natural probabilistic model for motif discovery. In this model, there are $k$ background sequences, and each character in a background sequence is a random character from an alphabet {$ \Sigma $}. A motif {$ G = g_1, g_2, \ldots {}, g_m $} is a string of {$m$} characters. Each background sequence is implanted with a probabilistically generated approximate copy of {$G$}. For a probabilistically generated approximate copy {$ b_1, b_2, \ldots {}, b_m $} of {$G$}, every character is probabilistically generated such that the probability for {$ b_i \neq g_i $} is at most {$ \alpha $}. In this article, we develop an efficient algorithm that can discover a hidden motif from a set of sequences for any alphabet {$ \Sigma $} with {$ | \Sigma | \geq 2 $} and is applicable to DNA motif discovery. We prove that for {$ \alpha < 1 / 8 (1 - 1 / | \Sigma |) $}, there exist positive constants {$ c_0 $}, {$ \epsilon $}, and {$ \delta_2 $} such that if there are at least $ c_0 \log n $ input sequences, then in {$ O(n^2 / h (\log n)^{O(1)}) $} time this algorithm finds the motif with probability at least {$ 3 / 4 $} for every {$ G \in \Sigma^\rho - \Psi_{\rho, h, \epsilon }(\Sigma) $}, where {$n$} the length of longest sequences, {$ \rho $} is the length of the motif, {$h$} is a parameter with $ \rho \geq 4 h \geq \delta_2 \log n $, and {$ \Psi_{\rho, h, \epsilon }(\Sigma) $} is a small subset of at most {$ 2^{ - \Theta (\epsilon^2 h)} $} fraction of the sequences in {$ \Sigma^\rho $}.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Nong:2011:CIS, author = "Ge Nong and Sen Zhang and Wai Hong Chan", title = "Computing the {Inverse Sort Transform} in linear time", journal = j-TALG, volume = "7", number = "2", pages = "27:1--27:??", month = mar, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1921659.1921673", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:38 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Sort Transform (ST) can significantly speed up the block sorting phase of the Burrows-Wheeler Transform (BWT) by sorting the limited order contexts. However, the best result obtained so far for the inverse ST has a time complexity {$ O(N \log k) $} and a space complexity {$ O(N) $}, where {$N$} and {$k$} are the text size and the context order of the transform, respectively. In this article, we present a novel algorithm that can compute the inverse ST for any {$k$}-order contexts in an {$ O(N) $} time and space complexity, a linear result independent of {$k$}. The main idea behind the design of this linear algorithm is a set of cycle properties of {$k$}-order contexts that we explore for this work. These newly discovered cycle properties allow us to quickly compute the Longest Common Prefix (LCP) between any pair of adjacent {$k$}-order contexts that may belong to two different cycles, which eventually leads to the proposed linear-time solution.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Friggstad:2011:MMM, author = "Zachary Friggstad and Mohammad R. Salavatipour", title = "Minimizing movement in mobile facility location problems", journal = j-TALG, volume = "7", number = "3", pages = "28:1--28:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978783", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the mobile facility location problem, which is a variant of the classical facility location, each facility and client is assigned to a start location in a metric graph and our goal is to find a destination node for each client and facility such that every client is sent to a node which is the destination of some facility. The quality of a solution can be measured either by the total distance clients and facilities travel or by the maximum distance traveled by any client or facility. As we show in this article (by an approximation-preserving reduction), the problem of minimizing the total movement of facilities and clients generalizes the classical $k$-median problem. The class of movement problems was introduced by Demaine et al. [2007] where a simple 2-approximation was proposed for the minimum maximum movement mobile facility location problem while an approximation for the minimum total movement variant and hardness results for both were left as open problems. Our main result here is an 8-approximation algorithm for the minimum total movement mobile facility location problem. Our algorithm is obtained by rounding an LP relaxation in five phases. For the minimum maximum movement mobile facility location problem, we show that we cannot have a better than a 2-approximation for the problem, unless P = NP so the simple algorithm proposed by Demaine et al. [2007] is essentially best possible.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borodin:2011:HWC, author = "Allan Borodin and David Cashman and Avner Magen", title = "How well can primal-dual and local-ratio algorithms perform?", journal = j-TALG, volume = "7", number = "3", pages = "29:1--29:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978784", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We define an algorithmic paradigm, the stack model, that captures many primal-dual and local-ratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations and hence our approximation bounds are independent of the P versus NP question. Using the stack model, we bound the performance of a broad class of primal-dual and local-ratio algorithms and supply a $ (\log n + 1) / 2 $ inapproximability result for set cover, a $ 4 / 3 $ inapproximability for min Steiner tree, and a $ 0.913 $ inapproximability for interval scheduling on two machines.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chung:2011:CDK, author = "Kai-Min Chung and Omer Reingold and Salil Vadhan", title = "{S}-{T} connectivity on digraphs with a known stationary distribution", journal = j-TALG, volume = "7", number = "3", pages = "30:1--30:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978785", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a deterministic logspace algorithm for solving S-T Connectivity on directed graphs if: (i) we are given a stationary distribution of the random walk on the graph in which both of the input vertices $s$ and $t$ have nonnegligible probability mass and (ii) the random walk which starts at the source vertex $s$ has polynomial mixing time. This result generalizes the recent deterministic logspace algorithm for {$S$}--{$T$} Connectivity on undirected graphs [Reingold, 2008]. It identifies knowledge of the stationary distribution as the gap between the {$S$}--{$T$} Connectivity problems we know how to solve in logspace (L) and those that capture all of randomized logspace (RL).", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gairing:2011:RSF, author = "Martin Gairing and Burkhard Monien and Karsten Tiemann", title = "Routing (un-) splittable flow in games with player-specific affine latency functions", journal = j-TALG, volume = "7", number = "3", pages = "31:1--31:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978786", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this work we study weighted network congestion games with player-specific latency functions where selfish players wish to route their traffic through a shared network. We consider both the case of splittable and unsplittable traffic. Our main findings are as follows. For routing games on parallel links with linear latency functions, we introduce two new potential functions for unsplittable and for splittable traffic, respectively. We use these functions to derive results on the convergence to pure Nash equilibria and the computation of equilibria. For several generalizations of these routing games, we show that such potential functions do not exist. We prove tight upper and lower bounds on the price of anarchy for games with polynomial latency functions. All our results on the price of anarchy translate to general congestion games.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Rosen:2011:RVB, author = "Adi Ros{\'e}n and Gabriel Scalosub", title = "Rate vs. buffer size --- greedy information gathering on the line", journal = j-TALG, volume = "7", number = "3", pages = "32:1--32:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978787", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider packet networks with limited buffer space at the nodes, and are interested in the question of maximizing the number of packets that arrive to destination rather than being dropped due to full buffers. We initiate a more refined analysis of the throughput competitive ratio of admission and scheduling policies in the Competitive Network Throughput model [Aiello et al. 2005], taking into account not only the network size but also the buffer size and the injection rate of the traffic. We specifically consider the problem of information gathering on the line, with limited buffer space, under adversarial traffic. We examine how the buffer size and the injection rate of the traffic affect the performance of the greedy protocol for this problem. We establish upper bounds on the competitive ratio of the greedy protocol in terms of the network size, the buffer size, and the adversary's rate, and present lower bounds which are tight up to constant factors. These results show, for example, that provisioning the network with sufficiently large buffers may substantially improve the performance of the greedy protocol in some cases, whereas for some high-rate adversaries, using larger buffers does not have any effect on the competitive ratio of the protocol.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bonifaci:2011:MFT, author = "Vincenzo Bonifaci and Peter Korteweg and Alberto Marchetti-Spaccamela and Leen Stougie", title = "Minimizing flow time in the wireless gathering problem", journal = j-TALG, volume = "7", number = "3", pages = "33:1--33:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978788", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We address the problem of efficient data gathering in a wireless network through multihop communication. We focus on two objectives related to flow times, that is, the times spent by data packets in the system: minimization of the maximum flow time and minimization of the average flow time of the packets. For both problems we prove that, unless P = NP, no polynomial-time algorithm can approximate the optimal solution within a factor less than {$ \Omega (m^{1 - \epsilon }) $} for any {$ 0 < \epsilon < 1 $}, where {$m$} is the number of packets. We then assess the performance of two natural algorithms by proving that their cost remains within the optimal cost of the respective problem if we allow the algorithms to transmit data at a speed 5 times higher than that of the optimal solutions to which we compare them.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kranakis:2011:RRL, author = "Evangelos Kranakis and Danny Krizanc and Pat Morin", title = "Randomized rendezvous with limited memory", journal = j-TALG, volume = "7", number = "3", pages = "34:1--34:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978789", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a trade-off between the expected time for two identical agents to rendezvous on a synchronous, anonymous, oriented ring and the memory requirements of the agents. In particular, we show there exists a $ 2^t $ state agent which can achieve rendezvous on an $n$-node ring in expected time {$ O(n^2 / 2^t + 2^t) $} and that any {$ t / 2 $} state agent requires expected time {$ \Omega (n^2 / 2^t) $}. As a corollary we observe that {$ \Theta (\log \log n) $} bits of memory are necessary and sufficient to achieve rendezvous in linear time.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pemmaraju:2011:MCO, author = "Sriram V. Pemmaraju and Rajiv Raman and Kasturi Varadarajan", title = "Max-coloring and online coloring with bandwidths on interval graphs", journal = j-TALG, volume = "7", number = "3", pages = "35:1--35:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978790", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a graph $ G = (V, E) $ and positive integral vertex weights $ w \colon V \to N $, the max-coloring problem seeks to find a proper vertex coloring of $G$ whose color classes $ C_1, C_2, \ldots {}, C_k $, minimize $ \Sigma_i = 1^k \max_v \in C^i w(v) $. This problem, restricted to interval graphs, arises whenever there is a need to design dedicated memory managers that provide better performance than the general-purpose memory management of the operating system. Though this problem seems similar to the dynamic storage allocation problem, there are fundamental differences. We make a connection between max-coloring and online graph coloring and use this to devise a simple 2-approximation algorithm for max-coloring on interval graphs. We also show that a simple first-fit strategy, that is a natural choice for this problem, yields an 8-approximation algorithm. We show this result by proving that the first-fit algorithm for online coloring an interval graph $G$ uses no more than $ 8 c \chi (G) $ colors, significantly improving the bound of $ 26 c \chi (G) $ by Kierstead and Qin [1995]. We also show that the max-coloring problem is NP-hard. The problem of online coloring of intervals with bandwidths is a simultaneous generalization of online interval coloring and online bin packing. The input is a set $I$ of intervals, each interval $ i \in I $ having an associated bandwidth $ b(i) \in (0, 1] $. We seek an online algorithm that produces a coloring of the intervals such that for any color $c$ and any real $r$, the sum of the bandwidths of intervals containing $r$ and colored $c$ is at most $1$. Motivated by resource allocation problems, Adamy and Erlebach [2003] consider this problem and present an algorithm that uses at most 195 times the number of colors used by an optimal offline algorithm. Using the new analysis of first-fit coloring of interval graphs, we show that the Adamy-Erlebach algorithm is 35-competitive. Finally, we generalize the Adamy-Erlebach algorithm to a class of algorithms and show that a different instance from this class is 30-competitive.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Khuller:2011:FFG, author = "Samir Khuller and Azarakhsh Malekian and Juli{\'a}n Mestre", title = "To fill or not to fill: {The} gas station problem", journal = j-TALG, volume = "7", number = "3", pages = "36:1--36:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978791", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we study several routing problems that generalize shortest paths and the traveling salesman problem. We consider a more general model that incorporates the actual cost in terms of gas prices. We have a vehicle with a given tank capacity. We assume that at each vertex gas may be purchased at a certain price. The objective is to find the cheapest route to go from $s$ to $t$, or the cheapest tour visiting a given set of locations. We show that the problem of finding a cheapest plan to go from $s$ to $t$ can be solved in polynomial time. For most other versions, however, the problem is NP-complete and we develop polynomial-time approximation algorithms for these versions.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Coppersmith:2011:OOG, author = "Don Coppersmith and Tomasz Nowicki and Giuseppe Paleologo and Charles Tresser and Chai Wah Wu", title = "The optimality of the online greedy algorithm in carpool and chairman assignment problems", journal = j-TALG, volume = "7", number = "3", pages = "37:1--37:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978792", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study several classes of related scheduling problems including the carpool problem, its generalization to arbitrary inputs and the chairman assignment problem. We derive both lower and upper bounds for online algorithms solving these problems. We show that the greedy algorithm is optimal among online algorithms for the chairman assignment problem and the generalized carpool problem. We also consider geometric versions of these problems and show how the bounds adapt to these cases.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bille:2011:TIP, author = "Philip Bille and Inge Li Gortz", title = "The tree inclusion problem: {In} linear space and faster", journal = j-TALG, volume = "7", number = "3", pages = "38:1--38:47", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978793", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given two rooted, ordered, and labeled trees {$P$} and {$T$} the tree inclusion problem is to determine if {$P$} can be obtained from {$T$} by deleting nodes in {$T$}. This problem has recently been recognized as an important query primitive in XML databases. Kilpel{\"a}inen and Mannila [1995] presented the first polynomial-time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when {$P$} and {$T$} have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. Let {n$_S$}, {l$_S$}, and {d$_S$} denote the number of nodes, the number of leaves, and the depth of a tree {$ S \in P, T $}. In this article we show that the tree inclusion problem can be solved in space {$ O(n_T) $} and time: { $$ O(\min \left \{ l_P n_T, l_P n_T \log \log n_T + n_T, (n_P n_T) / (\log n_T) + n_T \log n_T \right \}) $$} This improves or matches the best known time complexities while using only linear space instead of quadratic. This is particularly important in practical applications, such as XML databases, where the space is likely to be a bottleneck.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Laber:2011:IAH, author = "Eduardo Laber and Marco Molinaro", title = "Improved approximations for the hotlink assignment problem", journal = j-TALG, volume = "7", number = "3", pages = "39:1--39:??", month = jul, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/1978782.1978794", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:40 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$ G = (V, E) $} be a graph representing a Web site, where nodes correspond to pages and arcs to hyperlinks. In this context, hotlinks are defined as shortcuts (new arcs) added to Web pages of {$G$} in order to reduce the time spent by users to reach their desired information. In this article, we consider the problem where {$G$} is a rooted directed tree and the goal is minimizing the expected time spent by users by assigning at most {$k$} hotlinks to each node. For the most studied version of this problem where at most one hotlink can be added to each node, we prove the existence of two FPTAS's which optimize different objectives considered in the literature: one minimizes the expected user path length and the other maximizes the expected reduction in user path lengths. These results improve over a constant factor approximation for the expected length and over a PTAS for the expected reduction, both obtained recently in Jacobs [2007]. Indeed, these FPTAS's are essentially the best possible results one can achieve under the assumption that P {$ \neq $} NP. Another contribution we give here is a 16-approximation algorithm for the most general version of the problem where up to {$k$} hotlinks can be assigned from each node. This algorithm runs in {$ O(|V| \log |V|) $} time and it turns to be the first algorithm with constant approximation for this problem.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Salvy:2011:PFF, author = "Bruno Salvy and Bob Sedgewick and Michele Soria and Wojciech Szpankowski and Brigitte Vallee", title = "{Philippe Flajolet}, the father of analytic combinatorics", journal = j-TALG, volume = "7", number = "4", pages = "40:1--40:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000808", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dvorak:2011:TCT, author = "Zdenek Dvor{\'a}k and Ken-Ichi Kawarabayashi and Robin Thomas", title = "Three-coloring triangle-free planar graphs in linear time", journal = j-TALG, volume = "7", number = "4", pages = "41:1--41:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000809", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Gr{\"o}tzsch's theorem states that every triangle-free planar graph is 3-colorable, and several relatively simple proofs of this fact were provided by Thomassen and other authors. It is easy to convert these proofs into quadratic-time algorithms to find a 3-coloring, but it is not clear how to find such a coloring in linear time (Kowalik used a nontrivial data structure to construct an {$ O(n \log n) $} algorithm). We design a linear-time algorithm to find a 3-coloring of a given triangle-free planar graph. The algorithm avoids using any complex data structures, which makes it easy to implement. As a by-product, we give a yet simpler proof of Gr{\"o}tzsch's theorem.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Moran:2011:PCR, author = "Shlomo Moran and Sagi Snir and Wing-Kin Sung", title = "Partial convex recolorings of trees and galled networks: {Tight} upper and lower bounds", journal = j-TALG, volume = "7", number = "4", pages = "42:1--42:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000810", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A coloring of a graph is convex if the vertices that pertain to any color induce a connected subgraph; a partial coloring (which assigns colors to a subset of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring has applications in fields such as phylogenetics, communication or transportation networks, etc. When a coloring of a graph is not convex, a natural question is how far it is from a convex one. This problem is denoted as convex recoloring (CR). While the initial works on CR defined and studied the problem on trees, recent efforts aim at either generalizing the underlying graphs or specializing the input colorings. In this work, we extend the underlying graph and the input coloring to partially colored galled networks. We show that although determining whether a coloring is convex on an arbitrary network is hard, it can be found efficiently on galled networks. We present a fixed parameter tractable algorithm that finds the recoloring distance of such a network whose running time is quadratic in the network size and exponential in that distance. This complexity is achieved by amortized analysis that uses a novel technique for contracting colored graphs that seems to be of independent interest.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cabello:2011:GCF, author = "Sergio Cabello and Panos Giannopoulos and Christian Knauer and D{\'a}niel Marx and G{\"u}nter Rote", title = "Geometric clustering: {Fixed-parameter} tractability and lower bounds with respect to the dimension", journal = j-TALG, volume = "7", number = "4", pages = "43:1--43:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000811", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the parameterized complexity of the $k$-center problem on a given $n$-point set {$P$} in {$ R^d $}, with the dimension {$d$} as the parameter. We show that the rectilinear 3-center problem is fixed-parameter tractable, by giving an algorithm that runs in {$ O(n \log n) $} time for any fixed dimension d. On the other hand, we show that this is unlikely to be the case with both the Euclidean and rectilinear {$k$}-center problems for any {$ k \geq 2 $} and {$ k \geq 4 $} respectively. In particular, we prove that deciding whether {$P$} can be covered by the union of 2 balls of given radius or by the union of 4 cubes of given side length is W[1]-hard with respect to {$d$}, and thus not fixed-parameter tractable unless FPT = W[1]. For the Euclidean case, we also show that even an {$ n^{o(d)} $}-time algorithm does not exist, unless there is a {2$^{o(n)}$}-time algorithm for $n$-variable 3SAT, that is, the Exponential Time Hypothesis fails.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bonsma:2011:TBF, author = "Paul Bonsma and Frederic Dorn", title = "Tight bounds and a fast {FPT} algorithm for directed {Max-Leaf Spanning Tree}", journal = j-TALG, volume = "7", number = "4", pages = "44:1--44:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000812", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An out-tree {$T$} of a directed graph {$D$} is a rooted tree subgraph with all arcs directed outwards from the root. An out-branching is a spanning out-tree. By {$ l(D) $} and {$ l_s(D) $}, we denote the maximum number of leaves over all out-trees and out-branchings of {$D$}, respectively. We give fixed parameter tractable algorithms for deciding whether {$ l_s(D) \geq k $} and whether {$ l(D) \geq k $} for a digraph {$D$} on {$n$} vertices, both with time complexity {$ 2^{o(k \log k)} \cdot n^{o(1)} $}. This answers an open question whether the problem for out-branchings is in FPT, and improves on the previous complexity of {$ 2^{o(k \log 2 k)} \cdot n^{o(1)} $} in the case of out-trees. To obtain the complexity bound in the case of out-branchings, we prove that when all arcs of {$D$} are part of at least one out-branching, {$ l_s(D) \geq l(D) / 3 $}. The second bound we prove in this article states that for strongly connected digraphs {$D$} with minimum in-degree {$ 3, l_s(D) \geq \Theta (\sqrt n) $}, where previously {$ l_s(D) \geq \Theta (3 \sqrt n) $} was the best known bound. This bound is tight, and also holds for the larger class of digraphs with minimum in-degree {$3$} in which every arc is part of at least one out-branching.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Roditty:2011:APS, author = "Liam Roditty and Asaf Shapira", title = "All-pairs shortest paths with a sublinear additive error", journal = j-TALG, volume = "7", number = "4", pages = "45:1--45:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000813", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that, for every $ 0 \leq p \leq 1 $, there is an {$ O(n^{2.575 - p / (7.4 - 2.3 p)}) $}-time algorithm that given a directed graph with small positive integer weights, estimates the length of the shortest path between every pair of vertices {$ u, v $} in the graph to within an additive error {$ \delta^p(u, v) $}, where {$ \delta (u, v) $} is the exact length of the shortest path between $u$ and $v$. This algorithm runs faster than the fastest algorithm for computing exact shortest paths for any $ 0 < p \leq 1 $. Previously the only way to ``beat'' the running time of the exact shortest path algorithms was by applying an algorithm of Zwick [2002] that approximates the shortest path distances within a multiplicative error of $ (1 + \epsilon) $. Our algorithm thus gives a smooth qualitative and quantitative transition between the fastest exact shortest paths algorithm, and the fastest approximation algorithm with a linear additive error. In fact, the main ingredient we need in order to obtain the above result, which is also interesting in its own right, is an algorithm for computing $ (1 + \epsilon) $ multiplicative approximations for the shortest paths, whose running time is faster than the running time of Zwick's approximation algorithm when $ \epsilon \ll 1 $ and the graph has small integer weights.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pritchard:2011:FCS, author = "David Pritchard and Ramakrishna Thurimella", title = "Fast computation of small cuts via cycle space sampling", journal = j-TALG, volume = "7", number = "4", pages = "46:1--46:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000814", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a new sampling-based method to determine cuts in an undirected graph. For a graph {$ (V, E) $}, its cycle space is the family of all subsets of {$E$} that have even degree at each vertex. We prove that with high probability, sampling the cycle space identifies the cuts of a graph. This leads to simple new linear-time sequential algorithms for finding all cut edges and cut pairs (a set of 2 edges that form a cut) of a graph. In the model of distributed computing in a graph {$ G = (V, E) $} with {$ O(\log |V|) $}-bit messages, our approach yields faster algorithms for several problems. The diameter of {$G$} is denoted by {$D$}, and the maximum degree by {$ \Delta $}. We obtain simple {$ O(D) $}-time distributed algorithms to find all cut edges, 2-edge-connected components, and cut pairs, matching or improving upon previous time bounds. Under natural conditions these new algorithms are universally optimal-that is, a {$ \Omega (D) $}-time lower bound holds on every graph. We obtain a {$ O(D + \Delta / \log |V|) $}-time distributed algorithm for finding cut vertices; this is faster than the best previous algorithm when {$ \Delta, D = O(\sqrt |V|) $}. A simple extension of our work yields the first distributed algorithm with sub-linear time for 3-edge-connected components. The basic distributed algorithms are Monte Carlo, but they can be made Las Vegas without increasing the asymptotic complexity. In the model of parallel computing on the EREW PRAM, our approach yields a simple algorithm with optimal time complexity {$ O(\log V) $} for finding cut pairs and 3-edge-connected components.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chang:2011:BSA, author = "Jessica Chang and Thomas Erlebach and Renars Gailis and Samir Khuller", title = "Broadcast scheduling: {Algorithms} and complexity", journal = j-TALG, volume = "7", number = "4", pages = "47:1--47:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000815", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Broadcast Scheduling is a popular method for disseminating information in response to client requests. There are $n$ pages of information, and clients request pages at different times. However, multiple clients can have their requests satisfied by a single broadcast of the requested page. In this article, we consider several related broadcast scheduling problems. One central problem we study simply asks to minimize the maximum response time (over all requests). Another related problem we consider is the version in which every request has a release time and a deadline, and the goal is to maximize the number of requests that meet their deadlines. While approximation algorithms for both these problems were proposed several years back, it was not known if they were NP-complete. One of our main results is that both these problems are NP-complete. In addition, we use the same unified approach to give a simple NP-completeness proof for minimizing the sum of response times. A very complicated proof was known for this version. Furthermore, we give a proof that FIFO is a 2-competitive online algorithm for minimizing the maximum response time (this result had been claimed earlier with no proof) and that there is no better deterministic online algorithm (this result was claimed earlier as well, but with an incorrect proof).", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Calinescu:2011:IAA, author = "Gruia Calinescu and Amit Chakrabarti and Howard Karloff and Yuval Rabani", title = "An improved approximation algorithm for resource allocation", journal = j-TALG, volume = "7", number = "4", pages = "48:1--48:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000816", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the problem of finding a most profitable subset of $n$ given tasks, each with a given start and finish time as well as profit and resource requirement, that at no time exceeds the quantity {$B$} of available resource. We show that this NP-hard Resource Allocation problem can be {$ (1 / 2 - \epsilon) $}-approximated in randomized polynomial time, which improves upon earlier approximation results.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fotakis:2011:MFL, author = "Dimitris Fotakis", title = "Memoryless facility location in one pass", journal = j-TALG, volume = "7", number = "4", pages = "49:1--49:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000817", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the first one-pass memoryless algorithm for metric Facility Location that maintains a set of facilities approximating the optimal facility configuration within a constant factor. The algorithm is randomized and very simple to state and implement. It processes the demand points one-by-one as they arrive, and keeps in memory only the facility locations currently open. We prove that its competitive ratio is less than 14 in the special case of uniform facility costs, and less than 49 in the general case of nonuniform facility costs.", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Han:2011:NUB, author = "Xin Han and Francis Y. L. Chin and Hing-Fung Ting and Guochuan Zhang and Yong Zhang", title = "A new upper bound $ 2.5545 $ on {$2$D} {Online Bin Packing}", journal = j-TALG, volume = "7", number = "4", pages = "50:1--50:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000818", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The 2D Online Bin Packing is a fundamental problem in Computer Science and the determination of its asymptotic competitive ratio has research attention. In a long series of papers, the lower bound of this ratio has been improved from 1.808, 1.856 to 1.907 and its upper bound reduced from 3.25, 3.0625, 2.8596, 2.7834 to 2.66013. In this article, we rewrite the upper bound record to 2.5545. Our idea for the improvement is as follows. In 2002, Seiden and van Stee [Seiden and van Stee 2003] proposed an elegant algorithm called {$ H \otimes C $}, comprised of the Harmonic algorithm {$H$} and the Improved Harmonic algorithm {$C$}, for the two-dimensional online bin packing problem and proved that the algorithm has an asymptotic competitive ratio of at most 2.66013. Since the best known online algorithm for one-dimensional bin packing is the Super Harmonic algorithm [Seiden 2002], a natural question to ask is: could a better upper bound be achieved by using the Super Harmonic algorithm instead of the Improved Harmonic algorithm? However, as mentioned in Seiden and van Stee [2003], the previous analysis framework does not work. In this article, we give a positive answer for this question. A new upper bound of 2.5545 is obtained for 2-dimensional online bin packing. The main idea is to develop new weighting functions for the Super Harmonic algorithm and propose new techniques to bound the total weight in a rectangular bin.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Edmonds:2011:CCR, author = "Jeff Edmonds and Kirk Pruhs", title = "Cake cutting really is not a piece of cake", journal = j-TALG, volume = "7", number = "4", pages = "51:1--51:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000819", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the well-known cake cutting problem in which a protocol wants to divide a cake among $ n \geq 2 $ players in such a way that each player believes that they got a fair share. The standard Robertson-Webb model allows the protocol to make two types of queries, Evaluation and Cut, to the players. A deterministic divide-and-conquer protocol with complexity {$ O(n \log n) $} is known. We provide the first a {$ \Omega (n \log n) $} lower bound on the complexity of any deterministic protocol in the standard model. This improves previous lower bounds, in that the protocol is allowed to assign to a player a piece that is a union of intervals and only guarantee approximate fairness. We accomplish this by lower bounding the complexity to find, for a single player, a piece of cake that is both rich in value, and thin in width. We then introduce a version of cake cutting in which the players are able to cut with only finite precision. In this case, we can extend the {$ \Omega (n \log n) $} lower bound to include randomized protocols.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Barbay:2011:SIS, author = "J{\'e}r{\'e}my Barbay and Meng He and J. Ian Munro and Srinivasa Rao Satti", title = "Succinct indexes for strings, binary relations and multilabeled trees", journal = j-TALG, volume = "7", number = "4", pages = "52:1--52:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000820", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We define and design succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the information-theoretic lower bound on the space required to encode the given data, and support an extended set of operations using the basic operators defined in the ADT. The main advantage of succinct indexes as opposed to succinct (integrated data/index) encodings is that we make assumptions only on the ADT through which the main data is accessed, rather than the way in which the data is encoded. This allows more freedom in the encoding of the main data. In this article, we present succinct indexes for various data types, namely strings, binary relations and multilabeled trees. Given the support for the interface of the ADTs of these data types, we can support various useful operations efficiently by constructing succinct indexes for them. When the operators in the ADTs are supported in constant time, our results are comparable to previous results, while allowing more flexibility in the encoding of the given data. Using our techniques, we design a succinct encoding that represents a string of length $n$ over an alphabet of size $ \sigma $ using {$ n H_k (S) + \lg \sigma \cdot o(n) + O(n \lg \sigma / \lg \lg \lg \sigma) $} bits to support access\slash rank\slash select operations in {$ o((\lg \lg \sigma)^{1 + \epsilon }) $} time, for any fixed constant {$ \epsilon > 0 $}. We also design a succinct text index using {$ n H_0 (S) + O(n \lg \sigma / \lg \lg \sigma) $} bits that supports finding all the occ occurrences of a given pattern of length {$m$} in {$ O(m \lg \lg \sigma + {\rm occ} \lg n / \lg^\epsilon \sigma) $} time, for any fixed constant {$ 0 < \epsilon < 1 $}. Previous results on these two problems either have a {$ \lg \sigma $} factor instead of {$ \lg \lg \sigma $} in the running time, or are not compressed. Finally, we present succinct encodings of binary relations and multi-labeled trees that are more compact than previous structures.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Russo:2011:FCS, author = "Lu{\'\i}s M. S. Russo and Gonzalo Navarro and Arlindo L. Oliveira", title = "{Fully} compressed suffix trees", journal = j-TALG, volume = "7", number = "4", pages = "53:1--53:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000821", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Suffix trees are by far the most important data structure in stringology, with a myriad of applications in fields like bioinformatics and information retrieval. Classical representations of suffix trees require {$ \Theta (n \log n) $} bits of space, for a string of size {$n$}. This is considerably more than the {$ n \log_2 \sigma $} bits needed for the string itself, where {$ \sigma $} is the alphabet size. The size of suffix trees has been a barrier to their wider adoption in practice. Recent compressed suffix tree representations require just the space of the compressed string plus {$ \Theta (n) $} extra bits. This is already spectacular, but the linear extra bits are still unsatisfactory when {$ \sigma $} is small as in DNA sequences. In this article, we introduce the first compressed suffix tree representation that breaks this {$ \Theta (n) $}-bit space barrier. The Fully Compressed Suffix Tree (FCST) representation requires only sublinear space on top of the compressed text size, and supports a wide set of navigational operations in almost logarithmic time. This includes extracting arbitrary text substrings, so the FCST replaces the text using almost the same space as the compressed text. An essential ingredient of FCSTs is the lowest common ancestor (LCA) operation. We reveal important connections between LCAs and suffix tree navigation. We also describe how to make FCSTs dynamic, that is, support updates to the text. The dynamic FCST also supports several operations. In particular, it can build the static FCST within optimal space and polylogarithmic time per symbol. Our theoretical results are also validated experimentally, showing that FCSTs are very effective in practice as well.", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Izsak:2011:CPM, author = "Alexander Izsak and Nicholas Pippenger", title = "Carry propagation in multiplication by constants", journal = j-TALG, volume = "7", number = "4", pages = "54:1--54:??", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1145/2000807.2000822", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Dec 8 09:35:43 MST 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Suppose that a random $n$-bit number V is multiplied by an odd constant {$ M \geq 3 $}, by adding shifted versions of the number {$V$} corresponding to the {$1$} s in the binary representation of the constant {$M$}. Suppose further that the additions are performed by carry-save adders until the number of summands is reduced to two, at which time the final addition is performed by a carry-propagate adder. We show that in this situation the distribution of the length of the longest carry-propagation chain in the final addition is the same (up to terms tending to {$0$} as {$ n \to \infty $}) as when two independent {$n$}-bit numbers are added, and in particular the mean and variance are the same (again up to terms tending to 0). This result applies to all possible orders of performing the carry-save additions.", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Guha:2012:AUR, author = "Sudipto Guha and Kamesh Munagala", title = "Adaptive Uncertainty Resolution in {Bayesian} Combinatorial Optimization Problems", journal = j-TALG, volume = "8", number = "1", pages = "1:1--1:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071380", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some objective function over the parameters) is significantly improved if some of these parameters can be probed or observed. In a resource constrained situation, deciding which parameters to observe in order to optimize system performance, itself becomes an interesting and important optimization problem. This general problem is the focus of this article. One of the most important considerations in this framework is whether adaptivity is required for the observations. Adaptive observations introduce blocking or sequential operations in the system whereas nonadaptive observations can be performed in parallel. One of the important questions in this regard is to characterize the benefit of adaptivity for probes and observation. We present general techniques for designing constant factor approximations to the optimal observation schemes for several widely used scheduling and metric objective functions. We show a unifying technique that relates this optimization problem to the outlier version of the corresponding deterministic optimization. By making this connection, our technique shows constant factor upper bounds for the benefit of adaptivity of the observation schemes. We show that while probing yields significant improvement in the objective function, being adaptive about the probing is not beneficial beyond constant factors.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mahdian:2012:OOU, author = "Mohammad Mahdian and Hamid Nazerzadeh and Amin Saberi", title = "Online {Optimization} with {Uncertain Information}", journal = j-TALG, volume = "8", number = "1", pages = "2:1--2:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071381", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a new framework for designing online algorithms that can incorporate additional information about the input sequence, while maintaining a reasonable competitive ratio if the additional information is incorrect. Within this framework, we present online algorithms for several problems including allocation of online advertisement space, load balancing, and facility location.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Haeupler:2012:ICD, author = "Bernhard Haeupler and Telikepalli Kavitha and Rogers Mathew and Siddhartha Sen and Robert E. Tarjan", title = "Incremental {Cycle Detection}, {Topological Ordering}, and {Strong Component Maintenance}", journal = j-TALG, volume = "8", number = "1", pages = "3:1--3:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071382", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present two online algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in {$ O(m^{3 / 2}) $} time. For sparse graphs {$ (m / n = O(1)) $}, this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural locality property. Our second algorithm handles an arbitrary sequence of arc additions in {$ O(n^{5 / 2}) $} time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take {$ \Omega (n^2 2^{\sqrt {2 \lg n}}) $} time by relating its performance to a generalization of the {$k$}-levels problem of combinatorial geometry. A completely different algorithm running in {$ \Theta (n^2 \log n) $} time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Frigo:2012:COA, author = "Matteo Frigo and Charles E. Leiserson and Harald Prokop and Sridhar Ramachandran", title = "Cache-Oblivious Algorithms", journal = j-TALG, volume = "8", number = "1", pages = "4:1--4:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071383", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article presents asymptotically optimal algorithms for rectangular matrix transpose, fast Fourier transform (FFT), and sorting on computers with multiple levels of caching. Unlike previous optimal algorithms, these algorithms are cache oblivious: no variables dependent on hardware parameters, such as cache size and cache-line length, need to be tuned to achieve optimality. Nevertheless, these algorithms use an optimal amount of work and move data optimally among multiple levels of cache. For a cache with size {$M$} and cache-line length {$B$} where {$ M = \Omega (B^2) $}, the number of cache misses for an {$ m \times n $} matrix transpose is {$ \Theta (1 + m n / B) $}. The number of cache misses for either an {$n$}-point FFT or the sorting of {$n$} numbers is {$ \Theta (1 + (n / B)(1 + \log M n)) $}. We also give a {$ \Theta (m n p) $}-work algorithm to multiply an {$ m \times n $} matrix by an {$ n \times p $} matrix that incurs {$ \Theta (1 + (m n + n p + m p) / B + m n p / B \sqrt {M}) $} cache faults. We introduce an `ideal-cache' model to analyze our algorithms. We prove that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal for multiple levels and that the assumption of optimal replacement in the ideal-cache model can be simulated efficiently by LRU replacement. We offer empirical evidence that cache-oblivious algorithms perform well in practice.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chlebus:2012:AQM, author = "Bogdan S. Chlebus and Dariusz R. Kowalski and Mariusz A. Rokicki", title = "Adversarial Queuing on the Multiple Access Channel", journal = j-TALG, volume = "8", number = "1", pages = "5:1--5:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071384", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study deterministic broadcasting on multiple access channels when packets are injected continuously. The quality of service is considered in the framework of adversarial queuing. An adversary is determined by injection rate and burstiness, the latter denoting the number of packets that can be injected simultaneously in a round. We consider only injection rates that are less than $1$. A protocol is stable when the numbers of packets in queues stay bounded at all rounds, and it is of fair latency when waiting times of packets in queues are {$ O({\rm burstiness} / {\rm rate}) $}. For channels with collision detection, we give a full-sensing protocol of fair latency for injection rates that are at most {$ 1 \over 2 (\lceil \lg n \rceil + 1) $}, where {$n$} is the number of stations, and show that fair latency is impossible to achieve for injection rates that are {$ \omega (1 \over \log n) $}. For channels without collision detection, we present a full-sensing protocol of fair latency for injection rates that are at most $ 1 \over c \lg^2 n $, for some $ c > 0 $. We show that there exists an acknowledgment-based protocol that has fair latency for injection rates that are at most $ 1 \over c n \lg^2 n $, for some $ c > 0 $, and develop an explicit acknowledgment-based protocol of fair latency for injection rates that are at most $ 1 \over 27 n^2 \ln n $. Regarding impossibility to achieve just stability by restricted protocols, we prove that no acknowledgment-based protocol can be stable for injection rates larger than $ 3 \over 1 + \lg n $.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chen:2012:IEC, author = "Jianer Chen and Yang Liu and Songjian Lu and Sing-Hoi Sze and Fenghui Zhang", title = "Iterative Expansion and Color Coding: An Improved Algorithm for {$3$D}-Matching", journal = j-TALG, volume = "8", number = "1", pages = "6:1--6:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071385", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The research in the parameterized 3d-matching problem has yielded a number of new algorithmic techniques and an impressive list of improved algorithms. In this article, a new deterministic algorithm for the problem is developed that integrates and improves a number of known techniques, including greedy localization, dynamic programming, and color coding. The new algorithm, which either constructs a matching of $k$ triples in a given triple set or correctly reports that no such a matching exists, runs in time {$ O*(2.80^3 k) $}, improving a long list of previous algorithms for the problem.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bocker:2012:IFP, author = "Sebastian B{\"o}cker and Quang Bao Anh Bui and Anke Truss", title = "Improved Fixed-Parameter Algorithms for Minimum-Flip Consensus Trees", journal = j-TALG, volume = "8", number = "1", pages = "7:1--7:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071386", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In computational phylogenetics, the problem of constructing a consensus tree for a given set of rooted input trees has frequently been addressed. In this article we study the Minimum-Flip Problem: the input trees are transformed into a binary matrix, and we want to find a perfect phylogeny for this matrix using a minimum number of flips, that is, corrections of single entries in the matrix. The graph-theoretical formulation of the problem is as follows: Given a bipartite graph {$ G = (V t \cup V c, E) $}, the task is to find a minimum set of edge modifications such that the resulting graph has no induced path with four edges that starts and ends in Vt, where Vt corresponds to the taxa set and Vc corresponds to the character set. We present two fixed-parameter algorithms for the Minimum-Flip Problem, one with running time {$ O(4.83 k + \poly (m, n)) $} and another one with running time {$ O(4.42 k + \poly (m, n)) $} for {$n$} taxa, {$m$} characters, {$k$} flips, and $ \poly (m, n) $ denotes a polynomial function in $m$ and $n$. Additionally, we discuss several heuristic improvements. We also report computational results on phylogenetic data.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cygan:2012:EFE, author = "Marek Cygan and Marcin Pilipczuk", title = "Even Faster Exact Bandwidth", journal = j-TALG, volume = "8", number = "1", pages = "8:1--8:??", month = jan, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2071379.2071387", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Mar 16 15:33:03 MDT 2012", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We deal with exact algorithms for Bandwidth, a long studied NP-hard problem. For a long time nothing better than the trivial {$ O^\ast (n!)^1 $} exhaustive search was known. In 2000, Feige and Kilian [Feige 2000] came up with a {$ O^\ast (10 n) $}-time and polynomial space algorithm. In this article we present a new algorithm that solves Bandwidth in {$ O^\ast (5 n) $} time and {$ O^\ast (2 n) $} space. Then, we take a closer look and introduce a major modification that makes it run in {$ O(4.83 n) $} time with a cost of a {$ O^\ast (4 n) $} space complexity. This modification allowed us to perform the Measure \& Conquer analysis for the time complexity which was not used for graph layout problems before.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aumann:2012:DIG, author = "Yonatan Aumann and Moshe Lewenstein and Oren Melamud and Ron Pinter and Zohar Yakhini", title = "Dotted interval graphs", journal = j-TALG, volume = "8", number = "2", pages = "9:1--9:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151172", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a generalization of interval graphs, which we call Dotted Interval Graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (dotted intervals). Coloring of dotted interval graphs naturally arises in the context of high throughput genotyping. We study the properties of dotted interval graphs, with a focus on coloring. We show that any graph is a DIG, but that DIG$_d$ graphs, that is, DIGs in which the arithmetic progressions have a jump of at most $d$, form a strict hierarchy. We show that coloring DIG$_d$ graphs is NP-complete even for $ d = 2 $. For any fixed $d$, we provide a $ 5 / 6 d + o(d) $ approximation for the coloring of DIG$_d$ graphs. Finally, we show that finding the maximal clique in DIG$_d$ graphs is fixed parameter tractable in $d$.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bose:2012:SGI, author = "Prosenjit Bose and Eric Y. Chen and Meng He and Anil Maheshwari and Pat Morin", title = "Succinct geometric indexes supporting point location queries", journal = j-TALG, volume = "8", number = "2", pages = "10:1--10:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151173", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose designing data structures called succinct geometric indexes of negligible space (more precisely, $ o(n) $ bits) that support geometric queries in optimal time, by taking advantage of the $n$ points in the dataset permuted and stored elsewhere as a sequence. Our first and main result is a succinct geometric index that can answer point location queries, a fundamental problem in computational geometry, on planar triangulations in {$ O(\lg n) $} time. We also design three variants of this index. The first supports point location using {$ \lg n + 2 \sqrt {\lg n} + O(\lg^{1 / 4} n) $} point-line comparisons. The second supports point location in {$ o(\lg n) $} time when the coordinates are integers bounded by {$U$}. The last variant can answer point location queries in {$ O(H + 1) $} expected time, where {$H$} is the entropy of the query distribution. These results match the query efficiency of previous point location structures that occupy {$ O(n) $} words or {$ O(n \lg n) $} bits, while saving drastic amounts of space. We generalize our succinct geometric index to planar subdivisions, and design indexes for other types of queries. Finally, we apply our techniques to design the first implicit data structures that support point location in {$ O(\lg^2 n) $} time.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Drmota:2012:PAC, author = "Michael Drmota and Reinhard Kutzelnigg", title = "A precise analysis of {Cuckoo} hashing", journal = j-TALG, volume = "8", number = "2", pages = "11:1--11:36", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151174", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/hash.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Cuckoo hashing was introduced by Pagh and Rodler in 2001. Its main feature is that it provides constant worst-case search time. The aim of this article is to present a precise average case analysis of Cuckoo hashing. In particular, we determine the probability that Cuckoo hashing produces no conflicts and give an upper bound for the construction time, that is linear in the size of the table. The analysis rests on a generating function approach to the so called Cuckoo Graph, a random bipartite graph, and an application of a double saddle point method to obtain asymptotic expansions. Furthermore, we provide some results concerning the structure of these kinds of random graphs. Our results extend the analysis of Devroye and Morin [2003]. Additionally, we provide numerical results confirming the mathematical analysis.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Yi:2012:MOT, author = "Ke Yi and Qin Zhang", title = "Multidimensional online tracking", journal = j-TALG, volume = "8", number = "2", pages = "12:1--12:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151175", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose and study a new class of online problems, which we call online tracking. Suppose an observer, say Alice, observes a multivalued function {$ f : Z^+ \to Z^d $} over time in an online fashion, that is, she only sees {$ f(t) $} for {$ t \leq t_{\rm now} $} where {$ t_{\rm now} $} is the current time. She would like to keep a tracker, say Bob, informed of the current value of $f$ at all times. Under this setting, Alice could send new values of $f$ to Bob from time to time, so that the current value of $f$ is always within a distance of {$ \Delta $} to the last value received by Bob. We give competitive online algorithms whose communication costs are compared with the optimal offline algorithm that knows the entire {$f$} in advance. We also consider variations of the problem where Alice is allowed to send predictions to Bob, to further reduce communication for well-behaved functions. These online tracking problems have a variety of application, ranging from sensor monitoring, location-based services, to publish/subscribe systems.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2012:PAN, author = "Erik D. Demaine and Mohammadtaghi Hajiaghayi and Hamid Mahini and Morteza Zadimoghaddam", title = "The price of anarchy in network creation games", journal = j-TALG, volume = "8", number = "2", pages = "13:1--13:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151176", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study Nash equilibria in the setting of network creation games introduced recently by Fabrikant, Luthra, Maneva, Papadimitriou, and Shenker. In this game we have a set of selfish node players, each creating some incident links, and the goal is to minimize $ \alpha $ times the cost of the created links plus sum of the distances to all other players. Fabrikant et al. proved an upper bound {$ O(\sqrt \alpha) $} on the price of anarchy: the relative cost of the lack of coordination. Albers, Eilts, Even-Dar, Mansour, and Roditty show that the price of anarchy is constant for {$ \alpha = O(\sqrt n) $} and for {$ \alpha \geq 12 n \lceil \lg n \rceil $}, and that the price of anarchy is {$ 15 (1 + (\min {\alpha^2 / n, n^2 / \alpha })^{1 / 3}) $} for any {$ \alpha $}. The latter bound shows the first sublinear worst-case bound, {$ O(n^{1 / 3}) $}, for all {$ \alpha $}. But no better bound is known for {$ \alpha $} between {$ \omega (\sqrt n) $} and $ o(n \lg n) $. Yet $ \alpha \approx n $ is perhaps the most interesting range, for it corresponds to considering the average distance (instead of the sum of distances) to other nodes to be roughly on par with link creation (effectively dividing $ \alpha $ by $n$). In this article, we prove the first $ o(n^\epsilon) $ upper bound for general $ \alpha $, namely {$ 2^{O(\sqrt {\lg n})} $}. We also prove a constant upper bound for {$ \alpha = O({n^{1 \epsilon }}) $} for any fixed {$ \epsilon > 0 $}, substantially reducing the range of {$ \alpha $} for which constant bounds have not been obtained. Along the way, we also improve the constant upper bound by Albers et al. (with the lead constant of {$ 15 $}) to $6$ for $ \alpha < (n / 2)^{1 / 2} $ and to $4$ for $ \alpha < (n / 2)^{1 / 3} $. Next we consider the bilateral network variant of Corbo and Parkes, in which links can be created only with the consent of both endpoints and the link price is shared equally by the two. Corbo and Parkes show an upper bound of {$ O(\sqrt \alpha) $} and a lower bound of {$ \Omega (\lg \alpha) $} for {$ \alpha \leq n $}. In this article, we show that in fact the upper bound {$ O(\sqrt \alpha) $} is tight for {$ \alpha \leq n $}, by proving a matching lower bound of {$ \Omega (\sqrt \alpha) $}. For {$ \alpha > n $}, we prove that the price of anarchy is {$ \Theta (n / \sqrt \alpha) $}. Finally we introduce a variant of both network creation games, in which each player desires to minimize {$ \alpha $} times the cost of its created links plus the maximum distance (instead of the sum of distances) to the other players. This variant of the problem is naturally motivated by considering the worst case instead of the average case. Interestingly, for the original (unilateral) game, we show that the price of anarchy is at most {$2$} for {$ \alpha \geq n $}, {$ O(\min \{ 4^{\sqrt {\lg n}}, (n / \alpha)^{1 / 3} \}) $} for {$ 2 \sqrt {\lg n} \leq \alpha \leq n $}, and {$ O(n^{2 / \alpha }) $} for {$ \alpha < 2 \sqrt {\lg n} $}. For the bilateral game, we prove matching upper and lower bounds of {$ \Theta (n / \alpha + 1) $} for {$ \alpha \leq n $}, and an upper bound of {$2$} for {$ \alpha > n $}.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ye:2012:EG, author = "Yuli Ye and Allan Borodin", title = "Elimination graphs", journal = j-TALG, volume = "8", number = "2", pages = "14:1--14:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151177", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article we study graphs with inductive neighborhood properties. Let {$P$} be a graph property, a graph {$ G = (V, E) $} with {$n$} vertices is said to have an inductive neighborhood property with respect to {$P$} if there is an ordering of vertices {$ v_1 $}, \ldots, {$ v_n $} such that the property {$P$} holds on the induced subgraph {$ G[N(v_i) \cap V_i] $}, where {$ N(v_i) $} is the neighborhood of {$ v_i $} and {$ V_i = \{ v_i, \ldots, v_n \} $}. It turns out that if we take {$P$} as a graph with maximum independent set size no greater than {$k$}, then this definition gives a natural generalization of both chordal graphs and {$ (k + 1) $}-claw-free graphs. We refer to such graphs as inductive {$k$}-independent graphs. We study properties of such families of graphs, and we show that several natural classes of graphs are inductive $k$-independent for small $k$. In particular, any intersection graph of translates of a convex object in a two dimensional plane is an inductive $3$-independent graph; furthermore, any planar graph is an inductive $3$-independent graph. For any fixed constant $k$, we develop simple, polynomial time approximation algorithms for inductive $k$-independent graphs with respect to several well-studied NP-complete problems. Our generalized formulation unifies and extends several previously known results.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fischer:2012:QCT, author = "Eldar Fischer and Oded Lachish and Arie Matsliah and Ilan Newman and Orly Yahalom", title = "On the query complexity of testing orientations for being {Eulerian}", journal = j-TALG, volume = "8", number = "2", pages = "15:1--15:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151178", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider testing directed graphs Eulerianity in the orientation model introduced in Halevy et al. [2005]. Despite the local nature of the Eulerian property, it turns out to be significantly harder to test than other properties studied in the orientation model. We show a nonconstant lower bound on the query complexity of $2$-sided tests and a linear lower bound on the query complexity of $1$-sided tests for this property. On the positive side, we give several $1$-sided and $2$-sided tests, including a sublinear query complexity $2$-sided test, for general graphs. For special classes of graphs, including bounded-degree graphs and expander graphs, we provide improved results. In particular, we give a $2$-sided test with constant query complexity for dense graphs, as well as for expander graphs with a constant expansion parameter.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fujito:2012:HTM, author = "Toshihiro Fujito", title = "How to trim a {MST}: a $2$-approximation algorithm for minimum cost-tree cover", journal = j-TALG, volume = "8", number = "2", pages = "16:1--16:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151179", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The minimum cost-tree cover problem is to compute a minimum cost-tree {$T$} in a given connected graph {$G$} with costs on the edges, such that the vertices spanned by {$T$} form a vertex cover for {$G$}. The problem is supposed to occur in applications of vertex cover and in edge-dominating sets when additional connectivity is required for solutions. Whereas a linear-time {$2$}-approximation algorithm for the unweighted case has been known for quite a while, the best approximation ratio known for the weighted case is {$3$}. Moreover, the {$3$}-approximation algorithms for such cases are far from practical due to their inefficiency. In this article we present a fast, purely combinatorial $2$-approximation algorithm for the minimum cost-tree cover problem. It constructs a good approximate solution by trimming some leaves within a minimum spanning tree (MST); and, to determine which leaves to trim, it uses both the primal-dual schema and an instance layering technique adapted from the local ratio method.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Manthey:2012:AMT, author = "Bodo Manthey", title = "On approximating multicriteria {TSP}", journal = j-TALG, volume = "8", number = "2", pages = "17:1--17:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151180", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present approximation algorithms for almost all variants of the multicriteria traveling salesman problem (TSP). First, we devise randomized approximation algorithms for multicriteria maximum traveling salesman problems (Max-TSP). For multicriteria Max-STSP where the edge weights have to be symmetric, we devise an algorithm with an approximation ratio of $ 2 / 3 - \epsilon $ . For multicriteria Max-ATSP where the edge weights may be asymmetric, we present an algorithm with a ratio of $ 1 / 2 - \epsilon $. Our algorithms work for any fixed number $k$ of objectives. Furthermore, we present a deterministic algorithm for bicriteria Max-STSP that achieves an approximation ratio of $ 7 / 27 $. Finally, we present a randomized approximation algorithm for the asymmetric multicriteria minimum TSP with triangle inequality (Min-ATSP). This algorithm achieves a ratio of $ \log n + \epsilon $.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bjorklund:2012:TSP, author = "Andreas Bj{\"o}rklund and Thore Husfeldt and Petteri Kaski and Mikko Koivisto", title = "The traveling salesman problem in bounded degree graphs", journal = j-TALG, volume = "8", number = "2", pages = "18:1--18:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151181", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that the traveling salesman problem in bounded-degree graphs can be solved in time {$ O((2 - \epsilon)^n) $}, where {$ \epsilon > 0 $} depends only on the degree bound but not on the number of cities, {$n$}. The algorithm is a variant of the classical dynamic programming solution due to Bellman, and, independently, Held and Karp. In the case of bounded integer weights on the edges, we also give a polynomial-space algorithm with running time {$ O((2 - \epsilon)^n) $} on bounded-degree graphs. In addition, we present an analogous analysis of Ryser's algorithm for the permanent of matrices with a bounded number of nonzero entries in each column.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Krokhin:2012:HLW, author = "Andrei Krokhin and D{\'a}niel Marx", title = "On the hardness of losing weight", journal = j-TALG, volume = "8", number = "2", pages = "19:1--19:??", month = apr, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2151171.2151182", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:57 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a better (lighter, i.e., having strictly less Hamming weight) solution within a given distance from the initial solution. We classify the complexity, both classical and parameterized, of such problems by a Schaefer-style dichotomy result, that is, with a restricted set of allowed types of constraints. Our results show that there is a considerable amount of such problems that are NP-hard, but fixed-parameter tractable when parameterized by the distance.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bateni:2012:APC, author = "Mohammadhossein Bateni and Mohammadtaghi Hajiaghayi", title = "Assignment problem in content distribution networks: {Unsplittable} hard-capacitated facility location", journal = j-TALG, volume = "8", number = "3", pages = "20:1--20:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229164", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server because of the routing protocol used. The goal is to minimize the total cost of these assignments-cost of each is proportional to the distance between the client and the server as well as the request size-while the load on each server is kept below its bandwidth limit. When each server also has a setup cost, this is an unsplittable hard-capacitated facility location problem. As much attention as facility location problems have received, there has been no nontrivial approximation algorithm when we have hard capacities (i.e., there can only be one copy of each facility whose capacity cannot be violated) and demands are unsplittable (i.e., all the demand from a client has to be assigned to a single facility). We observe it is NP-hard to approximate the cost to within any bounded factor in this case. Thus, for an arbitrary constant $ \epsilon > 0 $, we relax the capacities to a $ 1 + \epsilon $ factor. For the case where capacities are almost uniform, we give a bicriteria {$ O(\log n, 1 + \epsilon) $}-approximation algorithm for general metrics and a {$ (1 + \epsilon, 1 + \epsilon) $}-approximation algorithm for tree metrics. A bicriteria {$ (\alpha, \beta) $}-approximation algorithm produces a solution of cost at most {$ \alpha $} times the optimum, while violating the capacities by no more than a $ \beta $ factor. We can get the same guarantees for nonuniform capacities if we allow quasipolynomial running time. In our algorithm, some clients guess the facility they are assigned to, and facilities decide the size of the clients they serve. A straightforward approach results in exponential running time. When costs do not satisfy metricity, we show that a 1.5 violation of capacities is necessary to obtain any approximation. It is worth noting that our results generalize bin packing (zero connection costs and facility costs equal to one), knapsack (single facility with all costs being zero), minimum makespan scheduling for related machines (all connection costs being zero), and some facility location problems.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Panconesi:2012:EPS, author = "Alessandro Panconesi and Jaikumar Radhakrishnan", title = "Expansion properties of (secure) wireless networks", journal = j-TALG, volume = "8", number = "3", pages = "21:1--21:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229165", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that some topologies arising naturally in the context of wireless networking are low-degree, expander graphs.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Meyer:2012:ESP, author = "Ulrich Meyer and Norbert Zeh", title = "{I/O}-efficient shortest path algorithms for undirected graphs with random or bounded edge lengths", journal = j-TALG, volume = "8", number = "3", pages = "22:1--22:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229166", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present I/O-efficient single-source shortest path algorithms for undirected graphs. Our main result is an algorithm with I/O complexity {$ O(\sqrt (n m \log L) / B + {\rm MST}(n, m)) $} on graphs with {$n$} vertices, {$m$} edges, and arbitrary edge lengths between {$1$} and {$L$}; {$ {\rm MST}(n, m) $} denotes the I/O complexity of computing a minimum spanning tree; {$B$} denotes the disk block size. If the edge lengths are drawn uniformly at random from $ (0, 1] $, the expected I/O complexity of the algorithm is $ O(\sqrt n m / B + (m / B) \log B + {\rm MST}(n, m)) $. A simpler algorithm has expected I/O complexity $ O(\sqrt (n m \log B) / B + {\rm MST}(n, m)) $ for uniformly random edge lengths.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chekuri:2012:IAO, author = "Chandra Chekuri and Nitish Korula and Martin P{\'a}l", title = "Improved algorithms for orienteering and related problems", journal = j-TALG, volume = "8", number = "3", pages = "23:1--23:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229167", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider the orienteering problem in undirected and directed graphs and obtain improved approximation algorithms. The point to point-orienteering problem is the following: Given an edge-weighted graph {$ G = (V, E) $} (directed or undirected), two nodes {$ s, t \in V $} and a time limit {$B$}, find an {$s$}--{$t$} walk in {$G$} of total length at most {$B$} that maximizes the number of distinct nodes visited by the walk. This problem is closely related to tour problems such as TSP as well as network design problems such as {$k$}-MST. Orienteering with time-windows is the more general problem in which each node {$v$} has a specified time-window {$ [R(v), D(v)] $} and a node {$v$} is counted as visited by the walk only if {$v$} is visited during its time-window. We design new and improved algorithms for the orienteering problem and orienteering with time-windows. Our main results are the following: --- A {$ (2 + \epsilon) $} approximation for orienteering in undirected graphs, improving upon the $3$-approximation of Bansal et al. [2004]. --- An {$ O(\log^2 {\rm OPT}) $} approximation for orienteering in directed graphs, where {$ {\rm OPT} \leq n $} is the number of vertices visited by an optimal solution. Previously, only a quasipolynomial-time algorithm due to Chekuri and P{\'a}l [2005] achieved a polylogarithmic approximation (a ratio of {$ O(\log {\rm OPT}) $}). --- Given an {$ \alpha $} approximation for orienteering, we show an {$ O(\alpha c \{ {\rm maxlog} {\rm OPT}, \log l_{\rm max} / l_{\rm min} \}) $} approximation for orienteering with time-windows, where {$ l_{\rm max} $} and {$ l_{\rm min} $} are the lengths of the longest and shortest time-windows respectively.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Asadpour:2012:SCM, author = "Arash Asadpour and Uriel Feige and Amin Saberi", title = "{Santa Claus} meets hypergraph matchings", journal = j-TALG, volume = "8", number = "3", pages = "24:1--24:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229168", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the restricted assignment version of the problem of max-min fair allocation of indivisible goods, also known as the Santa Claus problem. There are $m$ items and $n$ players. Every item has some nonnegative value, and every player is interested in only some of the items. The goal is to distribute the items to the players in a way that maximizes the minimum of the sum of the values of the items given to any player. It was previously shown via a nonconstructive proof that uses the Lov{\'a}sz local lemma that the integrality gap of a certain configuration LP for the problem is no worse than some (unspecified) constant. This gives a polynomial-time algorithm to estimate the optimum value of the problem within a constant factor, but does not provide a polynomial-time algorithm for finding a corresponding allocation. We use a different approach to analyze the integrality gap. Our approach is based upon local search techniques for finding perfect matchings in certain classes of hypergraphs. As a result, we prove that the integrality gap of the configuration LP is no worse than $ 1 / 4 $. Our proof provides a local search algorithm which finds the corresponding allocation, but is nonconstructive in the sense that this algorithm is not known to converge to a local optimum in a polynomial number of steps.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fanelli:2012:SCC, author = "Angelo Fanelli and Michele Flammini and Luca Moscardelli", title = "The speed of convergence in congestion games under best-response dynamics", journal = j-TALG, volume = "8", number = "3", pages = "25:1--25:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229169", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate the speed of convergence of best response dynamics to approximately optimal solutions in congestion games with linear delay functions. In Ackermann et al. [2008] it has been shown that the convergence time of such dynamics to Nash equilibrium may be exponential in the number of players $n$. Motivated by such a negative result, we focus on the study of the states (not necessarily being equilibria) reached after a limited number of players' selfish moves, and we show that {$ \Theta (n \log \log n) $} best responses are necessary and sufficient to achieve states that approximate the optimal solution by a constant factor, under the assumption that every {$ O(n) $} steps each player performs a constant (and nonnull) number of best responses. We show that such result is tight also for the simplest case of singleton congestion games.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baptiste:2012:PTA, author = "Philippe Baptiste and Marek Chrobak and Christoph D{\"u}rr", title = "Polynomial-time algorithms for minimum energy scheduling", journal = j-TALG, volume = "8", number = "3", pages = "26:1--26:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229170", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The aim of power management policies is to reduce the amount of energy consumed by computer systems while maintaining a satisfactory level of performance. One common method for saving energy is to simply suspend the system during idle times. No energy is consumed in the suspend mode. However, the process of waking up the system itself requires a certain fixed amount of energy, and thus suspending the system is beneficial only if the idle time is long enough to compensate for this additional energy expenditure. In the specific problem studied in the article, we have a set of jobs with release times and deadlines that need to be executed on a single processor. Preemptions are allowed. The processor requires energy $L$ to be woken up and, when it is on, it uses one unit of energy per one unit of time. It has been an open problem whether a schedule minimizing the overall energy consumption can be computed in polynomial time. We solve this problem in positive, by providing an {$ O(n^5) $}-time algorithm. In addition we provide an {$ O(n^4) $}-time algorithm for computing the minimum energy schedule when all jobs have unit length.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Diedrich:2012:TAA, author = "Florian Diedrich and Klaus Jansen and Lars Pr{\"a}del and Ulrich M. Schwarz and Ola Svensson", title = "Tight approximation algorithms for scheduling with fixed jobs and nonavailability", journal = j-TALG, volume = "8", number = "3", pages = "27:1--27:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229171", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, for example, in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of $ 3 / 2 $. For scheduling with fixed jobs, a lower bound of $ 3 / 2 $ on the approximation ratio has been obtained by Scharbrodt et al. [1999]; for scheduling with nonavailability we provide the same lower bound. We use dual approximation, creation of a gap structure, and a PTAS for the multiple subset sum problem, combined with a postprocessing step to assign large jobs.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Edmonds:2012:SSP, author = "Jeff Edmonds and Kirk Pruhs", title = "Scalably scheduling processes with arbitrary speedup curves", journal = j-TALG, volume = "8", number = "3", pages = "28:1--28:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229172", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a scalable ($ (1 + \epsilon) $-speed {$ O(1) $}-competitive) nonclairvoyant algorithm for scheduling jobs with sublinear nondecreasing speedup curves on multiple processors with the objective of average response time.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Collette:2012:ETP, author = "S{\'e}bastien Collette and Vida Dujmovi{\'c} and John Iacono and Stefan Langerman and Pat Morin", title = "Entropy, triangulation, and point location in planar subdivisions", journal = j-TALG, volume = "8", number = "3", pages = "29:1--29:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229173", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a connected planar subdivision {$G$} of size {$n$} and a query distribution {$D$} to produce a point location data structure for {$G$}. The expected number of point-line comparisons performed by this data structure, when the queries are distributed according to {$D$}, is {$ \tilde {H} + O(\tilde {H}^{1 / 2} + 1) $} where {$ \tilde {H} = \tilde {H}(G, D) $} is a lower bound on the expected number of point-line comparisons performed by any linear decision tree for point location in {$G$} under the query distribution {$D$}. The preprocessing algorithm runs in {$ O(n \log n) $} time and produces a data structure of size {$ O(n) $}. These results are obtained by creating a Steiner triangulation of {$G$} that has near-minimum entropy.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Damerow:2012:SAL, author = "Valentina Damerow and Bodo Manthey and Friedhelm {Meyer Auf Der Heide} and Harald R{\"a}cke and Christian Scheideler and Christian Sohler and Till Tantau", title = "Smoothed analysis of left-to-right maxima with applications", journal = j-TALG, volume = "8", number = "3", pages = "30:1--30:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229174", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A left-to-right maximum in a sequence of $n$ numbers $ s_1 $, \ldots {}, $ s_n $ is a number that is strictly larger than all preceding numbers. In this article we present a smoothed analysis of the number of left-to-right maxima in the presence of additive random noise. We show that for every sequence of $n$ numbers $ s_i \in [0, 1] $ that are perturbed by uniform noise from the interval $ [ - \epsilon, \epsilon] $, the expected number of left-to-right maxima is {$ \Theta (\sqrt n / \epsilon + \log n) $} for {$ \epsilon > 1 / n $}. For Gaussian noise with standard deviation {$ \sigma $} we obtain a bound of {$ O((\log^{3 / 2} n) / \sigma + \log n) $}. We apply our results to the analysis of the smoothed height of binary search trees and the smoothed number of comparisons in the quicksort algorithm and prove bounds of {$ \Theta (\sqrt n / \epsilon + \log n) $} and {$ \Theta (n / \epsilon + 1 \sqrt n / \epsilon + n \log n) $}, respectively, for uniform random noise from the interval {$ [ - \epsilon, \epsilon] $}. Our results can also be applied to bound the smoothed number of points on a convex hull of points in the two-dimensional plane and to smoothed motion complexity, a concept we describe in this article. We bound how often one needs to update a data structure storing the smallest axis-aligned box enclosing a set of points moving in d -dimensional space.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bassino:2012:COF, author = "Fr{\'e}d{\'e}rique Bassino and Julien Cl{\'e}ment and Pierre Nicod{\`e}me", title = "Counting occurrences for a finite set of words: combinatorial methods", journal = j-TALG, volume = "8", number = "3", pages = "31:1--31:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229175", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we provide the multivariate generating function counting texts according to their length and to the number of occurrences of words from a finite set. The application of the inclusion-exclusion principle to word counting due to Goulden and Jackson [1979, 1983] is used to derive the result. Unlike some other techniques which suppose that the set of words is reduced (i.e., where no two words are factor of one another), the finite set can be chosen arbitrarily. Noonan and Zeilberger [1999] already provided a Maple package treating the nonreduced case, without giving an expression of the generating function or a detailed proof. We provide a complete proof validating the use of the inclusion-exclusion principle. Some formul{\ae} for expected values, variance, and covariance for number of occurrences when considering two arbitrary sets of finite words are given as an application of our methodology.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Arvind:2012:TNG, author = "V. Arvind and Piyush P. Kurur", title = "Testing nilpotence of {Galois} groups in polynomial time", journal = j-TALG, volume = "8", number = "3", pages = "32:1--32:??", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2229163.2229176", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:09:59 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give the first polynomial-time algorithm for checking whether the Galois group {$ {\rm Gal}(f) $} of an input polynomial {$ f(X) \in Q[X] $} is nilpotent: the running time of our algorithm is bounded by a polynomial in the size of the coefficients of {$f$} and the degree of {$f$}. Additionally, we give a deterministic polynomial-time algorithm that, when given as input a polynomial {$ f(X) \in Q[X] $} with nilpotent Galois group, computes for each prime factor {$p$} of {$ \# {\rm Gal}(f) $}, a polynomial {$ g_p(X) \in Q[X] $} whose Galois group of is the {$p$}-Sylow subgroup of {$ {\rm Gal}(f) $}.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Roditty:2012:RPS, author = "Liam Roditty and Uri Zwick", title = "Replacement paths and $k$ simple shortest paths in unweighted directed graphs", journal = j-TALG, volume = "8", number = "4", pages = "33:1--33:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344423", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let {$ G = (V, E) $} be a directed graph and let {$P$} be a shortest path from {$s$} to {$t$} in {$G$}. In the replacement paths problem, we are required to find, for every edge {$e$} on {$P$}, a shortest path from {$s$} to {$t$} in {$G$} that avoids {$e$}. The only known algorithm for solving the problem, even for unweighted directed graphs, is the trivial algorithm in which each edge on the path, in its turn, is excluded from the graph and a shortest paths tree is computed from {$s$}. The running time is {$ O(m n + n^2 \log n) $}. The replacement paths problem is strongly motivated by two different applications: (1) The fastest algorithm to compute the {$k$} simple shortest paths between {$s$} and {$t$} in directed graphs [Yen 1971; Lawler 1972] computes the replacement paths between $s$ and $t$. Its running time is {$ \tilde {O}(m n k) $}. (2) The replacement paths problem is used to compute the Vickrey pricing of edges in a distributed network. It was raised as an open problem by Nisan and Ronen [2001] whether it is possible to compute the Vickrey pricing faster than {$n$} computations of a shortest paths tree. In this article we present the first nontrivial algorithm for computing replacement paths in unweighted directed graphs (and in graphs with small integer weights). Our algorithm is Monte-Carlo and its running time is {$ \tilde {O}(m \sqrt n) $}. This result immediately improves the running time of the two applications mentioned above in a factor of {$ \sqrt n $}. We also show how to reduce the problem of computing {$k$} simple shortest paths between {$s$} and $t$ to {$ O(k) $} computations of a second simple shortest path from {$s$} to {$t$} each time in a different subgraph of {$G$}. The importance of this result is that computing a second simple shortest path may turn out to be an easier problem than computing the replacement paths, thus, we can focus our efforts to improve the k simple shortest paths algorithm in obtaining a faster algorithm for the second shortest path problem.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2012:APS, author = "Timothy M. Chan", title = "All-pairs shortest paths for unweighted undirected graphs in $ o(m n) $ time", journal = j-TALG, volume = "8", number = "4", pages = "34:1--34:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344424", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We revisit the all-pairs-shortest-paths problem for an unweighted undirected graph with $n$ vertices and $m$ edges. We present new algorithms with the following running times: {$ O(m n / \log n) $} if {$ m > n \log n \log \log \log n O(m n \log \log n / \log n) $} if {$ m > n \log \log n O(n^2 \log^2 \log n / \log n) $} if {$ m \leq n \log \log n $}. These represent the best time bounds known for the problem for all {$ m \ll n^{1.376} $} . We also obtain a similar type of result for the diameter problem for unweighted directed graphs.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Baswana:2012:FDR, author = "Surender Baswana and Sumeet Khurana and Soumojit Sarkar", title = "Fully dynamic randomized algorithms for graph spanners", journal = j-TALG, volume = "8", number = "4", pages = "35:1--35:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344425", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Spanner of an undirected graph {$ G = (V, E) $} is a subgraph that is sparse and yet preserves all-pairs distances approximately. More formally, a spanner with stretch {$ t \in N $} is a subgraph {$ (V, E_S) $}, {E$_S \subseteq E$} such that the distance between any two vertices in the subgraph is at most {$t$} times their distance in {$G$}. Though {$G$} is trivially a {$t$}-spanner of itself, the research as well as applications of spanners invariably deal with a {$t$}-spanner that has as small number of edges as possible. We present fully dynamic algorithms for maintaining spanners in centralized as well as synchronized distributed environments. These algorithms are designed for undirected unweighted graphs and use randomization in a crucial manner. Our algorithms significantly improve the existing fully dynamic algorithms for graph spanners. The expected size (number of edges) of a {$t$}-spanner maintained at each stage by our algorithms matches, up to a polylogarithmic factor, the worst case optimal size of a $t$-spanner. The expected amortized time (or messages communicated in distributed environment) to process a single insertion\slash deletion of an edge by our algorithms is close to optimal.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Swamy:2012:ESS, author = "Chaitanya Swamy", title = "The effectiveness of {Stackelberg} strategies and tolls for network congestion games", journal = j-TALG, volume = "8", number = "4", pages = "36:1--36:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344426", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "It is well known that in a network with arbitrary (convex) latency functions that are a function of edge traffic, the worst-case ratio, over all inputs, of the system delay caused due to selfish behavior versus the system delay of the optimal centralized solution may be unbounded even if the system consists of only two parallel links. This ratio is called the price of anarchy (PoA). In this article, we investigate ways by which one can reduce the performance degradation due to selfish behavior. We investigate two primary methods (a) Stackelberg routing strategies, where a central authority, for example, network manager, controls a fixed fraction of the flow, and can route this flow in any desired way so as to influence the flow of selfish users; and (b) network tolls, where tolls are imposed on the edges to modify the latencies of the edges, and thereby influence the induced Nash equilibrium. We obtain results demonstrating the effectiveness of both Stackelberg strategies and tolls in controlling the price of anarchy. For Stackelberg strategies, we obtain the first results for nonatomic routing in graphs more general than parallel-link graphs, and strengthen existing results for parallel-link graphs. (i) In series-parallel graphs, we show that Stackelberg routing reduces the PoA to a constant (depending on the fraction of flow controlled). (ii) For general graphs, we obtain latency-class specific bounds on the PoA with Stackelberg routing, which give a continuous trade-off between the fraction of flow controlled and the price of anarchy. (iii) In parallel-link graphs, we show that for any given class L of latency functions, Stackelberg routing reduces the PoA to at most {$ \alpha + (1 - \alpha) c \rho (L) $}, where {$ \alpha $} is the fraction of flow controlled and {$ \rho (L) $} is the PoA of class {$L$} (when {$ \alpha = 0 $}). For network tolls, motivated by the known strong results for nonatomic games, we consider the more general setting of atomic splittable routing games. We show that tolls inducing an optimal flow always exist, even for general asymmetric games with heterogeneous users, and can be computed efficiently by solving a convex program. This resolves a basic open question about the effectiveness of tolls for atomic splittable games. Furthermore, we give a complete characterization of flows that can be induced via tolls.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Czyzowicz:2012:HMA, author = "Jurek Czyzowicz and Andrzej Pelc and Arnaud Labourel", title = "How to meet asynchronously (almost) everywhere", journal = j-TALG, volume = "8", number = "4", pages = "37:1--37:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344427", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Two mobile agents (robots) with distinct labels have to meet in an arbitrary, possibly infinite, unknown connected graph or in an unknown connected terrain in the plane. Agents are modeled as points, and the route of each of them only depends on its label and on the unknown environment. The actual walk of each agent also depends on an asynchronous adversary that may arbitrarily vary the speed of the agent, stop it, or even move it back and forth, as long as the walk of the agent is continuous, does not leave its route and covers all of it. Meeting in a graph means that both agents must be at the same time in some node or in some point inside an edge of the graph, while meeting in a terrain means that both agents must be at the same time in some point of the terrain. Does there exist a deterministic algorithm that allows any two agents to meet in any unknown environment in spite of this very powerful adversary? We give deterministic rendezvous algorithms for agents starting at arbitrary nodes of any anonymous connected graph (finite or infinite) and for agents starting at any interior points with rational coordinates in any closed region of the plane with path-connected interior. In the geometric scenario agents may have different compasses and different units of length. While our algorithms work in a very general setting --- agents can, indeed, meet almost everywhere --- we show that none of these few limitations imposed on the environment can be removed. On the other hand, our algorithm also guarantees the following approximate rendezvous for agents starting at arbitrary interior points of a terrain as previously stated agents will eventually get to within an arbitrarily small positive distance from each other.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Binkele-Raible:2012:KPN, author = "Daniel Binkele-Raible and Henning Fernau and Fedor V. Fomin and Daniel Lokshtanov and Saket Saurabh and Yngve Villanger", title = "Kernel(s) for problems with no kernel: On out-trees with many leaves", journal = j-TALG, volume = "8", number = "4", pages = "38:1--38:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344428", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The $k$-Leaf Out-Branching problem is to find an out-branching, that is a rooted oriented spanning tree, with at least k leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized algorithms. Here, we take a kernelization based approach to the $k$-Leaf-Out-Branching problem. We give the first polynomial kernel for Rooted $k$-Leaf-Out-Branching, a variant of $k$-Leaf-Out-Branching where the root of the tree searched for is also a part of the input. Our kernel with O(k$^3$) vertices is obtained using extremal combinatorics. For the $k$-Leaf-Out-Branching problem, we show that no polynomial-sized kernel is possible unless coNP is in NP/poly. However, our positive results for Rooted $k$-Leaf-Out-Branching immediately imply that the seemingly intractable k Leaf-Out-Branching problem admits a data reduction to $n$ independent polynomial-sized kernels. These two results, tractability and intractability side by side, are the first ones separating Karp kernelization from Turing kernelization. This answers affirmatively an open problem regarding ``cheat kernelization'' raised by Mike Fellows and Jiong Guo independently.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Im:2012:OSA, author = "Sungjin Im and Benjamin Moseley", title = "An online scalable algorithm for average flow time in broadcast scheduling", journal = j-TALG, volume = "8", number = "4", pages = "39:1--39:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344429", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, the online pull-based broadcast model is considered. In this model, there are $n$ pages of data stored at a server and requests arrive for pages online. When the server broadcasts page p, all outstanding requests for the same page p are simultaneously satisfied. We consider the problem of minimizing average (total) flow time online where all pages are unit-sized. For this problem, there has been a decade-long search for an online algorithm which is scalable, that is, $ (1 + \epsilon) $-speed {$ O(1) $}-competitive for any fixed {$ \epsilon > 0 $}. In this article, we give the first analysis of an online scalable algorithm.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Karakostas:2012:FMT, author = "George Karakostas and Stavros G. Kolliopoulos and Jing Wang", title = "An {FPTAS} for the minimum total weighted tardiness problem with a fixed number of distinct due dates", journal = j-TALG, volume = "8", number = "4", pages = "40:1--40:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344430", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a sequencing of jobs on a single machine, each one with a weight, processing time, and a due date, the tardiness of a job is the time needed for its completion beyond its due date. We present an FPTAS for the basic scheduling problem of minimizing the total weighted tardiness when the number of distinct due dates is fixed. Previously, an FPTAS was known only for the case where all jobs have a common due date.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Deshpande:2012:PPF, author = "Amol Deshpande and Lisa Hellerstein", title = "Parallel pipelined filter ordering with precedence constraints", journal = j-TALG, volume = "8", number = "4", pages = "41:1--41:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344431", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the parallel pipelined filter ordering problem, we are given a set of $n$ filters that run in parallel. The filters need to be applied to a stream of elements, to determine which elements pass all filters. Each filter has a rate limit r$_i$ on the number of elements it can process per unit time, and a selectivity p$_i$, which is the probability that a random element will pass the filter. The goal is to maximize throughput. This problem appears naturally in a variety of settings, including parallel query optimization in databases and query processing over Web services. We present an O(n$^3$) algorithm for this problem, given tree-structured precedence constraints on the filters. This extends work of Condon et al. [2009] and Kodialam [2001], who presented algorithms for solving the problem without precedence constraints. Our algorithm is combinatorial and produces a sparse solution. Motivated by join operators in database queries, we also give algorithms for versions of the problem in which ``filter'' selectivities may be greater than or equal to 1. We prove a strong connection between the more classical problem of minimizing total work in sequential filter ordering (A), and the parallel pipelined filter ordering problem (B). More precisely, we prove that A is solvable in polynomial time for a given class of precedence constraints if and only if B is as well. This equivalence allows us to show that B is NP-Hard in the presence of arbitrary precedence constraints (since A is known to be NP-Hard in that setting).", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{He:2012:SOT, author = "Meng He and J. Ian Munro and Srinivasa Rao Satti", title = "Succinct ordinal trees based on tree covering", journal = j-TALG, volume = "8", number = "4", pages = "42:1--42:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344432", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Various methods have been used to represent a tree on $n$ nodes in essentially the information-theoretic minimum space while supporting various navigational operations in constant time, but different representations usually support different operations. Our main contribution is a succinct representation of ordinal trees, based on that of Geary et al. [2006], that supports all the navigational operations supported by various succinct tree representations while requiring only 2 n + o (n) bits. It also supports efficient level-order traversal, a useful ordering previously supported only with a very limited set of operations. Our second contribution expands on the notion of a single succinct representation supporting more than one traversal ordering, by showing that our method supports two other encoding schemes as abstract data types. In particular, it supports extracting a word ({$ O(\lg n) $} bits) of the balanced parenthesis sequence or depth first unary degree sequence in {$ O(f (n)) $} time, using at most {$ n / f (n) + o (n) $} additional bits, for any {$ f(n) $} in {$ O(\lg n) $} and {$ \Omega (1) $}.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2012:RSU, author = "Pankaj K. Agarwal and Siu-Wing Cheng and Ke Yi", title = "Range searching on uncertain data", journal = j-TALG, volume = "8", number = "4", pages = "43:1--43:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344433", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Querying uncertain data has emerged as an important problem in data management due to the imprecise nature of many measurement data. In this article, we study answering range queries over uncertain data. Specifically, we are given a collection {$P$} of {$n$} uncertain points in {$R$}, each represented by its one-dimensional probability density function (pdf). The goal is to build a data structure on {$P$} such that, given a query interval {$I$} and a probability threshold {$ \tau $}, we can quickly report all points of {$P$} that lie in {$I$} with probability at least {$ \tau $}. We present various structures with linear or near-linear space and (poly)logarithmic query time. Our structures support pdf's that are either histograms or more complex ones such as Gaussian or piecewise algebraic.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andoni:2012:SCE, author = "Alexandr Andoni and Robert Krauthgamer", title = "The smoothed complexity of edit distance", journal = j-TALG, volume = "8", number = "4", pages = "44:1--44:??", month = sep, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2344422.2344434", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:02 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We initiate the study of the smoothed complexity of sequence alignment, by proposing a semi-random model of edit distance between two input strings, generated as follows: First, an adversary chooses two binary strings of length d and a longest common subsequence A of them. Then, every character is perturbed independently with probability p, except that A is perturbed in exactly the same way inside the two strings. We design two efficient algorithms that compute the edit distance on smoothed instances up to a constant factor approximation. The first algorithm runs in near-linear time, namely d$^{{1 + \epsilon }}$ for any fixed $ \epsilon > 0 $. The second one runs in time sublinear in $d$, assuming the edit distance is not too small. These approximation and runtime guarantees are significantly better than the bounds that were known for worst-case inputs. Our technical contribution is twofold. First, we rely on finding matches between substrings in the two strings, where two substrings are considered a match if their edit distance is relatively small, a prevailing technique in commonly used heuristics, such as PatternHunter of Ma et al. [2002]. Second, we effectively reduce the smoothed edit distance to a simpler variant of (worst-case) edit distance, namely, edit distance on permutations (a.k.a. Ulam's metric). We are thus able to build on algorithms developed for the Ulam metric, whose much better algorithmic guarantees usually do not carry over to general edit distance.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Nutov:2012:AMC, author = "Zeev Nutov", title = "Approximating minimum-cost connectivity problems via uncrossable bifamilies", journal = j-TALG, volume = "9", number = "1", pages = "1:1--1:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390177", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give approximation algorithms for the Survivable Network problem. The input consists of a graph $ G = (V, E) $ with edge/node-costs, a node subset $ S \subseteq V $, and connectivity requirements $ \{ r(s, t) : s, t \in T \subseteq V \} $. The goal is to find a minimum cost subgraph $H$ of $G$ that for all $ s, t \in T $ contains $ r(s, t) $ pairwise edge-disjoint $ s t $-paths such that no two of them have a node in $ S \{ s, t \} $ in common. Three extensively studied particular cases are: Edge-Connectivity Survivable Network ($ S = \oslash $), Node-Connectivity Survivable Network ($ S = V $), and Element-Connectivity Survivable Network ($ r(s, t) = 0 $ whenever $ s \in S $ or $ t \in S $). Let $ k = \max \{_{s, t \in T} \} r(s, t) $. In Rooted Survivable Network, there is $ s \in T $ such that $ r(u, t) = 0 $ for all $ u \neq s $, and in the Subset $k$-Connected Subgraph problem $ r(s, t) = k $ for all $ s, t \in T $. For edge-costs, our ratios are $ O(k \log k) $ for Rooted Survivable Network and $ O(k^2 \log k) $ for Subset $k$-Connected Subgraph. This improves the previous ratio $ O(k^2 \log n) $, and for constant values of $k$ settles the approximability of these problems to a constant. For node-costs, our ratios are as follows. --- $ O(k \log | T |) $ for Element-Connectivity Survivable Network, matching the best known ratio for Edge-Connectivity Survivable Network. --- $ O(k^2 \log | T |) $ for Rooted Survivable Network and $ O(k^3 \log | T |) $ for Subset $k$-Connected Subgraph, improving the ratio $ O(k^8 \log^2 | T |) $. --- $ O(k^4 \log^2 | T |) $ for Survivable Network; this is the first nontrivial approximation algorithm for the node-costs version of the problem.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hajiaghayi:2012:PCS, author = "Mohammadtaghi Hajiaghayi and Rohit Khandekar and Guy Kortsarz and Zeev Nutov", title = "Prize-collecting {Steiner} network problems", journal = j-TALG, volume = "9", number = "1", pages = "2:1--2:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390178", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the Steiner Network problem, we are given a graph {$G$} with edge-costs and connectivity requirements {$ r_{u v} $} between node pairs {$ u, v $}. The goal is to find a minimum-cost subgraph {$H$} of {$G$} that contains {$ r_{uv} $} edge-disjoint paths for all {$ u, v \in V $}. In Prize-Collecting Steiner Network problems, we do not need to satisfy all requirements, but are given a penalty function for violating the connectivity requirements, and the goal is to find a subgraph {$H$} that minimizes the cost plus the penalty. The case when {$ r_{uv} \in \{ 0, 1 \} $} is the classic Prize-Collecting Steiner Forest problem. In this article, we present a novel linear programming relaxation for the Prize-Collecting Steiner Network problem, and by rounding it, obtain the first constant-factor approximation algorithm for submodular and monotone nondecreasing penalty functions. In particular, our setting includes all-or-nothing penalty functions, which charge the penalty even if the connectivity requirement is slightly violated; this resolves an open question posed by Nagarajan et al. [2008]. We further generalize our results for element-connectivity and node-connectivity.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Awerbuch:2012:DAM, author = "Baruch Awerbuch and Rohit Khandekar and Satish Rao", title = "Distributed algorithms for multicommodity flow problems via approximate steepest descent framework", journal = j-TALG, volume = "9", number = "1", pages = "3:1--3:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390179", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider solutions for distributed multicommodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. We show first distributed solutions that allow $ (1 + \epsilon) $ approximation and whose convergence time is essentially linear in the maximal path length, and is independent of the number of commodities and the size of the graph. Our algorithms use a very natural approximate steepest descent framework, combined with a blocking flow technique to speed up the convergence in distributed and parallel environment. Previously known solutions that achieved comparable convergence time and approximation ratio required exponential computational and space overhead per agent.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chen:2012:CRS, author = "Wei Chen and Christian Sommer and Shang-Hua Teng and Yajun Wang", title = "A compact routing scheme and approximate distance oracle for power-law graphs", journal = j-TALG, volume = "9", number = "1", pages = "4:1--4:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390180", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Compact routing addresses the tradeoff between table sizes and stretch, which is the worst-case ratio between the length of the path a packet is routed through by the scheme and the length of an actual shortest path from source to destination. We adapt the compact routing scheme by Thorup and Zwick [2001] to optimize it for power-law graphs. We analyze our adapted routing scheme based on the theory of unweighted random power-law graphs with fixed expected degree sequence by Aiello et al. [2000]. Our result is the first analytical bound coupled to the parameter of the power-law graph model for a compact routing scheme. Let $n$ denote the number of nodes in the network. We provide a labeled routing scheme that, after a stretch--5 handshaking step (similar to DNS lookup in TCP/IP), routes messages along stretch--3 paths. We prove that, instead of routing tables with {$ \tilde {O}(n^{1 / 2}) $} bits ({$ \tilde {O} $} suppresses factors logarithmic in {$n$}) as in the general scheme by Thorup and Zwick, expected sizes of {$ O(n^\gamma \log n) $} bits are sufficient, and that all the routing tables can be constructed at once in expected time {$ O(n^{1 + \gamma } \log n) $}, with {$ \gamma = \tau - 22 / \tau - 3 + \epsilon $}, where {$ \tau \in (2, 3) $} is the power-law exponent and {$ \epsilon 0 $} (which implies $ \epsilon < \gamma < 1 / 3 + \epsilon $). Both bounds also hold with probability at least $ 1 - 1 / n $ (independent of $ \epsilon $). The routing scheme is a labeled scheme, requiring a stretch--5 handshaking step. The scheme uses addresses and message headers with {$ O(\log n \log \log n) $} bits, with probability at least {$ 1 - o(1) $}. We further demonstrate the effectiveness of our scheme by simulations on real-world graphs as well as synthetic power-law graphs. With the same techniques as for the compact routing scheme, we also adapt the approximate distance oracle by Thorup and Zwick [2001, 2005] for stretch-3 and we obtain a new upper bound of expected {$ \tilde {O}(n^{1 + \gamma }) $} for space and preprocessing for random power-law graphs. Our distance oracle is the first one optimized for power-law graphs. Furthermore, we provide a linear-space data structure that can answer 5--approximate distance queries in time at most {$ \tilde {O}(n^{1 / 4 + \epsilon }) $} (similar to {$ \gamma $}, the exponent actually depends on {$ \tau $} and lies between {$ \epsilon $} and $ 1 / 4 + \epsilon $).", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jez:2012:OSP, author = "Lukasz Jez and Fei Li and Jay Sethuraman and Clifford Stein", title = "Online scheduling of packets with agreeable deadlines", journal = j-TALG, volume = "9", number = "1", pages = "5:1--5:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390181", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article concerns an online packet scheduling problem that arises as a natural model for buffer management at a network router. Packets arrive at a router at integer time steps, and are buffered upon arrival. Packets have non-negative weights and integer deadlines that are (weakly) increasing in their arrival times. In each integer time step, at most one packet can be sent. The objective is to maximize the sum of the weights of the packets that are sent by their deadlines. The main results include an optimal $ (\phi := (1 + \sqrt 5) / 2 \approx 1.618) $-competitive deterministic online algorithm, a $ (4 / 3 \approx 1.33) $-competitive randomized online algorithm against an oblivious adversary, and a $2$-speed $1$-competitive deterministic online algorithm. The analysis does not use a potential function explicitly, but instead modifies the adversary's buffer and credits the adversary to account for these modifications.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bonifaci:2012:ACP, author = "Vincenzo Bonifaci and Ho-Leung Chan and Alberto Marchetti-Spaccamela and Nicole Megow", title = "Algorithms and complexity for periodic real-time scheduling", journal = j-TALG, volume = "9", number = "1", pages = "6:1--6:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390182", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate the preemptive scheduling of periodic tasks with hard deadlines. We show that, even in the uniprocessor case, no pseudopolynomial-time algorithm can test the feasibility of a task system within a constant speedup bound, unless P = NP. This result contrasts with recent results for sporadic task systems. For two special cases, synchronous task systems and systems with a constant number of different task types, we provide the first polynomial-time constant-speedup feasibility tests for multiprocessor platforms. Furthermore, we show that the problem of testing feasibility is coNP-hard for synchronous multiprocessor task systems. The complexity of some of these problems has been open for a long time. We also propose a weight maximization variant of the feasibility problem, where every task has a nonnegative weight, and the goal is to find a subset of tasks that can be scheduled feasibly and has maximum weight. We give the first constant-speed, constant-approximation algorithm for the case of synchronous task systems, together with related hardness results.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Halldorsson:2012:WSP, author = "Magn{\'u}s M. Halld{\'o}rsson", title = "Wireless scheduling with power control", journal = j-TALG, volume = "9", number = "1", pages = "7:1--7:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390183", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints. We give an algorithm that attains an approximation ratio of {$ O(\log n c \log \log \Delta) $}, where {$n$} is the number of links and {$ \Delta $} is the ratio between the longest and the shortest link length. Under the natural assumption that lengths are represented in binary, this gives the first approximation ratio that is polylogarithmic in the size of the input. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We give evidence that this dependence on {$ \Delta $} is unavoidable, showing that any reasonably behaving oblivious power assignment results in a {$ \Omega (\log \log \Delta) $}-approximation. These results hold also for the (weighted) capacity problem of finding a maximum (weighted) subset of links that can be scheduled in a single time slot. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard {$2$}-dimensional Euclidean plane to doubling metrics. Finally, we explore the utility of graph models in capturing wireless interference.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ebrahimi:2012:CAW, author = "Javad B. Ebrahimi and Christina Fragouli", title = "Combinatiorial algorithms for wireless information flow", journal = j-TALG, volume = "9", number = "1", pages = "8:1--8:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390184", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr et al. [2007b] proposed a linear deterministic model that takes into account the shared nature of wireless channels, focusing on the signal interactions rather than the background noise. They generalized the min-cut max-flow theorem for graphs to networks of deterministic channels and proved that the capacity can be achieved using information theoretical tools. They showed that the value of the minimum cut is in this case the minimum rank of all the adjacency matrices describing source-destination cuts. In this article, we develop a polynomial-time algorithm that discovers the relay encoding strategy to achieve the min-cut value in linear deterministic (wireless) networks, for the case of a unicast connection. Our algorithm crucially uses a notion of linear independence between channels to calculate the capacity in polynomial time. Moreover, we can achieve the capacity by using very simple one-symbol processing at the intermediate nodes, thereby constructively yielding finite-length strategies that achieve the unicast capacity of the linear deterministic (wireless) relay network.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chekuri:2012:SMP, author = "Chandra Chekuri and Kenneth L. Clarkson and Sariel Har-Peled", title = "On the set multicover problem in geometric settings", journal = j-TALG, volume = "9", number = "1", pages = "9:1--9:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390185", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the set multicover problem in geometric settings. Given a set of points {$P$} and a collection of geometric shapes (or sets) {$F$}, we wish to find a minimum cardinality subset of {$F$} such that each point {$ p \in P $} is covered by (contained in) at least {$ d(p) $} sets. Here, {$ d(p) $} is an integer demand (requirement) for {$p$}. When the demands $ d(p) = 1 $ for all $p$, this is the standard set cover problem. The set cover problem in geometric settings admits an approximation ratio that is better than that for the general version. In this article, we show that similar improvements can be obtained for the multicover problem as well. In particular, we obtain an {$ O(\log {\rm opt}) $} approximation for set systems of bounded VC-dimension, and an {$ O(1) $} approximation for covering points by half-spaces in three dimensions and for some other classes of shapes.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Giesen:2012:APC, author = "Joachim Giesen and Martin Jaggi and S{\"o}ren Laue", title = "Approximating parameterized convex optimization problems", journal = j-TALG, volume = "9", number = "1", pages = "10:1--10:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390186", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider parameterized convex optimization problems over the unit simplex, that depend on one parameter. We provide a simple and efficient scheme for maintaining an $ \epsilon $-approximate solution (and a corresponding $ \epsilon $-coreset) along the entire parameter path. We prove correctness and optimality of the method. Practically relevant instances of the abstract parameterized optimization problem are for example regularization paths of support vector machines, multiple kernel learning, and minimum enclosing balls of moving points.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Philip:2012:PKD, author = "Geevarghese Philip and Venkatesh Raman and Somnath Sikdar", title = "Polynomial kernels for dominating set in graphs of bounded degeneracy and beyond", journal = j-TALG, volume = "9", number = "1", pages = "11:1--11:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390187", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that for every fixed $ j \geq i \geq 1 $, the $k$-Dominating Set problem restricted to graphs that do not have {$ K_{ij} $} (the complete bipartite graph on {$ (i + j) $} vertices, where the two parts have {$i$} and {$j$} vertices, respectively) as a subgraph is fixed parameter tractable (FPT) and has a polynomial kernel. We describe a polynomial-time algorithm that, given a {$ K_{i, j} $}-free graph {$G$} and a nonnegative integer {$k$}, constructs a graph {$H$} (the ``kernel'') and an integer {$ k' $} such that (1) {$G$} has a dominating set of size at most {$k$} if and only if {$H$} has a dominating set of size at most {$ k' $}, (2) {$H$} has {$ O((j + 1)^{i + 1} k^{i^2}) $} vertices, and (3) {$ k' = O((j + 1)^{i + 1} k^{i^2}) $}. Since {$d$}-degenerate graphs do not have {$ K_{d + 1, d + 1} $} as a subgraph, this immediately yields a polynomial kernel on {$ O((d + 2)^{d + 2} {k^{(d + 1)}}^2) $} vertices for the {$k$}-Dominating Set problem on {$d$}-degenerate graphs, solving an open problem posed by Alon and Gutner [Alon and Gutner 2008; Gutner 2009]. The most general class of graphs for which a polynomial kernel was previously known for {$k$}-Dominating Set is the class of {$ K_h $}-topological-minor-free graphs [Gutner 2009]. Graphs of bounded degeneracy are the most general class of graphs for which an FPT algorithm was previously known for this problem. {$ K_h $}-topological-minor-free graphs are {$ K_{i, j} $}-free for suitable values of {$i$}, {$j$} (but not vice-versa), and so our results show that {$k$}-Dominating Set has both FPT algorithms and polynomial kernels in strictly more general classes of graphs. Using the same techniques, we also obtain an {$ O(j k^i) $} vertex-kernel for the {$k$}-Independent Dominating Set problem on {$ K_{i, j} $}-free graphs.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bodlaender:2012:EAT, author = "Hans L. Bodlaender and Fedor V. Fomin and Arie M. C. A. Koster and Dieter Kratsch and Dimitrios M. Thilikos", title = "On exact algorithms for treewidth", journal = j-TALG, volume = "9", number = "1", pages = "12:1--12:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390188", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential-time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time O *(2 $^n$). This algorithm is based on the old dynamic programming method introduced by Held and Karp for the Traveling Salesman problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. We also consider the problem of computing Treewidth under the restriction that the space used is only polynomial and give a simple O *(4 $^n$) algorithm that requires polynomial space. We also show that with a more complicated algorithm using balanced separators, Treewidth can be computed in O *(2.9512 $^n$) time and polynomial space.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Amir:2012:CDC, author = "Amihood Amir and Estrella Eisenberg and Avivit Levy and Ely Porat and Natalie Shapira", title = "Cycle detection and correction", journal = j-TALG, volume = "9", number = "1", pages = "13:1--13:??", month = dec, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1145/2390176.2390189", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 2 10:10:04 MST 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Assume that a natural cyclic phenomenon has been measured, but the data is corrupted by errors. The type of corruption is application-dependent and may be caused by measurements errors, or natural features of the phenomenon. We assume that an appropriate metric exists, which measures the amount of corruption experienced. This article studies the problem of recovering the correct cycle from data corrupted by various error models, formally defined as the period recovery problem. Specifically, we define a metric property which we call pseudolocality and study the period recovery problem under pseudolocal metrics. Examples of pseudolocal metrics are the Hamming distance, the swap distance, and the interchange (or Cayley) distance. We show that for pseudolocal metrics, periodicity is a powerful property allowing detecting the original cycle and correcting the data, under suitable conditions. Some surprising features of our algorithm are that we can efficiently identify the period in the corrupted data, up to a number of possibilities logarithmic in the length of the data string, even for metrics whose calculation is NP-hard. For the Hamming metric, we can reconstruct the corrupted data in near-linear time even for unbounded alphabets. This result is achieved using the property of separation in the self-convolution vector and Reed--Solomon codes. Finally, we employ our techniques beyond the scope of pseudo-local metrics and give a recovery algorithm for the non-pseudolocal Levenshtein edit metric.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Weimann:2013:RPD, author = "Oren Weimann and Raphael Yuster", title = "Replacement Paths and Distance Sensitivity Oracles via Fast Matrix Multiplication", journal = j-TALG, volume = "9", number = "2", pages = "14:1--14:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438646", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A distance sensitivity oracle of an $n$-vertex graph {$ G = (V, E) $} is a data structure that can report shortest paths when edges of the graph fail. A query ({$ u \in V $}, {$ v \in V $}, {$ S \subseteq E $}) to this oracle returns a shortest $u$-to-$v$ path in the graph {$ G' = (V, E \backslash S) $}. We present randomized (Monte Carlo) algorithms for constructing a distance sensitivity oracle of size {$ \tilde {O}(n^{3 - \alpha }) $} for {$ | S | = O(\lg n / \lg \lg n) $} and any choice of $ 0 < \alpha < 1 $. For real edge-lengths, the oracle is constructed in {$ O(n^{4 - \alpha }) $} time and a query to this oracle takes {$ \tilde {O} (n^{2 - 2(1 - \alpha) / |S|}) $} time. For integral edge-lengths in {$ \{ - M, \ldots {}, M \} $}, using the current $ \omega < 2.376 $ matrix multiplication exponent, the oracle is constructed in {$ O(M n^{3.376 - \alpha }) $} time with {$ \tilde {O}({n^{2 - (1 - \alpha) / |S|}}) $} query, or alternatively in {$ O(M^{0.681} n^{3.575 - \alpha }) $} time with {$ \tilde {O}(n^{2 - 2(1 - \alpha) / |S|}) $} query. Distance sensitivity oracles generalize the replacement paths problem in which $u$ and $v$ are known in advance and {$ | S | = 1 $}. In other words, if {$P$} is a shortest path from $u$ to $v$ in {$G$}, then the replacement paths problem asks to compute, for every edge $e$ on {$P$}, a shortest $u$-to-$v$ path that avoids $e$. Our new technique for constructing distance sensitivity oracles using fast matrix multiplication also yields the first subcubic-time algorithm for the replacement paths problem when the edge-lengths are small integers. In particular, it yields a randomized (Monte Carlo) {$ \tilde {O}(M n^{2.376} + M^{2 / 3} n^{2.584}) $}-time algorithm for the replacement paths problem assuming {$ M \leq n^{0.624} $}. Finally, we mention that both our replacement paths algorithm and our distance sensitivity oracle can be made to work, in the same time and space bounds, for the case of failed vertices rather than edges, that is, when {$S$} is a set of vertices and we seek a shortest $u$-to-$v$ path in the graph obtained from {$G$} by removing all vertices in {$S$} and their adjacent edges.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Roditty:2013:AG, author = "Liam Roditty and Roei Tov", title = "Approximating the Girth", journal = j-TALG, volume = "9", number = "2", pages = "15:1--15:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438647", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article considers the problem of computing a minimum weight cycle in weighted undirected graphs. Given a weighted undirected graph {$ G = (V, E, w) $}, let {$C$} be a minimum weight cycle of G, let w (C) be the weight of {$C$}, and let {$ w_{\rm max}(C) $} be the weight of the maximum edge of {$C$}. We obtain three new approximation algorithms for the minimum weight cycle problem: (1) for integral weights from the range {$ [1, M] $}, an algorithm that reports a cycle of weight at most {$ 4 / 3 w (C) $} in {$ O(n^2 \log n (\log n + \log M)) $} time; (2) For integral weights from the range {$ [1, M] $}, an algorithm that reports a cycle of weight at most {$ w(C) + w_{\rm max}(C) $} in {$ O(n^2 \log n (\log n + \log M)) $} time; (3) For nonnegative real edge weights, an algorithm that for any $ \epsilon > 0 $ reports a cycle of weight at most {$ (4 / 3 + \epsilon) w(C) $} in {$ O(1 \epsilon n^2 \log n (\log \log n)) $} time. In a recent breakthrough, Williams and Williams [2010] showed that a subcubic algorithm, that computes the exact minimum weight cycle in undirected graphs with integral weights from the range {$ [1, M] $}, implies a subcubic algorithm for computing all-pairs shortest paths in directed graphs with integral weights from the range {$ [ - M, M] $}. This implies that in order to get a subcubic algorithm for computing a minimum weight cycle, we have to relax the problem and to consider an approximated solution. Lingas and Lundell [2009] were the first to consider approximation in the context of minimum weight cycle in weighted graphs. They presented a 2-approximation algorithm for integral weights with {$ O(n^2 \log n (\log n + \log M)) $} running time. They also posed, as an open problem, the question whether it is possible to obtain a subcubic algorithm with a $c$ approximation, where $ c < 2 $. The current article answers this question in the affirmative, by presenting an algorithm with 4/3-approximation and the same running time. Surprisingly, the approximation factor of 4/3 is not accidental. We show, using the new result of Williams and Williams [2010], that a subcubic combinatorial algorithm with $ (4 / 3 - \epsilon) $-approximation, where $ 0 < \epsilon \leq 1 / 3 $, implies a subcubic combinatorial algorithm for multiplying two boolean matrices.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kawarabayashi:2013:LAA, author = "Ken-Ichi Kawarabayashi and Yusuke Kobayashi", title = "An {$ O(\log n) $}-Approximation Algorithm for the Edge-Disjoint Paths Problem in {Eulerian} Planar Graphs", journal = j-TALG, volume = "9", number = "2", pages = "16:1--16:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438648", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we study an approximation algorithm for the maximum edge-disjoint paths problem. In this problem, we are given a graph and a collection of pairs of vertices, and the objective is to find the maximum number of pairs that can be connected by edge-disjoint paths. We give an {$ O(\log n) $}-approximation algorithm for the maximum edge-disjoint paths problem when an input graph is either 4-edge-connected planar or Eulerian planar. This improves an {$ O(\log^2 n) $}-approximation algorithm given by Kleinberg [2005] for Eulerian planar graphs. Our result also generalizes the result by Chekuri et al. [2004, 2005] who gave an {$ O(\log n) $}-approximation algorithm for the maximum edge-disjoint paths problem with congestion two when an input graph is planar.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fraigniaud:2013:DIE, author = "Pierre Fraigniaud and Andrzej Pelc", title = "Delays Induce an Exponential Memory Gap for Rendezvous in Trees", journal = j-TALG, volume = "9", number = "2", pages = "17:1--17:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438649", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The aim of rendezvous in a graph is meeting of two mobile agents at some node of an unknown anonymous connected graph. In this article, we focus on rendezvous in trees, and, analogously to the efforts that have been made for solving the exploration problem with compact automata, we study the size of memory of mobile agents that permits to solve the rendezvous problem deterministically. We assume that the agents are identical, and move in synchronous rounds. We first show that if the delay between the starting times of the agents is arbitrary, then the lower bound on memory required for rendezvous is {$ \Omega (\log n) $} bits, even for the line of length n. This lower bound meets a previously known upper bound of {$ O(\log n) $} bits for rendezvous in arbitrary graphs of size at most $n$. Our main result is a proof that the amount of memory needed for rendezvous with simultaneous start depends essentially on the number $l$ of leaves of the tree, and is exponentially less impacted by the number $n$ of nodes. Indeed, we present two identical agents with {$ O(\log l + \log \log n) $} bits of memory that solve the rendezvous problem in all trees with at most $n$ nodes and at most $l$ leaves. Hence, for the class of trees with polylogarithmically many leaves, there is an exponential gap in minimum memory size needed for rendezvous between the scenario with arbitrary delay and the scenario with delay zero. Moreover, we show that our upper bound is optimal by proving that {$ \Omega (\log l + \log \log n) $} bits of memory are required for rendezvous, even in the class of trees with degrees bounded by 3.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bansal:2013:SSA, author = "Nikhil Bansal and Ho-Leung Chan and Kirk Pruhs", title = "Speed Scaling with an Arbitrary Power Function", journal = j-TALG, volume = "9", number = "2", pages = "18:1--18:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438650", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article initiates a theoretical investigation into online scheduling problems with speed scaling where the allowable speeds may be discrete, and the power function may be arbitrary, and develops algorithmic analysis techniques for this setting. We show that a natural algorithm, which uses Shortest Remaining Processing Time for scheduling and sets the power to be one more than the number of unfinished jobs, is 3-competitive for the objective of total flow time plus energy. We also show that another natural algorithm, which uses Highest Density First for scheduling and sets the power to be the fractional weight of the unfinished jobs, is a 2-competitive algorithm for the objective of fractional weighted flow time plus energy.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hochbaum:2013:AAM, author = "Dorit S. Hochbaum and Asaf Levin", title = "Approximation Algorithms for a Minimization Variant of the Order-Preserving Submatrices and for Biclustering Problems", journal = j-TALG, volume = "9", number = "2", pages = "19:1--19:??", month = mar, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2438645.2438651", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:37 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Finding a largest Order-Preserving SubMatrix, OPSM, is an important problem arising in the discovery of patterns in gene expression. Ben-Dor et al. formulated the problem in Ben-Dor et al. [2003]. They further showed that the problem is NP-complete and provided a greedy heuristic for the problem. The complement of the OPSM problem, called MinOPSM, is to delete the least number of entries in the matrix so that the remaining submatrix is order preserving. We devise a 5-approximation algorithm for the MinOPSM based on a formulation of the problem as a quadratic, nonseparable set cover problem. An alternative formulation combined with a primal-dual algorithm improves the approximation factor to 3. The complexity of both algorithms for a matrix of size $ m \times n $ is {$ O(m^2 n) $}. We further comment on the related biclustering problem.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chawla:2013:FSI, author = "Shuchi Chawla and Prasad Raghavendra and Dana Randall", title = "Foreword to the {Special Issue on SODA'11}", journal = j-TALG, volume = "9", number = "3", pages = "20:1--20:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483700", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ailon:2013:AOU, author = "Nir Ailon and Edo Liberty", title = "An Almost Optimal Unrestricted Fast {Johnson--Lindenstrauss Transform}", journal = j-TALG, volume = "9", number = "3", pages = "21:1--21:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483701", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The problems of random projections and sparse reconstruction have much in common and individually received much attention. Surprisingly, until now they progressed in parallel and remained mostly separate. Here, we employ new tools from probability in Banach spaces that were successfully used in the context of sparse reconstruction to advance on an open problem in random projection. In particular, we generalize and use an intricate result by Rudelson and Veshynin [2008] for sparse reconstruction which uses Dudley's theorem for bounding Gaussian processes. Our main result states that any set of {$ N = \exp (\tilde {O}(n)) $} real vectors in $n$-dimensional space can be linearly mapped to a space of dimension {$ k = O(\log N \polylog (n)) $}, while (1) preserving the pairwise distances among the vectors to within any constant distortion and (2) being able to apply the transformation in time {$ O(n \log n) $} on each vector. This improves on the best known bound {$ N = \exp (\tilde {O}(n^{1 / 2})) $} achieved by Ailon and Liberty [2009] and {$ N = e x p(\tilde {O}(n^{1 / 3})) $} by Ailon and Chazelle [2010]. The dependence in the distortion constant however is suboptimal, and since the publication of an early version of the work, the gap between upper and lower bounds has been considerably tightened obtained by Krahmer and Ward [2011]. For constant distortion, this settles the open question posed by these authors up to a $ \polylog (n) $ factor while considerably simplifying their constructions.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2013:PPS, author = "Timothy M. Chan", title = "Persistent Predecessor Search and Orthogonal Point Location on the Word {RAM}", journal = j-TALG, volume = "9", number = "3", pages = "22:1--22:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483702", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We answer a basic data structuring question (e.g., raised by Dietz and Raman [1991]): Can van Emde Boas trees be made persistent, without changing their asymptotic query/update time? We present a (partially) persistent data structure that supports predecessor search in a set of integers in {$ \{ 1, \ldots {}, U \} $} under an arbitrary sequence of n insertions and deletions, with {$ O(\log \log U) $} expected query time and expected amortized update time, and {$ O(n) $} space. The query bound is optimal in {$U$} for linear-space structures and improves previous near-{$ O((\log \log U)^2) $} methods. The same method solves a fundamental problem from computational geometry: point location in orthogonal planar subdivisions (where edges are vertical or horizontal). We obtain the first static data structure achieving {$ O(\log \log U) $} worst-case query time and linear space. This result is again optimal in {$U$} for linear-space structures and improves the previous {$ O((\log \log U)^2) $} method by de Berg et al. [1995]. The same result also holds for higher-dimensional subdivisions that are orthogonal binary space partitions, and for certain nonorthogonal planar subdivisions such as triangulations without small angles. Many geometric applications follow, including improved query times for orthogonal range reporting for dimensions $ \geq 3 $ on the RAM. Our key technique is an interesting new van-Emde-Boas--style recursion that alternates between two strategies, both quite simple.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Daskalakis:2013:CAN, author = "Constantinos Daskalakis", title = "On the Complexity of Approximating a {Nash} Equilibrium", journal = j-TALG, volume = "9", number = "3", pages = "23:1--23:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483703", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that computing a relatively (i.e., multiplicatively as opposed to additively) approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first constant inapproximability result for Nash equilibrium, since the original results on the computational complexity of the problem [Daskalakis et al. 2006a; Chen and Deng 2006]. Moreover, it provides an apparent---assuming that PPAD is not contained in TIME({$ n^{O(\log n)} $})---dichotomy between the complexities of additive and relative approximations, as for constant values of additive approximation a quasi-polynomial-time algorithm is known [Lipton et al. 2003]. Such a dichotomy does not exist for values of the approximation that scale inverse-polynomially with the size of the game, where both relative and additive approximations are PPAD-complete [Chen et al. 2006]. As a byproduct, our proof shows that (unconditionally) the sparse-support lemma [Lipton et al. 2003] cannot be extended to relative notions of constant approximation.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eisenbrand:2013:PDP, author = "Friedrich Eisenbrand and D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi and Thomas Rothvo{\ss}", title = "Bin Packing via Discrepancy of Permutations", journal = j-TALG, volume = "9", number = "3", pages = "24:1--24:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483704", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A well-studied special case of bin packing is the 3-partition problem, where n items of size > 1/4 have to be packed in a minimum number of bins of capacity one. The famous Karmarkar-Karp algorithm transforms a fractional solution of a suitable LP relaxation for this problem into an integral solution that requires at most {$ O(\log n) $} additional bins. The three-permutations-problem of Beck is the following. Given any three permutations on n symbols, color the symbols red and blue, such that in any interval of any of those permutations, the number of red and blue symbols is roughly the same. The necessary difference is called the discrepancy. We establish a surprising connection between bin packing and Beck's problem: The additive integrality gap of the 3-partition linear programming relaxation can be bounded by the discrepancy of three permutations. This connection yields an alternative method to establish an {$ O(\log n) $} bound on the additive integrality gap of the 3-partition. Conversely, making use of a recent example of three permutations, for which a discrepancy of {$ \Omega (\log n) $} is necessary, we prove the following: The {$ O(\log^2 n) $} upper bound on the additive gap for bin packing with arbitrary item sizes cannot be improved by any technique that is based on rounding up items. This lower bound holds for a large class of algorithms including the Karmarkar-Karp procedure.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gawrychowski:2013:OPM, author = "Pawel Gawrychowski", title = "Optimal Pattern Matching in {LZW} Compressed Strings", journal = j-TALG, volume = "9", number = "3", pages = "25:1--25:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483705", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/string-matching.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the following variant of the classical pattern matching problem: given an uncompressed pattern $ p [1 \ldots {} m] $ and a compressed representation of a string {$ t [1 \ldots {} N] $}, does $p$ occur in $t$ ? When $t$ is compressed using the LZW method, we are able to detect the occurrence in optimal linear time, thus answering a question of Amir et al. [1994]. Previous results implied solutions with complexities {$ O(n \log m + m) $} Amir et al. [1994], {$ O(n + m^{1 + \epsilon }) $} [Kosaraju 1995], or (randomized) {$ O(n \log N n + m) $} [Farach and Thorup 1995], where $n$ is the size of the compressed representation of $t$. Our algorithm is conceptually simple and fully deterministic.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jayram:2013:OBJ, author = "T. S. Jayram and David P. Woodruff", title = "Optimal Bounds for {Johnson--Lindenstrauss Transforms} and Streaming Problems with Subconstant Error", journal = j-TALG, volume = "9", number = "3", pages = "26:1--26:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483706", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Johnson--Lindenstrauss transform is a dimensionality reduction technique with a wide range of applications to theoretical computer science. It is specified by a distribution over projection matrices from {$ R^n \to R^k $} where $ k ? n $ and states that {$ k = O(\epsilon^{-2} \log 1 / \delta) $} dimensions suffice to approximate the norm of any fixed vector in {$ R^n $} to within a factor of $ 1 \pm {} \epsilon $ with probability at least $ 1 - \delta $. In this article, we show that this bound on $k$ is optimal up to a constant factor, improving upon a previous {$ \Omega ((\epsilon^{-2} \log 1 / \delta) / \log (1 / \epsilon)) $} dimension bound of Alon. Our techniques are based on lower bounding the information cost of a novel one-way communication game and yield the first space lower bounds in a data stream model that depend on the error probability $ \delta $. For many streaming problems, the most na{\"\i}ve way of achieving error probability $ \delta $ is to first achieve constant probability, then take the median of {$ O(\log 1 / \delta) $} independent repetitions. Our techniques show that for a wide range of problems, this is in fact optimal! As an example, we show that estimating the $ l_p $-distance for any $ p \in [0, 2] $ requires {$ \Omega (\epsilon^{-2} \log n \log 1 / \delta) $} space, even for vectors in $ \{ 0, 1 \}^n $. This is optimal in all parameters and closes a long line of work on this problem. We also show the number of distinct elements requires {$ \Omega (\epsilon^{-2} \log 1 / \delta + \log n) $} space, which is optimal if {$ \epsilon^{-2} = \Omega (\log n) $}. We also improve previous lower bounds for entropy in the strict turnstile and general turnstile models by a multiplicative factor of {$ \Omega (\log 1 / \delta) $}. Finally, we give an application to one-way communication complexity under product distributions, showing that, unlike the case of constant $ \delta $, the VC-dimension does not characterize the complexity when $ \delta = o (1) $.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lacki:2013:IDA, author = "Jakub Lacki", title = "Improved Deterministic Algorithms for Decremental Reachability and Strongly Connected Components", journal = j-TALG, volume = "9", number = "3", pages = "27:1--27:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483707", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article presents a new deterministic algorithm for decremental maintenance of the transitive closure in a directed graph. The algorithm processes any sequence of edge deletions in {$ O(m n) $} time and answers queries in constant time. Previously, such time bound has only been achieved by a randomized Las Vegas algorithm. In addition to that, a few decremental algorithms for maintaining strongly connected components are shown, whose time complexity is {$ O(n^{1.5}) $} for planar graphs, {$ O(n \log n) $} for graphs with bounded treewidth and {$ O(m n) $} for general digraphs.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Solomon:2013:SES, author = "Shay Solomon", title = "Sparse {Euclidean} Spanners with Tiny Diameter", journal = j-TALG, volume = "9", number = "3", pages = "28:1--28:??", month = jun, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2483699.2483708", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jun 24 09:39:46 MDT 2013", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In STOC'95, Arya et al. [1995] showed that for any set of $n$ points in {$ R^d $}, a $ (1 + \epsilon) $-spanner with diameter at most $2$ (respectively, $3$ ) and {$ O(n \log n) $} edges (respectively, {$ O(n \log \log n) $} edges) can be built in {$ O(n \log n) $} time. Moreover, it was shown in Arya et al. [1995] and Narasimhan and Smid [2007] that for any $ k \geq 4 $, one can build in {$ O(n (\log n) 2^k \alpha_k(n)) $} time a $ (1 + \epsilon) $-spanner with diameter at most $ 2 k $ and {$ O(n 2^k \alpha_k(n)) $} edges. The function $ \alpha_k $ is the inverse of a certain function at the $ k / 2 $-th level of the primitive recursive hierarchy, where $ \alpha_0 (n) = n / 2 $, $ \alpha_1 (n) = \sqrt n $, $ \alpha_2 (n) = \log n $, $ \alpha_3 (n) = \log \log n $, $ \alpha_4 (n) = \log * n $, $ \alpha_5 (n) = 12 \log * n $, \ldots{}, etc. It is also known [Narasimhan and Smid 2007] that if one allows quadratic time, then these bounds can be improved. Specifically, for any $ k \geq 4 $, a $ (1 + \epsilon) $-spanner with diameter at most $k$ and {$ O(n k \alpha_k(n)) $} edges can be constructed in {$ O(n^2) $} time [Narasimhan and Smid 2007]. A major open question in this area is whether one can construct within time {$ O(n \log n + n k \alpha_k(n)) $} a $ (1 + \epsilon) $-spanner with diameter at most $k$ and {$ O(n k \alpha_k(n)) $} edges. In this article, we answer this question in the affirmative. Moreover, in fact, we provide a stronger result. Specifically, we show that for any $ k \geq 4 $, a $ (1 + \epsilon) $-spanner with diameter at most $k$ and {$ O(n \alpha_k(n)) $} edges can be built in optimal time {$ O(n \log n) $}.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Biedl:2013:MOP, author = "Therese Biedl and Anna Lubiw and Mark Petrick and Michael Spriggs", title = "Morphing orthogonal planar graph drawings", journal = j-TALG, volume = "9", number = "4", pages = "29:1--29:??", month = sep, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2500118", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:29 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give an algorithm to morph between two planar orthogonal drawings of a graph, preserving planarity and orthogonality. The morph uses a quadratic number of steps, where each step is a linear morph (a linear interpolation between two drawings). This is the first algorithm to provide planarity-preserving morphs with well-behaved complexity for a significant class of graph drawings. Our method is to morph until each edge is represented by a sequence of segments, with corresponding segments parallel in the two drawings. Then, in a result of independent interest, we morph such parallel planar orthogonal drawings, preserving edge directions and planarity.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Marx:2013:FSS, author = "D{\'a}aniel Marx and Barry O'Sullivan and Igor Razgon", title = "Finding small separators in linear time via treewidth reduction", journal = j-TALG, volume = "9", number = "4", pages = "30:1--30:??", month = sep, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2500119", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:29 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a method for reducing the treewidth of a graph while preserving all of its minimal $s$--$t$ separators up to a certain fixed size $k$. This technique allows us to solve $s$--$t$ Cut and Multicut problems with various additional restrictions (e.g., the vertices being removed from the graph form an independent set or induce a connected graph) in linear time for every fixed number $k$ of removed vertices. Our results have applications for problems that are not directly defined by separators, but the known solution methods depend on some variant of separation. For example, we can solve similarly restricted generalizations of Bipartization (delete at most $k$ vertices from $G$ to make it bipartite) in almost linear time for every fixed number $k$ of removed vertices. These results answer a number of open questions in the area of parameterized complexity. Furthermore, our technique turns out to be relevant for $ (H, C, K) $- and $ (H, C, \leq K) $-coloring problems as well, which are cardinality constrained variants of the classical H -coloring problem. We make progress in the classification of the parameterized complexity of these problems by identifying new cases that can be solved in almost linear time for every fixed cardinality bound.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ambuhl:2013:OLB, author = "Christoph Amb{\"u}hl and Bernd G{\"a}rtner and Bernhard von Stengel", title = "Optimal lower bounds for projective list update algorithms", journal = j-TALG, volume = "9", number = "4", pages = "31:1--31:??", month = sep, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2500120", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:29 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The list update problem is a classical online problem, with an optimal competitive ratio that is still open, known to be somewhere between 1.5 and 1.6. An algorithm with competitive ratio 1.6, the smallest known to date, is COMB, a randomized combination of BIT and the TIMESTAMP algorithm TS. This and almost all other list update algorithms, like MTF, are projective in the sense that they can be defined by looking only at any pair of list items at a time. Projectivity (also known as ``list factoring'') simplifies both the description of the algorithm and its analysis, and so far seems to be the only way to define a good online algorithm for lists of arbitrary length. In this article, we characterize all projective list update algorithms and show that their competitive ratio is never smaller than 1.6 in the partial cost model. Therefore, COMB is a best possible projective algorithm in this model.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bateni:2013:SSP, author = "Mohammadhossein Bateni and Mohammadtaghi Hajiaghayi and Morteza Zadimoghaddam", title = "Submodular secretary problem and extensions", journal = j-TALG, volume = "9", number = "4", pages = "32:1--32:??", month = sep, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2500121", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:29 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Online auction is the essence of many modern markets, particularly networked markets, in which information about goods, agents, and outcomes is revealed over a period of time, and the agents must make irrevocable decisions without knowing future information. Optimal stopping theory, especially the classic secretary problem, is a powerful tool for analyzing such online scenarios which generally require optimizing an objective function over the input. The secretary problem and its generalization the multiple-choice secretary problem were under a thorough study in the literature. In this article, we consider a very general setting of the latter problem called the submodular secretary problem, in which the goal is to select k secretaries so as to maximize the expectation of a (not necessarily monotone) submodular function which defines efficiency of the selected secretarial group based on their overlapping skills. We present the first constant-competitive algorithm for this case. In a more general setting in which selected secretaries should form an independent (feasible) set in each of $l$ given matroids as well, we obtain an $ O(l \log^2 r) $-competitive algorithm generalizing several previous results, where $r$ is the maximum rank of the matroids. Another generalization is to consider $l$ knapsack constraints (i.e., a knapsack constraint assigns a nonnegative cost to each secretary, and requires that the total cost of all the secretaries employed be no more than a budget value) instead of the matroid constraints, for which we present an $ O(l) $-competitive algorithm. In a sharp contrast, we show for a more general setting of subadditive secretary problem, there is no $ {\tilde o}(\sqrt n) $-competitive algorithm and thus submodular functions are the most general functions to consider for constant-competitiveness in our setting. We complement this result by giving a matching $ O(\sqrt n) $-competitive algorithm for the subadditive case. At the end, we consider some special cases of our general setting as well.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kaltofen:2013:MBM, author = "Erich Kaltofen and George Yuhasz", title = "On the matrix {Berlekamp--Massey} algorithm", journal = j-TALG, volume = "9", number = "4", pages = "33:1--33:??", month = sep, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2500122", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:29 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We analyze the Matrix Berlekamp/Massey algorithm, which generalizes the Berlekamp/Massey algorithm [Massey 1969] for computing linear generators of scalar sequences. The Matrix Berlekamp/Massey algorithm computes a minimal matrix generator of a linearly generated matrix sequence and has been first introduced by Rissanen [1972a], Dickinson et al. [1974], and Coppersmith [1994]. Our version of the algorithm makes no restrictions on the rank and dimensions of the matrix sequence. We also give new proofs of correctness and complexity for the algorithm, which is based on self-contained loop invariants and includes an explicit termination criterion for a given determinantal degree bound of the minimal matrix generator.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gandhi:2013:CIR, author = "Rajiv Gandhi and Magn{\'u}s M. Halld{\'o}rsson and Guy Kortsarz and Hadas Shachnai", title = "Corrigendum: {Improved results for data migration and open shop scheduling}", journal = j-TALG, volume = "9", number = "4", pages = "34:1--34:??", month = sep, year = "2013", CODEN = "????", DOI = "https://doi.org/10.1145/2500123", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:29 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", note = "See \cite{Gandhi:2006:IRD}.", abstract = "In Gandhi et al. [2006], we gave an algorithm for the data migration and non-deterministic open shop scheduling problems in the minimum sum version, that was claimed to achieve a 5.06-approximation. Unfortunately, it was pointed to us by Maxim Sviridenko that the argument contained an unfounded assumption that has eluded all of its readers until now. We detail in this document how this error can be amended. A side effect is an improved approximation ratio of 4.96.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bansal:2014:LAU, author = "Nikhil Bansal and Zachary Friggstad and Rohit Khandekar and Mohammad R. Salavatipour", title = "A logarithmic approximation for unsplittable flow on line graphs", journal = j-TALG, volume = "10", number = "1", pages = "1:1--1:??", month = jan, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2532645", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:30 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the unsplittable flow problem on a line. In this problem, we are given a set of n tasks, each specified by a start time $ s_i $, an end time $ t_i $, a demand $ d_i > 0 $, and a profit $ p_i > 0 $. A task, if accepted, requires $ d_i $ units of ``bandwidth'' from time $ s_i $ to $ t_i $ and accrues a profit of $ p_i $. For every time t, we are also specified the available bandwidth c$_t$, and the goal is to find a subset of tasks with maximum profit subject to the bandwidth constraints. We present the first polynomial time $ O(\log n) $ approximation algorithm for this problem. This significantly advances the state of the art, as no polynomial time $ o(n) $ approximation was known previously. Previous results for this problem were known only in more restrictive settings; in particular, either the instance satisfies the so-called ``no-bottleneck'' assumption: $ \max_i d_i \leq \min_t c_t $, or the ratio of both maximum to minimum demands and maximum to minimum capacities are polynomially (or quasi-polynomially) bounded in n. Our result, on the other hand, does not require these assumptions. Our algorithm is based on a combination of dynamic programming and rounding a natural linear programming relaxation for the problem. While there is an $ \Omega (n) $ integrality gap known for this LP relaxation, our key idea is to exploit certain structural properties of the problem to show that instances that are bad for the LP can in fact be handled using dynamic programming.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Mestre:2014:WPM, author = "Juli{\'a}n Mestre", title = "Weighted popular matchings", journal = j-TALG, volume = "10", number = "1", pages = "2:1--2:??", month = jan, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2556951", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:30 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the problem of assigning jobs to applicants. Each applicant has a weight and provides a preference list, which may contain ties, ranking a subset of the jobs. An applicant $x$ may prefer one matching to another (or be indifferent between them, in case of a tie) based on the jobs $x$ gets in the two matchings and $x$'s personal preference. A matching $M$ is popular if there is no other matching $ M' $ such that the weight of the applicants who prefer $ M' $ to $M$ exceeds the weight of those who prefer $M$ to $ M' $. We present algorithms to find a popular matching, or if none exists, to establish so. For instances with strict preference lists, we give an $ O(n + m) $ time algorithm. For preference lists with ties, we give a more involved algorithm that solves the problem in $ O(\min (k \sqrt n, n) m) $ time, where $k$ is the number of distinct weights the applicants are given.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Har-Peled:2014:FDR, author = "Sariel Har-Peled and Benjamin Raichel", title = "The {Fr{\'e}chet} distance revisited and extended", journal = j-TALG, volume = "10", number = "1", pages = "3:1--3:??", month = jan, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2532646", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:30 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given two simplicial complexes in $ R^d $ and start and end vertices in each complex, we show how to compute curves (in each complex) between these vertices, such that the weak Fr{\'e}chet distance between these curves is minimized. As a polygonal curve is a complex, this generalizes the regular notion of weak Fr{\'e}chet distance between curves. We also generalize the algorithm to handle an input of $k$ simplicial complexes. Using this new algorithm, we can solve a slew of new problems, from computing a mean curve for a given collection of curves to various motion planning problems. Additionally, we show that for the mean curve problem, when the $k$ input curves are $c$-packed, one can $ (1 + \epsilon) $-approximate the mean curve in near-linear time, for fixed $k$ and $ \epsilon $. Additionally, we present an algorithm for computing the strong Fr{\'e}chet distance between two curves, which is simpler than previous algorithms and avoids using parametric search.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Vigneron:2014:GOS, author = "Antoine Vigneron", title = "Geometric optimization and sums of algebraic functions", journal = j-TALG, volume = "10", number = "1", pages = "4:1--4:??", month = jan, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2532647", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:30 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Goel:2014:PBP, author = "Ashish Goel and Hamid Nazerzadeh", title = "Price-based protocols for fair resource allocation: Convergence time analysis and extension to {Leontief} utilities", journal = j-TALG, volume = "10", number = "2", pages = "5:1--5:??", month = feb, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2556949", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:32 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We analyze several distributed, continuous time protocols for a fair allocation of bandwidths to flows in a network (or resources to agents). Our protocols converge to an allocation that is a logarithmic approximation, simultaneously, to all canonical social welfare functions (i.e., functions that are symmetric, concave, and nondecreasing). These protocols can be started in an arbitrary state. Although a similar protocol was known before, it only applied to the simple bandwidth allocation problem, and its stability and convergence time were not understood. In contrast, our protocols also apply to the more general case of Leontief utilities, where each user may place a different requirement on each resource. Furthermore, we prove that our protocols converge in polynomial time. The best convergence time we prove is $ O(n \log n c_{\rm MAX} a_{\rm MAX} / c_{\rm MIN} a_{\rm MIN}) $, where $n$ is the number of agents in the network, $ c_{\rm MAX} $ and $ c_{\rm MIN} $ are the maximum and minimum capacity of the links, and $ a_{\rm max} $, $ a_{\rm min} $ are respectively the largest and smallest Leontief coefficients. This time is achieved by a simple Multiplicative Increase, Multiplicative Decrease (MIMD) protocol that had not been studied before in this setting. We also identify combinatorial properties of these protocols that may be useful in proving stronger convergence bounds. The final allocations by our protocols are supported by usage-sensitive dual prices that are fair in the sense that they shield light users of a resource from the impact of heavy users. Thus, our protocols can also be thought of as efficient distributed schemes for computing fair prices.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Rue:2014:DPG, author = "Juanjo Ru{\'e} and Ignasi Sau and Dimitrios M. Thilikos", title = "Dynamic programming for graphs on surfaces", journal = j-TALG, volume = "10", number = "2", pages = "8:1--8:??", month = feb, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2556952", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:32 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on $n$ vertices and branchwidth at most $k$. Our technique applies to general families of problems where standard dynamic programming runs in $ 2^O(k \cdot \log k) \cdot n $ steps. Our approach combines tools from topological graph theory and analytic combinatorics. In particular, we introduce a new type of branch decomposition called surface cut decomposition, generalizing sphere cut decompositions of planar graphs, which has nice combinatorial properties. Namely, the number of partial solutions that can be arranged on a surface cut decomposition can be upper-bounded by the number of noncrossing partitions on surfaces with boundary. It follows that partial solutions can be represented by a single-exponential (in the branchwidth $k$) number of configurations. This proves that, when applied on surface cut decompositions, dynamic programming runs in $ 2^{O(k)} \cdot n $ steps. That way, we considerably extend the class of problems that can be solved in running times with a single-exponential dependence on branchwidth and unify/improve most previous results in this direction.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Albers:2014:RIN, author = "Susanne Albers and Antonios Antoniadis", title = "Race to idle: New algorithms for speed scaling with a sleep state", journal = j-TALG, volume = "10", number = "2", pages = "9:1--9:??", month = feb, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2556953", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Mar 13 08:49:32 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study an energy conservation problem where a variable-speed processor is equipped with a sleep state. Executing jobs at high speeds and then setting the processor asleep is an approach that can lead to further energy savings compared to standard dynamic speed scaling. We consider classical deadline-based scheduling, that is, each job is specified by a release time, a deadline and a processing volume. For general convex power functions, Irani et al. [2007] devised an offline 2-approximation algorithm. Roughly speaking, the algorithm schedules jobs at a critical speed $ s_{crit} $ that yields the smallest energy consumption while jobs are processed. For power functions $ P(s) = s^\alpha \& \gamma $, where $s$ is the processor speed, Han et al. [2010] gave an $ \alpha^(\alpha + 2) $-competitive online algorithm. We investigate the offline setting of speed scaling with a sleep state. First, we prove NP-hardness of the optimization problem. Additionally, we develop lower bounds, for general convex power functions: No algorithm that constructs $ s_{\rm crit} $-schedules, which execute jobs at speeds of at least $ s_{\rm crit} $, can achieve an approximation factor smaller than $2$. Furthermore, no algorithm that minimizes the energy expended for processing jobs can attain an approximation ratio smaller than $2$. We then present an algorithmic framework for designing good approximation algorithms. For general convex power functions, we derive an approximation factor of $ 4 / 3 $. For power functions $ P(s) = \beta s^\alpha + \gamma $, we obtain an approximation of $ 137 / 117 > 1.171 $. We finally show that our framework yields the best approximation guarantees for the class of $ s_{\rm crit} $ -schedules. For general convex power functions, we give another $2$-approximation algorithm. For functions $ P(s) = \beta s^\alpha + \gamma $, we present tight upper and lower bounds on the best possible approximation factor. The ratio is exactly $ e W_{-1} ( - e^{-1 - 1 / e}) / (e W_{-1} ( - e^{-1 - 1 / e}) + 1) > 1.211 $, where $ W_{-1} $ is the lower branch of the Lambert $W$ function.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cheung:2014:AAL, author = "Ho Yee Cheung and Lap Chi Lau and Kai Man Leung", title = "Algebraic Algorithms for Linear Matroid Parity Problems", journal = j-TALG, volume = "10", number = "3", pages = "10:1--10:??", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2601066", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 16 07:33:55 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present fast and simple algebraic algorithms for the linear matroid parity problem and its applications. For the linear matroid parity problem, we obtain a simple randomized algorithm with running time $ O(m r^{\omega - 1}) $, where $m$ and $r$ are the number of columns and the number of rows, respectively, and $ \omega \approx 2.3727$ is the matrix multiplication exponent. This improves the $ O(m r^\omega)$-time algorithm by Gabow and Stallmann and matches the running time of the algebraic algorithm for linear matroid intersection, answering a question of Harvey. We also present a very simple alternative algorithm with running time $ O(m r^2)$, which does not need fast matrix multiplication. We further improve the algebraic algorithms for some specific graph problems of interest. For the Mader's disjoint $S$-path problem, we present an $ O(n^\omega)$-time randomized algorithm where $n$ is the number of vertices. This improves the running time of the existing results considerably and matches the running time of the algebraic algorithms for graph matching. For the graphic matroid parity problem, we give an $ O(n^4)$-time randomized algorithm where $n$ is the number of vertices, and an $ O(n^3)$-time randomized algorithm for a special case useful in designing approximation algorithms. These algorithms are optimal in terms of $n$ as the input size could be $ \Omega (n^4)$ and $ \Omega (n^3)$, respectively. The techniques are based on the algebraic algorithmic framework developed by Mucha and Sankowski, Harvey, and Sankowski. While linear matroid parity and Mader's disjoint $S$-path are challenging generalizations for the design of combinatorial algorithms, our results show that both the algebraic algorithms for linear matroid intersection and graph matching can be extended nicely to more general settings. All algorithms are still faster than the existing algorithms even if fast matrix multiplication is not used. These provide simple algorithms that can be easily implemented in practice.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Feigenbaum:2014:APF, author = "Joan Feigenbaum and Aaron D. Jaggard and Michael Schapira", title = "Approximate Privacy: Foundations and Quantification", journal = j-TALG, volume = "10", number = "3", pages = "11:1--11:??", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2601067", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 16 07:33:55 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The proliferation of online sensitive data about individuals and organizations makes concern about the privacy of these data a top priority. There have been many formulations of privacy and, unfortunately, many negative results about the feasibility of maintaining privacy of sensitive data in realistic networked environments. We formulate communication-complexity-based definitions, both worst case and average case, of a problem's privacy-approximation ratio. We use our definitions to investigate the extent to which approximate privacy is achievable in a number of standard problems: the 2$^{nd}$ -price Vickrey auction, Yao's millionaires problem, the public-good problem, and the set-theoretic disjointness and intersection problems. For both the 2$^{nd}$ -price Vickrey auction and the millionaires problem, we show that not only is perfect privacy impossible or infeasibly costly to achieve, but even close approximations of perfect privacy suffer from the same lower bounds. By contrast, if the inputs are drawn uniformly at random from $ \{ 0, \ldots {}, 2^k - 1 \} $, then, for both problems, simple and natural communication protocols have privacy-approximation ratios that are linear in $k$ (i.e., logarithmic in the size of the input space). We also demonstrate tradeoffs between privacy and communication in a family of auction protocols. We show that the privacy-approximation ratio provided by any protocol for the disjointness and intersection problems is necessarily exponential (in $k$). We also use these ratios to argue that one protocol for each of these problems is significantly fairer than the others we consider (in the sense of relative effects on the privacy of the different players).", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ta-Shma:2014:DRT, author = "Amnon Ta-Shma and Uri Zwick", title = "Deterministic Rendezvous, Treasure Hunts, and Strongly Universal Exploration Sequences", journal = j-TALG, volume = "10", number = "3", pages = "12:1--12:??", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2601068", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 16 07:33:55 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We obtain several improved solutions for the deterministic rendezvous problem in general undirected graphs. Our solutions answer several problems left open by Dessmark et al. We also introduce an interesting variant of the rendezvous problem, which we call the deterministic treasure hunt problem. Both the rendezvous and the treasure hunt problems motivate the study of universal traversal sequences and universal exploration sequences with some strengthened properties. We call such sequences strongly universal traversal (exploration) sequences. We give an explicit construction of strongly universal exploration sequences. The existence of strongly universal traversal sequences, as well as the solution of the most difficult variant of the deterministic treasure hunt problem, are left as intriguing open problems.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2014:NWS, author = "Erik D. Demaine and Mohammadtaghi Hajiaghayi and Philip N. Klein", title = "Node-Weighted {Steiner} Tree and Group {Steiner} Tree in Planar Graphs", journal = j-TALG, volume = "10", number = "3", pages = "13:1--13:??", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2601070", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 16 07:33:55 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We improve the approximation ratios for two optimization problems in planar graphs. For node-weighted Steiner tree, a classical network-optimization problem, the best achievable approximation ratio in general graphs is $ \Theta (\log n) $, and nothing better was previously known for planar graphs. We give a constant-factor approximation for planar graphs. Our algorithm generalizes to allow as input any nontrivial minor-closed graph family, and also generalizes to address other optimization problems such as Steiner forest, prize-collecting Steiner tree, and network-formation games. The second problem we address is group Steiner tree: given a graph with edge weights and a collection of groups (subsets of nodes), find a minimum-weight connected subgraph that includes at least one node from each group. The best approximation ratio known in general graphs is $ O(\log^3 n) $, or $ O(\log^2 n) $ when the host graph is a tree. We obtain an $ O(\log n \polyloglog n) $ approximation algorithm for the special case where the graph is planar embedded and each group is the set of nodes on a face. We obtain the same approximation ratio for the minimum-weight tour that must visit each group.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fakcharoenphol:2014:FAS, author = "Jittat Fakcharoenphol and Bundit Laekhanukit and Danupon Nanongkai", title = "Faster Algorithms for Semi-Matching Problems", journal = j-TALG, volume = "10", number = "3", pages = "14:1--14:??", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2601071", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 16 07:33:55 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of finding semi-matching in bipartite graphs, which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted cases. For the weighted case, we give an $ O(n m \log n)$-time algorithm, where $n$ is the number of vertices and $m$ is the number of edges, by exploiting the geometric structure of the problem. This improves the classical $ O(n^3)$-time algorithms by Horn [1973] and Bruno et al. [1974b]. For the unweighted case, the bound can be improved even further. We give a simple divide-and-conquer algorithm that runs in $ O(\sqrt n m \log n)$ time, improving two previous $ O(n m)$-time algorithms by Abraham [2003] and Harvey et al. [2003, 2006]. We also extend this algorithm to solve the Balanced Edge Cover problem in $ O(\sqrt n m \log n)$ time, improving the previous $ O(n m)$-time algorithm by Harada et al. [2008].", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2014:FCC, author = "T.-H. Hubert Chan and Li Ning", title = "Fast Convergence for Consensus in Dynamic Networks", journal = j-TALG, volume = "10", number = "3", pages = "15:1--15:??", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2601072", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 16 07:33:55 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we study the convergence time required to achieve consensus in dynamic networks. In each timestep, a node's value is updated to some weighted average of its neighbors and its old values. We study the case when the underlying network is dynamic and investigate different averaging models. Both our analysis and experiments show that dynamic networks exhibit fast convergence behavior, even under very mild connectivity assumptions.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Navarro:2014:FFS, author = "Gonzalo Navarro and Kunihiko Sadakane", title = "Fully Functional Static and Dynamic Succinct Trees", journal = j-TALG, volume = "10", number = "3", pages = "16:1--16:??", month = jun, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2601073", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 16 07:33:55 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose new succinct representations of ordinal trees and match various space/time lower bounds. It is known that any $n$-node static tree can be represented in $ 2 n + o(n)$ bits so that a number of operations on the tree can be supported in constant time under the word-RAM model. However, the data structures are complicated and difficult to dynamize. We propose a simple and flexible data structure, called the range min-max tree, that reduces the large number of relevant tree operations considered in the literature to a few primitives that are carried out in constant time on polylog-sized trees. The result is extended to trees of arbitrary size, retaining constant time and reaching $ 2 n + O(n / \polylog (n))$ bits of space. This space is optimal for a core subset of the operations supported and significantly lower than in any previous proposal. For the dynamic case, where insertion/deletion (indels) of nodes is allowed, the existing data structures support a very limited set of operations. Our data structure builds on the range min-max tree to achieve $ 2 n + O(n / \log n)$ bits of space and $ O(\log n)$ time for all operations supported in the static scenario, plus indels. We also propose an improved data structure using $ 2 n + O(n \log \log n / \log n)$ bits and improving the time to the optimal $ O(\log n / \log \log n)$ for most operations. We extend our support to forests, where whole subtrees can be attached to or detached from others, in time $ O(\log^{1 + \epsilon } n)$ for any $ \epsilon > 0$. Such operations had not been considered before. Our techniques are of independent interest. An immediate derivation yields an improved solution to range minimum/maximum queries where consecutive elements differ by $ \pm {} 1$, achieving $ n + O(n / \polylog (n))$ bits of space. A second one stores an array of numbers supporting operations sum and search and limited updates, in optimal time $ O(\log n / \log \log n)$. A third one allows representing dynamic bitmaps and sequences over alphabets of size $ \sigma $, supporting rank/select and indels, within zero-order entropy bounds and time $ O(\log n \log \sigma / (\log \log n)^2)$ for all operations. This time is the optimal $ O(\log n / \log \log n)$ on bitmaps and polylog-sized alphabets. This improves upon the best existing bounds for entropy-bounded storage of dynamic sequences, compressed full-text self-indexes, and compressed-space construction of the Burrows--Wheeler transform.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ron:2014:TPS, author = "Dana Ron and Gilad Tsur", title = "Testing Properties of Sparse Images", journal = j-TALG, volume = "10", number = "4", pages = "17:1--17:??", month = aug, year = "2014", DOI = "https://doi.org/10.1145/2635806", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 1 11:11:53 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We initiate the study of testing properties of images that correspond to sparse $0$ /$1$-valued matrices of size $ n \times n$. Our study is related to but different from the study initiated by Raskhodnikova (Proceedings of RANDOM, 2003 ), where the images correspond to dense $0$ /$1$-valued matrices. Specifically, in the model studied by Raskhodnikova, the distance that an image has to a specific property is the number of entries that should be modified in the corresponding matrix so that the property can be obtained, divided by the total number of entries: $ n^2$. In the model we consider, the distance is the number of entries that should be modified divided by the actual number of 1's in the matrix, which may be much smaller than $ n^2$. We study several natural properties: connectivity, convexity, monotonicity, and being a line. In all cases, we give testing algorithms with sublinear complexity, and, in some of the cases, we also provide corresponding lower bounds.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Makarychev:2014:MQA, author = "Konstantin Makarychev and Rajsekar Manokaran and Maxim Sviridenko", title = "Maximum Quadratic Assignment Problem: Reduction from Maximum Label Cover and {LP}-based Approximation Algorithm", journal = j-TALG, volume = "10", number = "4", pages = "18:1--18:??", month = aug, year = "2014", DOI = "https://doi.org/10.1145/2629672", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 1 11:11:53 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that for every positive $ \epsilon > 0 $, unless NP $ \subset $ BPQP, it is impossible to approximate the maximum quadratic assignment problem within a factor better than $ 2^{\log (1 - \epsilon) n} $ by a reduction from the maximum label cover problem. Our result also implies that Approximate Graph Isomorphism is not robust and is, in fact, $ 1 - \epsilon $ versus $ \epsilon $ hard assuming the Unique Games Conjecture. Then, we present an $ O(\sqrt n)$-approximation algorithm for the problem based on rounding of the linear programming relaxation often used in state-of-the-art exact algorithms.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kratsch:2014:CNC, author = "Stefan Kratsch", title = "Co-Nondeterminism in Compositions: a Kernelization Lower Bound for a {Ramsey}-Type Problem", journal = j-TALG, volume = "10", number = "4", pages = "19:1--19:??", month = aug, year = "2014", DOI = "https://doi.org/10.1145/2635808", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 1 11:11:53 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The field of kernelization offers a rigorous way of studying the ubiquitous technique of data reduction and preprocessing for combinatorially hard problems. A widely accepted definition of useful data reduction is that of a polynomial kernelization where the output instance is guaranteed to be of size polynomial in some parameter of the input. The fairly recent development of a framework for kernelization lower bounds has made this notion even more attractive as we can now classify many problems into admitting or not admitting polynomial kernelizations. The central notion of the framework is that of a polynomial-time composition algorithm due to Bodlaender et al. (ICALP 2008, JSCC 2009): given $t$ input instances, an or-composition algorithm returns a single-output instance with bounded parameter value that is yes if and only if one of $t$ input instances is yes; it encodes the logical OR of the input instances. Based on a result of Fortnow and Santhanam (STOC 2008, JSCC 2011), Bodlaender et al. show that an or-composition for an NP-hard problem rules out polynomial kernelizations for it unless NP $ \subseteq $ coNP/poly (which is known to imply a collapse of the polynomial hierarchy). It is implicit in the work of Fortnow and Santhanam that even co-nondeterministic composition algorithms suffice to rule out polynomial kernelizations. This was first observed in unpublished work of Chen and M{\"u}ller, and it is an explicit conclusion of recent results by Dell and van Melkebeek (STOC 2010). However, in contrast to the numerous applications of deterministic composition, the added power of co-nondeterminism has not yet been harnessed to obtain kernelization lower bounds. In this work, we present the first example of how co-nondeterminism can help to make a composition algorithm. We study the existence of polynomial kernels for a Ramsey-type problem where, given a graph $G$ and an integer $k$, the question is whether $G$ contains an independent set or a clique of size at least $k$. It was asked by Rod Downey whether this problem admits a polynomial kernelization with respect to k; such a result would greatly speed up the computation of Ramsey numbers. We provide a co-nondeterministic composition based on embedding $t$ instances into a single host graph $H$. The crux is that the host graph $H$ needs to observe a bound of $ l \in O(\log t)$ on both its maximum independent set and maximum clique size, while also having a cover of its vertex set by independent sets and cliques all of size $l$; the co-nondeterministic composition is built around the search for such graphs. Thus, we show that, unless NP $ \subseteq $ coNP/poly, the problem does not admit a kernelization with polynomial size guarantee.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kratsch:2014:CMR, author = "Stefan Kratsch and Magnus Wahlstr{\"o}m", title = "Compression via Matroids: a Randomized Polynomial Kernel for Odd Cycle Transversal", journal = j-TALG, volume = "10", number = "4", pages = "20:1--20:??", month = aug, year = "2014", DOI = "https://doi.org/10.1145/2635810", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 1 11:11:53 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Odd Cycle Transversal problem (OCT) asks whether a given undirected graph can be made bipartite by deleting at most $k$ of its vertices. In a breakthrough result, Reed, Smith, and Vetta (Operations Research Letters, 2004) gave a $ O(4^k k m n)$ time algorithm for it; this also implies that instances of the problem can be reduced to a so-called problem kernel of size $ O(4^k)$. Since then, the existence of a polynomial kernel for OCT (i.e., a kernelization with size bounded polynomially in $k$) has turned into one of the main open questions in the study of kernelization, open even for the special case of planar input graphs. This work provides the first (randomized) polynomial kernelization for OCT. We introduce a novel kernelization approach based on matroid theory, where we encode all relevant information about a problem instance into a matroid with a representation of size polynomial in k. This represents the first application of matroid theory to kernelization.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dell:2014:ETC, author = "Holger Dell and Thore Husfeldt and D{\'a}niel Marx and Nina Taslaman and Martin Wahl{\'e}n", title = "Exponential Time Complexity of the Permanent and the {Tutte} Polynomial", journal = j-TALG, volume = "10", number = "4", pages = "21:1--21:??", month = aug, year = "2014", DOI = "https://doi.org/10.1145/2635812", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 1 11:11:53 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show conditional lower bounds for well-studied \#P-hard problems: The number of satisfying assignments of a 2-CNF formula with $n$ variables cannot be computed in time $ \exp (o(n))$, and the same is true for computing the number of all independent sets in an $n$-vertex graph. The permanent of an $ n \times n$ matrix with entries $0$ and $1$ cannot be computed in time $ \exp (o(n))$. The Tutte polynomial of an $n$-vertex multigraph cannot be computed in time $ \exp (o(n))$ at most evaluation points $ (x, y)$ in the case of multigraphs, and it cannot be computed in time $ \exp (o(n / \polylog n))$ in the case of simple graphs. Our lower bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of $n$-variable 3-CNF formulas cannot be decided in time $ \exp (o(n))$. We relax this hypothesis by introducing its counting version \#ETH; namely, that the satisfying assignments cannot be counted in time $ \exp (o(n))$. In order to use \#ETH for our lower bounds, we transfer the sparsification lemma for $d$-CNF formulas to the counting setting.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Breslauer:2014:RTS, author = "Dany Breslauer and Zvi Galil", title = "Real-Time Streaming String-Matching", journal = j-TALG, volume = "10", number = "4", pages = "22:1--22:??", month = aug, year = "2014", DOI = "https://doi.org/10.1145/2635814", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 1 11:11:53 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/string-matching.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article presents a real-time randomized streaming string-matching algorithm that uses $ O(\log m) $ space. The algorithm only makes one-sided small probability false-positive errors, possibly reporting phantom occurrences of the pattern, but never missing an actual occurrence.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Belazzougui:2014:AIC, author = "Djamal Belazzougui and Gonzalo Navarro", title = "Alphabet-Independent Compressed Text Indexing", journal = j-TALG, volume = "10", number = "4", pages = "23:1--23:??", month = aug, year = "2014", DOI = "https://doi.org/10.1145/2635816", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 1 11:11:53 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Self-indexes are able to represent a text asymptotically within the information-theoretic lower bound under the $k$ th order entropy model and offer access to any text substring and indexed pattern searches. Their time complexities are not optimal, however; in particular, they are always multiplied by a factor that depends on the alphabet size. In this article, we achieve, for the first time, full alphabet independence in the time complexities of self-indexes while retaining space optimality. We also obtain some relevant byproducts.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Awerbuch:2014:PRM, author = "Baruch Awerbuch and Andrea Richa and Christian Scheideler and Stefan Schmid and Jin Zhang", title = "Principles of Robust Medium Access and an Application to Leader Election", journal = j-TALG, volume = "10", number = "4", pages = "24:1--24:??", month = aug, year = "2014", DOI = "https://doi.org/10.1145/2635818", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 1 11:11:53 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article studies the design of medium access control (MAC) protocols for wireless networks that are provably robust against arbitrary and unpredictable disruptions (e.g., due to unintentional external interference from co-existing networks or due to jamming). We consider a wireless network consisting of a set of $n$ honest and reliable nodes within transmission (and interference) range of each other, and we model the external disruptions with a powerful adaptive adversary. This adversary may know the protocol and its entire history and can use this knowledge to jam the wireless channel at will at any time. It is allowed to jam a $ (1 - \epsilon)$-fraction of the timesteps, for an arbitrary constant $ \epsilon > 0$ unknown to the nodes. The nodes cannot distinguish between the adversarial jamming or a collision of two or more messages that are sent at the same time. We demonstrate, for the first time, that there is a local-control MAC protocol requiring only very limited knowledge about the adversary and the network that achieves a constant (asymptotically optimal) throughput for the nonjammed time periods under any of the aforementioned adversarial strategies. The derived principles are also useful to build robust applications on top of the MAC layer, and we present an exemplary study for leader election, one of the most fundamental tasks in distributed computing.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dieudonne:2014:GDM, author = "Yoann Dieudonn{\'e} and Andrzej Pelc and David Peleg", title = "Gathering Despite Mischief", journal = j-TALG, volume = "11", number = "1", pages = "1:1--1:??", month = aug, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2629656", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 8 09:09:02 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, have to meet at the same node. Agents move in synchronous rounds. Each agent has a different label. Up to $f$ of the agents are Byzantine. We consider two levels of Byzantine behavior. A strongly Byzantine agent can choose an arbitrary port when it moves and it can convey arbitrary information to other agents, while a weakly Byzantine agent can do the same, except changing its label. What is the minimum number of good agents that guarantees deterministic gathering of all of them, with termination? We solve exactly this Byzantine gathering problem in arbitrary networks for weakly Byzantine agents and give approximate solutions for strongly Byzantine agents, both when the size of the network is known and when it is unknown. It turns out that both the strength versus the weakness of Byzantine behavior and the knowledge of network size significantly impact the results. For weakly Byzantine agents, we show that any number of good agents permits solving the problem for networks of known size. If the size is unknown, then this minimum number is $ f + 2$. More precisely, we show a deterministic polynomial algorithm that gathers all good agents in an arbitrary network, provided that there are at least $ f + 2$ of them. We also provide a matching lower bound: we prove that if the number of good agents is at most $ f + 1$, then they are not able to gather deterministically with termination in some networks. For strongly Byzantine agents, we give a lower bound of $ f + 1$, even when the graph is known: we show that f good agents cannot gather deterministically in the presence of f Byzantine agents even in a ring of known size. On the positive side, we give deterministic gathering algorithms for at least $ 2 f + 1$ good agents when the size of the network is known and for at least $ 4 f + 2$ good agents when it is unknown.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Berenbrink:2014:DSL, author = "Petra Berenbrink and Martin Hoefer and Thomas Sauerwald", title = "Distributed Selfish Load Balancing on Networks", journal = j-TALG, volume = "11", number = "1", pages = "2:1--2:??", month = aug, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2629671", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 8 09:09:02 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m {$ > $$ >$ } n selfish agents that unilaterally decide to move from one vertex to another if this improves their experienced load. We present several protocols for concurrent migration that satisfy desirable properties such as being based only on local information and computation and the absence of global coordination or cooperation of agents. Our main contribution is to show rapid convergence of the resulting migration process to states that satisfy different stability or balance criteria. In particular, the convergence time to a Nash equilibrium is only logarithmic in m and polynomial in n, where the polynomial depends on the graph structure. In addition, we show reduced convergence times to approximate Nash equilibria. Finally, we extend our results to networks of machines with different speeds or to agents that have different weights and show similar results for convergence to approximate and exact Nash equilibria.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bansal:2014:BSA, author = "Nikhil Bansal and Ravishankar Krishnaswamy and Viswanath Nagarajan", title = "Better Scalable Algorithms for Broadcast Scheduling", journal = j-TALG, volume = "11", number = "1", pages = "3:1--3:??", month = aug, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2636916", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 8 09:09:02 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the classical broadcast scheduling problem, there are n pages stored at a server, and requests for these pages arrive over time. Whenever a page is broadcast, it satisfies all outstanding requests for that page. The objective is to minimize average flow time of the requests. For any $ \epsilon > 0 $, we give a $ (1 + \epsilon)$-speed $ O(1 / \epsilon^3)$-competitive online algorithm for broadcast scheduling. This improves over the recent breakthrough result of Im and Moseley [2010], where they obtained a $ (1 + \epsilon)$-speed $ O(1 / \epsilon^{11})$-competitive algorithm. Our algorithm and analysis are considerably simpler than Im and Moseley [2010]. More importantly, our techniques also extend to the general setting of nonuniform page sizes and dependent requests. This is the first scalable algorithm for broadcast scheduling with varying size pages and resolves the main open question from Im and Moseley [2010].", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Grohe:2014:CSF, author = "Martin Grohe and D{\'a}niel Marx", title = "Constraint Solving via Fractional Edge Covers", journal = j-TALG, volume = "11", number = "1", pages = "4:1--4:??", month = aug, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2636918", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 8 09:09:02 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Many important combinatorial problems can be modeled as constraint satisfaction problems. Hence, identifying polynomial-time solvable classes of constraint satisfaction problems has received a lot of attention. In this article, we are interested in structural properties that can make the problem tractable. So far, the largest structural class that is known to be polynomial-time solvable is the class of bounded hypertree width instances introduced by Gottlob et al. [2002]. Here we identify a new class of polynomial-time solvable instances: those having bounded fractional edge cover number. Combining hypertree width and fractional edge cover number, we then introduce the notion of fractional hypertree width. We prove that constraint satisfaction problems with bounded fractional hypertree width can be solved in polynomial time (provided that the tree decomposition is given in the input). Together with a recent approximation algorithm for finding such decompositions [Marx 2010], it follows that bounded fractional hypertree width is now the most generally known structural property that guarantees polynomial-time solvability.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Berman:2014:AAM, author = "Piotr Berman and Sofya Raskhodnikova", title = "Approximation Algorithms for Min-Max Generalization Problems", journal = j-TALG, volume = "11", number = "1", pages = "5:1--5:??", month = aug, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2636920", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 8 09:09:02 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We provide improved approximation algorithms for the min-max generalization problems considered by Du, Eppstein, Goodrich, and Lueker [Du et al. 2009]. Generalization is widely used in privacy-preserving data mining and can also be viewed as a natural way of compressing a dataset. In min-max generalization problems, the input consists of data items with weights and a lower bound w$_{lb}$, and the goal is to partition individual items into groups of weight at least w$_{lb}$ while minimizing the maximum weight of a group. The rules of legal partitioning are specific to a problem. Du et al. consider several problems in this vein: (1) partitioning a graph into connected subgraphs, (2) partitioning unstructured data into arbitrary classes, and (3) partitioning a two-dimensional array into contiguous rectangles (subarrays) that satisfy these weight requirements. We significantly improve approximation ratios for all the problems considered by Du et al. and provide additional motivation for these problems. Moreover, for the first problem, whereas Du et al. give approximation algorithms for specific graph families, namely, 3-connected and 4-connected planar graphs, no approximation algorithm that works for all graphs was known prior to this work.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Alstrup:2014:UFC, author = "Stephen Alstrup and Mikkel Thorup and Inge Li G{\o}rtz and Theis Rauhe and Uri Zwick", title = "Union-Find with Constant Time Deletions", journal = j-TALG, volume = "11", number = "1", pages = "6:1--6:??", month = aug, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2636922", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 8 09:09:02 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A union-find data structure maintains a collection of disjoint sets under the operations makeset, union, and find. Kaplan, Shafrir, and Tarjan [SODA 2002] designed data structures for an extension of the union-find problem in which items of the sets maintained may be deleted. The cost of a delete operation in their implementations is essentially the same as the cost of a find operation; namely, $ O(\log n) $ worst-case and $ O(\alpha_{ \lceil M / N \rceil }(n)) $ amortized, where $n$ is the number of items in the set returned by the find operation, $N$ is the total number of makeset operations performed, $M$ is the total number of find operations performed, and $ \alpha_{ \lceil M / N \rceil } (n)$ is a functional inverse of Ackermann's function. They left open the question whether delete operations can be implemented more efficiently than find operations, for example, in $ o(\log n)$ worst-case time. We resolve this open problem by presenting a relatively simple modification of the classical union-find data structure that supports delete, as well as makeset and union operations, in constant worst-case time, while still supporting find operations in $ O(\log n)$ worst-case time and $ O(\alpha_{ \lceil M / N \rceil }(n))$ amortized time. Our analysis supplies, in particular, a very concise potential-based amortized analysis of the standard union-find data structure that yields an $ O(\alpha_{ \lceil M / N \rceil }(n))$ amortized bound on the cost of find operations. All previous potential-based analyses yielded the weaker amortized bound of $ O(\alpha_{ \lceil M / N \rceil } (N))$. Furthermore, our tighter analysis extends to one-path variants of the path compression technique such as path splitting.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chakrabarti:2014:ADS, author = "Amit Chakrabarti and Graham Cormode and Andrew Mcgregor and Justin Thaler", title = "Annotations in Data Streams", journal = j-TALG, volume = "11", number = "1", pages = "7:1--7:??", month = aug, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2636924", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Sep 8 09:09:02 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The central goal of data stream algorithms is to process massive streams of data using sublinear storage space. Motivated by work in the database community on outsourcing database and data stream processing, we ask whether the space usage of such algorithms can be further reduced by enlisting a more powerful ``helper'' that can annotate the stream as it is read. We do not wish to blindly trust the helper, so we require that the algorithm be convinced of having computed a correct answer. We show upper bounds that achieve a nontrivial tradeoff between the amount of annotation used and the space required to verify it. We also prove lower bounds on such tradeoffs, often nearly matching the upper bounds, via notions related to Merlin--Arthur communication complexity. Our results cover the classic data stream problems of selection, frequency moments, and fundamental graph problems such as triangle-freeness and connectivity. Our work is also part of a growing trend-including recent studies of multipass streaming, read/write streams, and randomly ordered streams-of asking more complexity-theoretic questions about data stream processing. It is a recognition that, in addition to practical relevance, the data stream model raises many interesting theoretical questions in its own right.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cheriyan:2014:ARS, author = "Joseph Cheriyan and Bundit Laekhanukit and Guyslain Naves and Adrian Vetta", title = "Approximating Rooted {Steiner} Networks", journal = j-TALG, volume = "11", number = "2", pages = "8:1--8:??", month = oct, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2650183", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 30 17:42:56 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Directed Steiner Tree (DST) problem is a cornerstone problem in network design. We focus on the generalization of the problem with higher connectivity requirements. The problem with one root and two sinks is APX-hard. The problem with one root and many sinks is as hard to approximate as the directed Steiner forest problem, and the latter is well known to be as hard to approximate as the label cover problem. Utilizing previous techniques, we strengthen these results and extend them to undirected graphs. Specifically, we give an $ \Omega (k^\epsilon) $ hardness bound for the rooted $k$-connectivity problem in undirected graphs. As a consequence, we obtain an $ \Omega (k^\epsilon)$ hardness bound for the undirected subset $k$-connectivity problem. Additionally, we give a result on the integrality ratio of the natural linear programming relaxation of the directed rooted $k$-connectivity problem.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Doerr:2014:QRS, author = "Benjamin Doerr and Tobias Friedrich and Thomas Sauerwald", title = "Quasirandom Rumor Spreading", journal = j-TALG, volume = "11", number = "2", pages = "9:1--9:??", month = oct, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2650185", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 30 17:42:56 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose and analyze a quasirandom analogue of the classical push model for disseminating information in networks (``randomized rumor spreading''). In the classical model, in each round, each informed vertex chooses a neighbor at random and informs it, if it was not informed before. It is known that this simple protocol succeeds in spreading a rumor from one vertex to all others within $ O(\log n) $ rounds on complete graphs, hypercubes, random regular graphs, Erd{\H{o}}s--R{\'e}nyi random graphs, and Ramanujan graphs with probability $ 1 - o(1) $. In the quasirandom model, we assume that each vertex has a (cyclic) list of its neighbors. Once informed, it starts at a random position on the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above-mentioned bounds still hold. In some cases, even better bounds than for the classical model can be shown.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dieudonne:2014:DNE, author = "Yoann Dieudonn{\'e} and Andrzej Pelc", title = "Deterministic Network Exploration by Anonymous Silent Agents with Local Traffic Reports", journal = j-TALG, volume = "11", number = "2", pages = "10:1--10:??", month = oct, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2594581", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 30 17:42:56 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A team consisting of an unknown number of mobile agents starting from different nodes of an unknown network, possibly at different times, have to explore the network: Every node must be visited by at least one agent, and all agents must eventually stop. Agents are anonymous (identical), execute the same deterministic algorithm, and move in synchronous rounds along links of the network. They are silent: They cannot send any messages to other agents or mark visited nodes in any way. In the absence of any additional information, exploration with termination of an arbitrary network in this model, devoid of any means of communication between agents, is impossible. Our aim is to solve the exploration problem by giving to agents very restricted local traffic reports. Specifically, an agent that is at a node $v$ in a given round is provided with three bits of information answering the following questions: Am I alone at $v$ ? Did any agent enter $v$ in this round? Did any agent exit $v$ in this round? We show that this small amount of information permits us to solve the exploration problem in arbitrary networks. More precisely, we give a deterministic terminating exploration algorithm working in arbitrary networks for all initial configurations that are not perfectly symmetric; that is, in which there are agents with different views of the network. The algorithm works in polynomial time in the (unknown) size of the network. A deterministic terminating exploration algorithm working for all initial configurations in arbitrary networks does not exist.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Tao:2014:DRS, author = "Yufei Tao", title = "Dynamic Ray Stabbing", journal = j-TALG, volume = "11", number = "2", pages = "11:1--11:??", month = oct, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2559153", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 30 17:42:56 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider maintaining a dynamic set $S$ of $N$ horizontal segments in $ R^2$ such that, given a vertical ray $Q$ in $ R^2$, the segments in $S$ intersecting $Q$ can be reported efficiently. In the external memory model, we give a structure that consumes $ O (N / B)$ space, answers a query in $ O(\log_B N + K / B)$ time (where $K$ is the number of reported segments), and can be updated in $ O (\log_B N)$ amortized time per insertion and deletion. With $B$ set to a constant, the structure also works in internal memory, consuming space $ O(N)$, answering a query in $ O (\log N + K)$ time, and supporting an update in $ O(\log N)$ amortized time.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cole:2014:TDP, author = "Richard Cole and Carmit Hazay and Moshe Lewenstein and Dekel Tsur", title = "Two-Dimensional Parameterized Matching", journal = j-TALG, volume = "11", number = "2", pages = "12:1--12:??", month = oct, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2650220", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 30 17:42:56 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/string-matching.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Two equal-length strings, or two equal-sized two-dimensional texts, parameterize match (p-match) if there is a one-one mapping (relative to the alphabet) of their characters. Two-dimensional parameterized matching is the task of finding all $ m \times m $ substrings of an $ n \times n $ text that p-match an $ m \times m $ pattern. This models searching for color images with changing of color maps, for example. We present two algorithms that solve the two-dimensional parameterized matching problem. The time complexities of our algorithms are $ O (n^2 \log^2 m) $ and $ O (n^2 + m^{2.5} \polylog (m)) $. Our algorithms are faster than the $ O (n^2 m \log^2 m \log \log m) $ time algorithm for this problem of Amir et al. [2006]. A key step in both of our algorithms is to count the number of distinct characters in every $ m \times m $ substring of an $ n \times n $ string. We show how to solve this problem in $ O (n^2) $ time. This result may be of independent interest.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dom:2014:KLB, author = "Michael Dom and Daniel Lokshtanov and Saket Saurabh", title = "Kernelization Lower Bounds Through Colors and {IDs}", journal = j-TALG, volume = "11", number = "2", pages = "13:1--13:??", month = oct, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2650261", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 30 17:42:56 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In parameterized complexity, each problem instance comes with a parameter $k$, and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size polynomial in $k$. Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the nonexistence of polynomial kernels for specific problems has been developed by Bodlaender et al. [2009] and Fortnow and Santhanam [2008]. With few exceptions, all known kernelization lower bounds results have been obtained by directly applying this framework. In this article, we show how to combine these results with combinatorial reductions that use colors and IDs in order to prove kernelization lower bounds for a variety of basic problems. To follow we give a summary of our main results. All results are under the assumption that the polynomial hierarchy does not collapse to the third level. -We show that the Steiner Tree problem parameterized by the number of terminals and solution size $k$, and the Connected Vertex Cover and Capacitated Vertex Cover problems do not admit a polynomial kernel. The two latter results are surprising because the closely related Vertex Cover problem admits a kernel with at most $ 2 k $ vertices. -Alon and Gutner [2008] obtain a $ k^{\poly (h)}$ kernel for Dominating Set in $H$-Minor Free Graphs parameterized by $ h = | H |$ and solution size $k$, and ask whether kernels of smaller size exist. We partially resolve this question by showing that Dominating Set in $H$-Minor Free Graphs does not admit a kernel with size polynomial in $ k + h$. -Harnik and Naor [2007] obtain a ``compression algorithm'' for the Sparse Subset Sum problem. We show that their algorithm is essentially optimal by showing that the instances cannot be compressed further. -The Hitting Set and Set Cover problems are among the most-studied problems in algorithmics. Both problems admit a kernel of size $ k^{O (d)}$ when parameterized by solution size $k$ and maximum set size $d$. We show that neither of them, along with the Unique Coverage and Bounded Rank Disjoint Sets problems, admits a polynomial kernel. The existence of polynomial kernels for several of the problems mentioned previously was an open problem explicitly stated in the literature [Alon and Gutner 2008; Betzler 2006; Guo and Niedermeier 2007; Guo et al. 2007; Moser et al. 2007]. Many of our results also rule out the existence of compression algorithms, a notion similar to kernelization defined by Harnik and Naor [2007], for the problems in question.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Demaine:2014:MMF, author = "Erik D. Demaine and Mohammadtaghi Hajiaghayi and D{\'a}niel Marx", title = "Minimizing Movement: Fixed-Parameter Tractability", journal = j-TALG, volume = "11", number = "2", pages = "14:1--14:??", month = oct, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2650247", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 30 17:42:56 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study an extensive class of movement minimization problems that arise from many practical scenarios but so far have little theoretical study. In general, these problems involve planning the coordinated motion of a collection of agents (representing robots, people, map labels, network messages, etc.) to achieve a global property in the network while minimizing the maximum or average movement (expended energy). The only previous theoretical results about this class of problems are about approximation and are mainly negative: many movement problems of interest have polynomial inapproximability. Given that the number of mobile agents is typically much smaller than the complexity of the environment, we turn to fixed-parameter tractability. We characterize the boundary between tractable and intractable movement problems in a very general setup: it turns out the complexity of the problem fundamentally depends on the treewidth of the minimal configurations. Thus, the complexity of a particular problem can be determined by answering a purely combinatorial question. Using our general tools, we determine the complexity of several concrete problems and fortunately show that many movement problems of interest can be solved efficiently.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lokshtanov:2014:FPA, author = "Daniel Lokshtanov and N. S. Narayanaswamy and Venkatesh Raman and M. S. Ramanujan and Saket Saurabh", title = "Faster Parameterized Algorithms Using Linear Programming", journal = j-TALG, volume = "11", number = "2", pages = "15:1--15:??", month = oct, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1145/2566616", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 30 17:42:56 MDT 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate the parameterized complexity of Vertex Cover parameterized by the difference between the size of the optimal solution and the value of the linear programming (LP) relaxation of the problem. By carefully analyzing the change in the LP value in the branching steps, we argue that combining previously known preprocessing rules with the most straightforward branching algorithm yields an $ O*(2.618^k) $ algorithm for the problem. Here, $k$ is the excess of the vertex cover size over the LP optimum, and we write $ O*(f(k))$ for a time complexity of the form $ O (f (k) n^{O (1)})$. We proceed to show that a more sophisticated branching algorithm achieves a running time of $ O*(2.3146^k)$. Following this, using previously known as well as new reductions, we give $ O*(2.3146^k)$ algorithms for the parameterized versions of Above Guarantee Vertex Cover, Odd Cycle Transversal, Split Vertex Deletion, and Almost 2-SAT, and $ O*(1.5214^k)$ algorithms for K{\"o}nig Vertex Deletion and Vertex Cover parameterized by the size of the smallest odd cycle transversal and K{\"o}nig vertex deletion set. These algorithms significantly improve the best known bounds for these problems. The most notable improvement among these is the new bound for Odd Cycle Transversal-this is the first algorithm that improves on the dependence on $k$ of the seminal $ O*(3^k)$ algorithm of Reed, Smith, and Vetta. Finally, using our algorithm, we obtain a kernel for the standard parameterization of Vertex Cover with at most $ 2 k - c \log k$ vertices. Our kernel is simpler than previously known kernels achieving the same size bound.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borradaile:2015:MSC, author = "Glencora Borradaile and Piotr Sankowski and Christian Wulff-Nilsen", title = "Min $ s t$-Cut Oracle for Planar Graphs with Near-Linear Preprocessing Time", journal = j-TALG, volume = "11", number = "3", pages = "16:1--16:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2684068", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For an undirected $n$-vertex planar graph $G$ with nonnegative edge weights, we consider the following type of query: given two vertices $s$ and $t$ in $G$, what is the weight of a min $ s t$-cut in $G$ ? We show how to answer such queries in constant time with $ O(n \log^4 n)$ preprocessing time and $ O(n \log n)$ space. We use a Gomory--Hu tree to represent all the pairwise min cuts implicitly. Previously, no subquadratic time algorithm was known for this problem. Since all-pairs min cut and the minimum-cycle basis are dual problems in planar graphs, we also obtain an implicit representation of a minimum-cycle basis in $ O(n \log^4 n)$ time and $ O(n \log n)$ space. Additionally, an explicit representation can be obtained in $ O(C)$ time and space where $C$ is the size of the basis. These results require that shortest paths are unique. This can be guaranteed either by using randomization without overhead or deterministically with an additional $ \log^2 n$ factor in the preprocessing times.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gerke:2015:MML, author = "Stefanie Gerke and Konstantinos Panagiotou and Justus Schwartz and Angelika Steger", title = "Maximizing the Minimum Load for Random Processing Times", journal = j-TALG, volume = "11", number = "3", pages = "17:1--17:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2651421", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider a stochastic variant of the so-called Santa Claus problem. The Santa Claus problem is equivalent to the problem of scheduling a set of $n$ jobs on $m$ parallel machines without preemption, so as to maximize the minimum load. We consider the identical machine version of this scheduling problem with the additional restriction that the scheduler has only a guess of the processing times; that is, the processing time of a job is a random variable. We show that there is a critical value $ \rho (n, m)$ such that if the duration of the jobs is exponentially distributed and the expected values deviate by less than a multiplicative factor of $ \rho (n, m)$ from each other, then a greedy algorithm has an expected competitive ratio arbitrarily close to one; that is, it performs in expectation almost as good as an algorithm that knows the actual values in advance. On the other hand, if the expected values deviate by more than a multiplicative factor of $ \rho (n, m)$, then the expected performance is arbitrarily bad for all algorithms.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Charron-Bost:2015:TCL, author = "Bernadette Charron-Bost and Matthias F{\"u}gger and Jennifer L. Welch and Josef Widder", title = "Time Complexity of Link Reversal Routing", journal = j-TALG, volume = "11", number = "3", pages = "18:1--18:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2644815", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Link reversal is a versatile algorithm design paradigm, originally proposed by Gafni and Bertsekas in 1981 for routing and subsequently applied to other problems including mutual exclusion, leader election, and resource allocation. Although these algorithms are well known, until now there have been only preliminary results on time complexity, even for the simplest link reversal algorithm for routing, called Full Reversal. In Full Reversal, a sink reverses all its incident links, whereas in other link reversal algorithms (e.g., Partial Reversal), a sink reverses only some of its incident links. Charron-Bost et al. introduced a generalization, called LR, that includes Full and Partial Reversal as special cases. In this article, we present an exact expression for the time complexity of LR. The expression is stated in terms of simple properties of the initial graph. The result specializes to exact formulas for the time complexity of any node in any initial acyclic directed graph for both Full and Partial Reversal. Having the exact formulas provides insight into the behavior of Full and Partial Reversal on specific graph families. Our first technical insight is to describe the behavior of Full Reversal as a dynamical system and to observe that this system is linear in min-plus algebra. Our second technical insight is to overcome the difficulty posed by the fact that LR is not linear by transforming every execution of LR from an initial graph into an execution of Full Reversal from a different initial graph while maintaining the execution's work and time complexity.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borradaile:2015:PTA, author = "Glencora Borradaile and Philip N. Klein and Claire Mathieu", title = "A Polynomial-Time Approximation Scheme for {Euclidean} {Steiner} Forest", journal = j-TALG, volume = "11", number = "3", pages = "19:1--19:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629654", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a randomized $ O(n \polylog n)$-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed $ \epsilon > 0$ and given $n$ terminals in the plane with connection requests between some pairs of terminals, our scheme finds a $ (1 + \epsilon)$ approximation to the minimum-length forest that connects every requested pair of terminals.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jez:2015:FFC, author = "Artur Jez", title = "Faster Fully Compressed Pattern Matching by Recompression", journal = j-TALG, volume = "11", number = "3", pages = "20:1--20:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2631920", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/datacompression.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs) --- that is, context-free grammars generating exactly one string; the term fully means that both the pattern and the text are given in the compressed form. The problem is approached using a recently developed technique of local recompression: the SLPs are refactored so that substrings of the pattern and text are encoded in both SLPs in the same way. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. This technique yields an $ O((n + m) \log M) $ algorithm for compressed pattern matching, assuming that $M$ fits in $ O(1) $ machine words, where $ n(m) $ is the size of the compressed representation of the text (pattern, respectively), and $M$ is the size of the decompressed pattern. If only $ m + n$ fits in $ O(1) $ machine words, the running time increases to $ O((n + m) \log M \log (n + m)) $. The previous best algorithm due to Lifshits has $ O(n^2 m) $ running time.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cao:2015:IDF, author = "Yixin Cao and D{\'a}niel Marx", title = "Interval Deletion Is Fixed-Parameter Tractable", journal = j-TALG, volume = "11", number = "3", pages = "21:1--21:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629595", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the minimum interval deletion problem, which asks for the removal of a set of at most $k$ vertices to make a graph of $n$ vertices into an interval graph. We present a parameterized algorithm of runtime $ 10^k \cdot n^{O(1)}$ for this problem --- that is, we show that the problem is fixed-parameter tractable.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Wild:2015:ACD, author = "Sebastian Wild and Markus E. Nebel and Ralph Neininger", title = "Average Case and Distributional Analysis of Dual-Pivot {Quicksort}", journal = j-TALG, volume = "11", number = "3", pages = "22:1--22:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629340", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In 2009, Oracle replaced the long-serving sorting algorithm in its Java 7 runtime library by a new dual-pivot Quicksort variant due to Vladimir Yaroslavskiy. The decision was based on the strikingly good performance of Yaroslavskiy's implementation in running time experiments. At that time, no precise investigations of the algorithm were available to explain its superior performance-on the contrary: previous theoretical studies of other dual-pivot Quicksort variants even discouraged the use of two pivots. In 2012, two of the authors gave an average case analysis of a simplified version of Yaroslavskiy's algorithm, proving that savings in the number of comparisons are possible. However, Yaroslavskiy's algorithm needs more swaps, which renders the analysis inconclusive. To force the issue, we herein extend our analysis to the fully detailed style of Knuth: we determine the exact number of executed Java Bytecode instructions. Surprisingly, Yaroslavskiy's algorithm needs sightly more Bytecode instructions than a simple implementation of classic Quicksort --- contradicting observed running times. As in Oracle's library implementation, we incorporate the use of Insertionsort on small subproblems and show that it indeed speeds up Yaroslavskiy's Quicksort in terms of Bytecodes; but even with optimal Insertionsort thresholds, the new Quicksort variant needs slightly more Bytecode instructions on average. Finally, we show that the (suitably normalized) costs of Yaroslavskiy's algorithm converge to a random variable whose distribution is characterized by a fixed-point equation. From that, we compute variances of costs and show that for large $n$, costs are concentrated around their mean.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gortz:2015:MMM, author = "Inge Li G{\o}rtz and Viswanath Nagarajan and R. Ravi", title = "Minimum Makespan Multi-Vehicle Dial-a-Ride", journal = j-TALG, volume = "11", number = "3", pages = "23:1--23:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629653", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Dial-a-Ride problems consist of a set $V$ of $n$ vertices in a metric space (denoting travel time between vertices) and a set of $m$ objects represented as source-destination pairs $ \{ (s_i, t_i) \}^m_{i = 1}$, where each object requires to be moved from its source to destination vertex. In the multi-vehicle Dial-a-Ride problem, there are $q$ vehicles, each having capacity $k$ and where each vehicle $ j \in [q]$ has its own depot-vertex $ r_j \in V$. A feasible schedule consists of a capacitated route for each vehicle (where vehicle $j$ originates and ends at its depot $ r_j$) that together move all objects from their sources to destinations. The objective is to find a feasible schedule that minimizes the maximum completion time (i.e., makespan) of vehicles, where the completion time of vehicle $j$ is the time when it returns to its depot $ r_j$ at the end of its route. We study the preemptive version of multi-vehicle Dial-a-Ride, in which an object may be left at intermediate vertices and transported by more than one vehicle, while being moved from source to destination. Our main results are an $ O(\log^3 n)$-approximation algorithm for preemptive multi-vehicle Dial-a-Ride, and an improved $ O(\log t)$-approximation for its special case when there is no capacity constraint (here $ t \leq n$ is the number of distinct depot-vertices). There is an $ \Omega (\log^{1 / 4 - \epsilon } n)$ hardness of approximation known even for single vehicle capacitated Dial-a-Ride [G{\o}rtz 2006]. For uncapacitated multi-vehicle Dial-a-Ride, we show that there are instances when natural lower bounds (used in our algorithm) are $ \tilde \Omega (\log t)$ factor away from the optimum. We also consider the special class of metrics induced by graphs excluding any fixed minor (e.g., planar metrics). In this case, we obtain improved guarantees of $ O(\log^2 n)$ for capacitated multi-vehicle Dial-a-Ride, and $ O(1)$ for the uncapacitated problem.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Levi:2015:QPT, author = "Reut Levi and Dana Ron", title = "A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor", journal = j-TALG, volume = "11", number = "3", pages = "24:1--24:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629508", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jan 13 18:05:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient partition oracles. A partition oracle is a procedure that, given access to the incidence lists representation of a bounded-degree graph $ G = (V, E) $ and a parameter $ \epsilon $, when queried on a vertex $ v \in V $, returns the part (subset of vertices) that $v$ belongs to in a partition of all graph vertices. The partition should be such that all parts are small, each part is connected, and if the graph has certain properties, the total number of edges between parts is at most $ \epsilon | V |$. In this work, we give a partition oracle for graphs with excluded minors whose query complexity is quasi-polynomial in $ 1 / \epsilon $, improving on the result of Hassidim et al. (Proceedings of FOCS 2009), who gave a partition oracle with query complexity exponential in $ 1 / \epsilon $. This improvement implies corresponding improvements in the complexity of testing planarity and other properties that are characterized by excluded minors as well as sublinear-time approximation algorithms that work under the promise that the graph has an excluded minor.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hohn:2015:PSR, author = "Wiebke H{\"o}hn and Tobias Jacobs", title = "On the Performance of {Smith}'s Rule in Single-Machine Scheduling with Nonlinear Cost", journal = j-TALG, volume = "11", number = "4", pages = "25:1--25:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629652", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a single-machine scheduling problem. Given some continuous, nondecreasing cost function, we aim to compute a schedule minimizing the weighted total cost, where the cost of each job is determined by the cost function value at its completion time. This problem is closely related to scheduling a single machine with nonuniform processing speed. We show that for piecewise linear cost functions it is strongly NP-hard. The main contribution of this article is a tight analysis of the approximation guarantee of Smith's rule under any convex or concave cost function. More specifically, for these wide classes of cost functions we reduce the task of determining a worst-case problem instance to a continuous optimization problem, which can be solved by standard algebraic or numerical methods. For polynomial cost functions with positive coefficients, it turns out that the tight approximation ratio can be calculated as the root of a univariate polynomial. We show that this approximation ratio is asymptotically equal to $ k^{(k - 1) / (k + 1)} $, denoting by $k$ the degree of the cost function. To overcome unrealistic worst-case instances, we also give tight bounds for the case of integral processing times that are parameterized by the maximum and total processing time.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chen:2015:CSP, author = "Danny Z. Chen and Haitao Wang", title = "Computing Shortest Paths among Curved Obstacles in the Plane", journal = j-TALG, volume = "11", number = "4", pages = "26:1--26:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2660771", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A fundamental problem in computational geometry is to compute an obstacle-avoiding Euclidean shortest path between two points in the plane. The case of this problem on polygonal obstacles is well studied. In this article, we consider the problem version on curved obstacles, which are commonly modeled as splinegons. A splinegon can be viewed as replacing each edge of a polygon by a convex curved edge (polygons are special splinegons), and the combinatorial complexity of each curved edge is assumed to be $ O(1) $. Given in the plane two points $s$ and $t$ and a set $s$ of $h$ pairwise disjoint splinegons with a total of $n$ vertices, after a bounded degree decomposition of $S$ is obtained, we compute a shortest $s$-to-$t$ path avoiding the splinegons in $ O(n + h \log h + k)$ time, where $k$ is a parameter sensitive to the geometric structures of the input and is upper bounded by $ O(h^2)$. The bounded degree decomposition of $S$, which is similar to the triangulation of the polygonal domains, can be computed in $ O(n \log n)$ time or $ O(n + h \log^{1 + \epsilon } h)$ time for any $ \epsilon > 0$. In particular, when all splinegons are convex, the decomposition can be computed in $ O(n + h \log h)$ time and $k$ is linear to the number of common tangents in the free space (called ``free common tangents'') among the splinegons. Our techniques also improve several previous results: (1) For the polygon case (i.e., when all splinegons are polygons), the shortest path problem was previously solved in $ O(n \log n)$ time, or in $ O(n + h^2 \log n)$ time. Thus, our algorithm improves the $ O(n + h^2 \log n)$ time result, and is faster than the $ O(n \log n)$ time solution for sufficiently small $h$, for example, $ h = o(\sqrt {n \log n})$. (2) Our techniques produce an optimal output-sensitive algorithm for a basic visibility problem of computing all free common tangents among $h$ pairwise disjoint convex splinegons with a total of $n$ vertices. Our algorithm runs in $ O(n + h \log h + k)$ time and $ O(n)$ working space, where $k$ is the number of all free common tangents. Note that $ k = O(h^2)$. Even for the special case where all splinegons are convex polygons, the previously best algorithm for this visibility problem takes $ O(n + h^2 \log n)$ time. (3) We improve the previous work for computing the shortest path between two points among convex pseudodisks of $ O(1)$ complexity each. In addition, a by-product of our techniques is an optimal $ O(n + h \log h)$ time and $ O(n)$ space algorithm for computing the Voronoi diagram of a set of $h$ pairwise disjoint convex splinegons with a total of $n$ vertices.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Marx:2015:FPA, author = "D{\'a}niel Marx and L{\'a}szl{\'o} A. V{\'e}gh", title = "Fixed-Parameter Algorithms for Minimum-Cost Edge-Connectivity Augmentation", journal = j-TALG, volume = "11", number = "4", pages = "27:1--27:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2700210", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider connectivity-augmentation problems in a setting where each potential new edge has a non-negative cost associated with it, and the task is to achieve a certain connectivity target with at most $p$ new edges of minimum total cost. The main result is that the minimum cost augmentation of edge-connectivity from $ k - 1$ to $k$ with at most $p$ new edges is fixed-parameter tractable parameterized by $p$ a polynomial kernel. We also prove the fixed-parameter tractability of increasing edge connectivity from $0$ to $2$ and increasing node connectivity from $1$ to $2$.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chitnis:2015:DSF, author = "Rajesh Chitnis and Marek Cygan and Mohammataghi Hajiaghayi and D{\'a}niel Marx", title = "Directed Subset Feedback Vertex Set Is Fixed-Parameter Tractable", journal = j-TALG, volume = "11", number = "4", pages = "28:1--28:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2700209", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a graph $G$ and an integer $k$, the Feedback Vertex Set (FVS) problem asks if there is a vertex set $T$ of size at most $k$ that hits all cycles in the graph. The first fixed-parameter algorithm for FVS in undirected graphs appeared in a monograph of Mehlhorn in 1984. The fixed-parameter tractability (FPT) status of FVS in directed graphs was a long-standing open problem until Chen et al. (STOC '08, JACM '08) showed that it is fixed-parameter tractable by giving a $ 4^k k! \cdot n^{O(1)}$ time algorithm. There are two subset versions of this problems: We are given an additional subset $S$ of vertices (resp., edges), and we want to hit all cycles passing through a vertex of $S$ (resp., an edge of $S$); the two variants are known to be equivalent in the parameterized sense. Recently, the Subset FVS problem in undirected graphs was shown to be FPT by Cygan et al. (ICALP'11, SIDMA'13) and independently by Kakimura et al. (SODA '12). We generalize the result of Chen et al. (STOC '08, JACM '08) by showing that a Subset FVS in directed graphs can be solved in time $ 2^{O(k^3)} c n^{O(1)}$ (i.e., FPT parameterized by size $k$ of the solution). By our result, we complete the picture for FVS problems and their subset versions in undirected and directed graphs. The technique of random sampling of important separators was used by Marx and Razgon (STOC '11, SICOMP '14) to show that Undirected Multicut is FPT, and it was generalized by Chitnis et al. (SODA '12, SICOMP '13) to directed graphs to show that Directed Multiway Cut is FPT. In addition to proving the FPT of a Directed Subset FVS, we reformulate the random sampling of important separators technique in an abstract way that can be used with a general family of transversal problems. We believe this general approach will be useful for showing the FPT of other problems in directed graphs. Moreover, we modify the probability distribution used in the technique to achieve better running time; in particular, this gives an improvement from $ 2^{2 O(k)}$ to $ 2^{O(k^2)}$ in the parameter dependence of the Directed Multiway Cut algorithm of Chitnis et al. (SODA '12, SICOMP '13).", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Avraham:2015:DSF, author = "Rinat Ben Avraham and Omrit Filtser and Haim Kaplan and Matthew J. Katz and Micha Sharir", title = "The Discrete and Semicontinuous {Fr{\'e}chet} Distance with Shortcuts via Approximate Distance Counting and Selection", journal = j-TALG, volume = "11", number = "4", pages = "29:1--29:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2700222", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Fr{\'e}chet distance is a well-studied similarity measure between curves. The discrete Fr{\'e}chet distance is an analogous similarity measure, defined for two sequences of $m$ and $n$ points, where the points are usually sampled from input curves. We consider a variant, called the discrete Fr{\'e}chet distance with shortcuts, which captures the similarity between (sampled) curves in the presence of outliers. When shortcuts are allowed only in one noise-containing curve, we give a randomized algorithm that runs in $ O((m + n)^{6 / 5 + \epsilon })$ expected time, for any $ \epsilon > 0$. When shortcuts are allowed in both curves, we give an $ O((m^{2 / 3} n^{2 / 3} + m + n) \log^3 (m + n))$-time deterministic algorithm. We also consider the semicontinuous Fr{\'e}chet distance with one-sided shortcuts, where we have a sequence of $m$ points and a polygonal curve of $n$ edges, and shortcuts are allowed only in the sequence. We show that this problem can be solved in randomized expected time $ O((m + n)^{2 / 3} m^{2 / 3} n^{1 / 3} \log (m + n))$. Our techniques are novel and may find further applications. One of the main new technical results is: Given two sets of points $A$ and $B$ in the plane and an interval $I$, we develop an algorithm that decides whether the number of pairs $ (x, y) \in A \times B$ whose distance $ {\rm dist}(x, y)$ is in $I$ is less than some given threshold $L$. The running time of this algorithm decreases as $L$ increases. In case there are more than $L$ pairs of points whose distance is in $I$, we can get a small sample of pairs that contain a pair at approximate median distance (i.e., we can approximately ``bisect'' $I$). We combine this procedure with additional ideas to search, with a small overhead, for the optimal one-sided Fr{\'e}chet distance with shortcuts, using a very fast decision procedure. We also show how to apply this technique for approximating distance selection (with respect to rank), and a somewhat more involved variant of this technique is used in the solution of the semicontinuous Fr{\'e}chet distance with one-sided shortcuts. In general, the new technique can be applied to optimization problems for which the decision procedure is very fast but standard techniques like parametric search makes the optimization algorithm substantially slower.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Haeupler:2015:RBT, author = "Bernhard Haeupler and Siddhartha Sen and Robert E. Tarjan", title = "Rank-Balanced Trees", journal = j-TALG, volume = "11", number = "4", pages = "30:1--30:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2689412", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Since the invention of AVL trees in 1962, many kinds of binary search trees have been proposed. Notable are red-black trees, in which bottom-up rebalancing after an insertion or deletion takes $ O(1) $ amortized time and $ O(1) $ rotations worst-case. But the design space of balanced trees has not been fully explored. We continue the exploration. Our contributions are three: We systematically study the use of ranks and rank differences to define height-based balance in binary trees. Different invariants on rank differences yield AVL trees, red-black trees, and other kinds of balanced trees. By relaxing AVL trees, we obtain a new kind of balanced binary tree, the weak AVL tree (wavl tree), whose properties we develop. Bottom-up rebalancing after an insertion or deletion takes $ O(1) $ amortized time and at most two rotations, improving the three or more rotations per deletion needed in all other kinds of balanced trees of which we are aware. The height bound of a wavl tree degrades gracefully from that of an AVL tree as the number of deletions increases and is never worse than that of a red-black tree. Wavl trees also support top-down, fixed look-ahead rebalancing in $ O(1) $ amortized time. Finally, we use exponential potential functions to prove that in wavl trees rebalancing steps occur exponentially infrequently in rank. Thus, most of the rebalancing is at the bottom of the tree, which is crucial in concurrent applications and in those in which rotations take time that depends on the subtree size.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Belazzougui:2015:OLU, author = "Djamal Belazzougui and Gonzalo Navarro", title = "Optimal Lower and Upper Bounds for Representing Sequences", journal = j-TALG, volume = "11", number = "4", pages = "31:1--31:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629339", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Sequence representations supporting the queries access, select, and rank are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how they relate to the space used. In this article, we prove a strong lower bound for rank, which holds for rather permissive assumptions on the space used, and give matching upper bounds that require only a compressed representation of the sequence. Within this compressed space, the operations access and select can be solved in constant or almost-constant time, which is optimal for large alphabets. Our new upper bounds dominate all of the previous work in the time/space map.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Angelini:2015:TPP, author = "Patrizio Angelini and Giuseppe {Di Battista} and Fabrizio Frati and V{\'\i}t Jel{\'\i}nek and Jan Kratochv{\'\i}l and Maurizio Patrignani and Ignaz Rutter", title = "Testing Planarity of Partially Embedded Graphs", journal = j-TALG, volume = "11", number = "4", pages = "32:1--32:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629341", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the following problem: given a planar graph $G$ and a planar drawing (embedding) of a subgraph of $G$, can such a drawing be extended to a planar drawing of the entire graph $G$ ? This problem fits the paradigm of extending a partial solution for a problem to a complete one, which has been studied before in many different settings. Unlike many cases, in which the presence of a partial solution in the input makes an otherwise easy problem hard, we show that the planarity question remains polynomial-time solvable. Our algorithm is based on several combinatorial lemmas, which show that the planarity of partially embedded graphs exhibits the `TONCAS' behavior ``the obvious necessary conditions for planarity are also sufficient.'' These conditions are expressed in terms of the interplay between (1) the rotation system and containment relationships between cycles and (2) the decomposition of a graph into its connected, biconnected, and triconnected components. This implies that no dynamic programming is needed for a decision algorithm and that the elements of the decomposition can be processed independently. Further, by equipping the components of the decomposition with suitable data structures and by carefully splitting the problem into simpler subproblems, we make our algorithm run in linear time. Finally, we consider several generalizations of the problem, such as minimizing the number of edges of the partial embedding that need to be rerouted to extend it, and argue that they are NP-hard. We also apply our algorithm to the simultaneous graph drawing problem Simultaneous Embedding with Fixed Edges (Sefe). There we obtain a linear-time algorithm for the case that one of the input graphs or the common graph has a fixed planar embedding.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chalopin:2015:MSP, author = "J{\'e}r{\'e}mie Chalopin and Shantanu Das and Yann Disser and Mat{\'u}s Mihal{\'a}k and Peter Widmayer", title = "Mapping Simple Polygons: The Power of Telling Convex from Reflex", journal = j-TALG, volume = "11", number = "4", pages = "33:1--33:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2700223", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the exploration of a simple polygon $P$ by a robot that moves from vertex to vertex along edges of the visibility graph of $P$. The visibility graph has a vertex for every vertex of $P$ and an edge between two vertices if they see each other-that is, if the line segment connecting them lies inside $P$ entirely. While located at a vertex, the robot is capable of ordering the vertices it sees in counterclockwise order as they appear on the boundary, and for every two such vertices, it can distinguish whether the angle between them is convex ($ \leq \pi $) or reflex ($ > \pi $). Other than that, distant vertices are indistinguishable to the robot. We assume that an upper bound on the number of vertices is known. We obtain the general result that a robot exploring any locally oriented, arc-labeled graph $G$ can always determine the base graph of $G$. Roughly speaking, this is the smallest graph that cannot be distinguished by a robot from $G$ by its observations alone, no matter how it moves. Combining this result with various other techniques allows the ability to show that a robot exploring a polygon $P$ with the preceding capabilities is always capable of reconstructing the visibility graph of $P$. We also show that multiple identical, indistinguishable, and deterministic robots of this kind can always solve the weak rendezvous problem in which they need to position themselves such that they mutually see each other-for instance, such that they form a clique in the visibility graph.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ehsani:2015:BBN, author = "Shayan Ehsani and Saber Shokat Fadaee and Mohammadamin Fazli and Abbas Mehrabian and Sina Sadeghian Sadeghabad and Mohammadali Safari and Morteza Saghafian", title = "A Bounded Budget Network Creation Game", journal = j-TALG, volume = "11", number = "4", pages = "34:1--34:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2701615", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce a network creation game in which each player (vertex) has a fixed budget to establish links to other players. In this model, each link has a unit price, and each agent tries to minimize its cost, which is either its eccentricity or its total distance to other players in the underlying (undirected) graph of the created network. Two versions of the game are studied: In the MAX version, the cost incurred to a vertex is the maximum distance between the vertex and other vertices, and, in the SUM version, the cost incurred to a vertex is the sum of distances between the vertex and other vertices. We prove that in both versions pure Nash equilibria exist, but the problem of finding the best response of a vertex is NP-hard. We take the social cost of the created network to be its diameter, and next we study the maximum possible diameter of an equilibrium graph with $n$ vertices in various cases. When the sum of players' budgets is $ n - 1$, the equilibrium graphs are always trees, and we prove that their maximum diameter is $ \Theta (n)$ and $ \Theta (\log n)$ in MAX and SUM versions, respectively. When each vertex has a unit budget (i.e., can establish a link to just one vertex), the diameter of any equilibrium graph in either version is $ \Theta (1)$. We give examples of equilibrium graphs in the MAX version, such that all vertices have positive budgets and yet the diameter is $ \Omega (\sqrt {\log n})$. This interesting (and perhaps counterintuitive) result shows that increasing the budgets may increase the diameter of equilibrium graphs and hence deteriorate the network structure. Then we prove that every equilibrium graph in the SUM version has diameter $ 2^{O(\sqrt {\log n})}$. Finally, we show that if the budget of each player is at least $k$, then every equilibrium graph in the SUM version is $k$-connected or has a diameter smaller than 4.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Avigdor-Elgrabli:2015:ICA, author = "Noa Avigdor-Elgrabli and Yuval Rabani", title = "An Improved Competitive Algorithm for Reordering Buffer Management", journal = j-TALG, volume = "11", number = "4", pages = "35:1--35:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2663347", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Aug 7 07:59:53 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We design and analyze an online reordering buffer management algorithm with improved $ O(\log k / \log \log k) $ competitive ratio for nonuniform costs, where $k$ is the buffer size. This improves on the best previous result (even for uniform costs) of Englert and Westermann (2005) giving $ O(\log k)$ competitive ratio, which was also the best (offline) polynomial time approximation guarantee for this problem. Our analysis is based on an intricate dual fitting argument using a linear programming relaxation for the problem that we introduce in this article.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Rabani:2016:ESI, author = "Yuval Rabani and Andrea Richa and Jared Saia and David P. Woodruff", title = "Editorial to the Special Issue on {SODA'12}", journal = j-TALG, volume = "12", number = "1", pages = "1:1--1:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2846001", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chuzhoy:2016:AAH, author = "Julia Chuzhoy and Yury Makarychev and Aravindan Vijayaraghavan and Yuan Zhou", title = "Approximation Algorithms and Hardness of the $k$-Route Cut Problem", journal = j-TALG, volume = "12", number = "1", pages = "2:1--2:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2644814", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the $k$-route cut problem: given an undirected edge-weighted graph $ G = (V, E)$, a collection $ \{ (s_1, t_1), (s_2, t_2), {\ldots }, (s_r, t_r) \} $ of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset $ E^\prime $ of edges to remove, such that the connectivity of every pair $ (s_i, t_i)$ falls below $k$. Specifically, in the edge-connectivity version, EC-kRC, the requirement is that there are at most $ (k - 1)$ edge-disjoint paths connecting $ s_i$ to $ t_i$ in $ G \setminus E^\prime $, while in the vertex-connectivity version, VC-kRC, the same requirement is for vertex-disjoint paths. Prior to our work, poly-logarithmic approximation algorithms have been known for the special case where $ k \leq 3$, but no non-trivial approximation algorithms were known for any value $ k > 3$, except in the single-source setting. We show an $ O (k \log^{3 / 2} r)$-approximation algorithm for EC-kRC with uniform edge weights, and several polylogarithmic bi-criteria approximation algorithms for EC-kRC and VC-kRC, where the connectivity requirement $k$ is violated by a constant factor. We complement these upper bounds by proving that VC-kRC is hard to approximate to within a factor of $ k^\epsilon $ for some fixed $ \epsilon > 0$. We then turn to study a simpler version of VC-kRC, where only one source-sink pair is present. We give a simple bi-criteria approximation algorithm for this case, and show evidence that even this restricted version of the problem may be hard to approximate. For example, we prove that the single source-sink pair version of VC-kRC has no constant-factor approximation, assuming Feige's Random $ \kappa $-AND assumption.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Moroz:2016:CDB, author = "Guillaume Moroz and Boris Aronov", title = "Computing the Distance between Piecewise-Linear Bivariate Functions", journal = j-TALG, volume = "12", number = "1", pages = "3:1--3:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2847257", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of computing the distance between two piecewise-linear bivariate functions $f$ and $g$ defined over a common domain $M$, induced by the $ L_2$ norm --- that is, $ | f - g |^2 = \sqrt {\int_M (f - g)^2}$. If $f$ is defined by linear interpolation over a triangulation of $M$ with $n$ triangles and $g$ is defined over another such triangulation, the obvious naive algorithm requires $ \Theta (n^2)$ arithmetic operations to compute this distance. We show that it is possible to compute it in $ O(n \log^4 n \log \log n)$ arithmetic operations by reducing the problem to multipoint evaluation of a certain type of polynomials. We also present several generalizations and an application to terrain matching.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bjorklund:2016:FZT, author = "Andreas Bj{\"o}rklund and Thore Husfeldt and Petteri Kaski and Mikko Koivisto and Jesper Nederlof and Pekka Parviainen", title = "Fast Zeta Transforms for Lattices with Few Irreducibles", journal = j-TALG, volume = "12", number = "1", pages = "4:1--4:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2629429", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate fast algorithms for changing between the standard basis and an orthogonal basis of idempotents for M{\"o}bius algebras of finite lattices. We show that every lattice with $v$ elements, $n$ of which are nonzero and join-irreducible (or, by a dual result, nonzero and meet-irreducible), has arithmetic circuits of size $ O (v n)$ for computing the zeta transform and its inverse, thus enabling fast multiplication in the M{\"o}bius algebra. Furthermore, the circuit construction in fact gives optimal (up to constants) monotone circuits for several lattices of combinatorial and algebraic relevance, such as the lattice of subsets of a finite set, the lattice of set partitions of a finite set, the lattice of vector subspaces of a finite vector space, and the lattice of positive divisors of a positive integer.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andoni:2016:WPS, author = "Alexandr Andoni and Huy L. Nguy{\^e}n", title = "Width of Points in the Streaming Model", journal = j-TALG, volume = "12", number = "1", pages = "5:1--5:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2847259", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we show how to compute the width of a dynamic set of low-dimensional points in the streaming model. In particular, we assume that the stream contains both insertions of points and deletions of points to a set $S$, and the goal is to compute the width of the set $S$, namely the minimal distance between two parallel hyperplanes sandwiching the point set $S$. Our algorithm $ (1 + \epsilon)$ approximates the width of the set $S$ using space polylogarithmic in the size of $S$ and the aspect ratio of $S$. This is the first such algorithm that supports both insertions and deletions of points to the set $S$: previous algorithms for approximating the width of a point set only supported additions [Agarwal et al. 2004; Chan 2006], or a sliding window [Chan and Sadjad 2006]. This solves an open question from the ``2009 Kanpur list'' of open problems in data streams, property testing, and related topics [Indyk et al. 2011].", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Guruswami:2016:BUS, author = "Venkatesan Guruswami and Prasad Raghavendra and Rishi Saket and Yi Wu", title = "Bypassing {UGC} from Some Optimal Geometric Inapproximability Results", journal = j-TALG, volume = "12", number = "1", pages = "6:1--6:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2737729", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Unique Games Conjecture (UGC) has emerged in recent years as the starting point for several optimal inapproximability results. While for none of these results a reverse reduction to Unique Games is known, the assumption of bijective projections in the Label Cover instance nevertheless seems critical in these proofs. In this work, we bypass the need for UGC assumption in inapproximability results for two geometric problems, obtaining a tight NP-hardness result in each case. The first problem, known as $ L_p $ Subspace Approximation, is a generalization of the classic least squares regression problem. Here, the input consists of a set of points $ X = \{ \alpha_1, \ldots, \alpha_m \} \subseteq R_n $ and a parameter $k$ (possibly depending on $n$). The goal is to find a subspace $H$ of $ R_n$ of dimension $k$ that minimizes the $ \ell_p$ norm of the Euclidean distances to the points in $X$. For $ p = 2$, $ k = n - 1$, this reduces to the least squares regression problem, while for $ p = \infty $, $ k = 0$ it reduces to the problem of finding a ball of minimum radius enclosing all the points. We show that for any fixed $ p \in (2, \infty)$, and for $ k = n - 1$, it is NP-hard to approximate this problem to within a factor of $ \gamma_p - \epsilon $ for constant $ \epsilon > 0$, where $ \gamma_p$ is the $p$ th norm of a standard Gaussian random variable. This matches the $ \gamma_p$ approximation algorithm obtained by Deshpande, Tulsiani, and Vishnoi who also showed the same hardness result under the UGC. The second problem we study is the related $ L_p$ Quadratic Grothendieck Maximization Problem, considered by Kindler, Naor, and Schechtman. Here, the input is a multilinear quadratic form $ \sum^n_{i, j = 1} a_{ij} x_i x_j$ and the goal is to maximize the quadratic form over the $ \ell_p$ unit ball, namely, all $x$ with $ \sum^n_{i = 1} | x_i |_p < 1$. The problem is polynomial time solvable for $ p = 2$. We show that for any constant $ p \in (2, \infty)$, it is NP-hard to approximate the quadratic form to within a factor of $ \gamma_{2p} - \epsilon $ for any $ \epsilon > 0$. The same hardness factor was shown under the UGC by Kindler et al. We also obtain a $ \gamma_{2p}$ approximation algorithm for the problem using the convex relaxation of the problem defined by Kindler et al. A $ \gamma_{2p}$ approximation algorithm has also been independently obtained by Naor and Schechtman. These are the first approximation thresholds, proven under P $ \not = $ NP, that involve the Gaussian random variable in a fundamental way. Note that the problem statements themselves do not explicitly involve the Gaussian distribution.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Neiman:2016:SDA, author = "Ofer Neiman and Shay Solomon", title = "Simple Deterministic Algorithms for Fully Dynamic Maximal Matching", journal = j-TALG, volume = "12", number = "1", pages = "7:1--7:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2700206", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of $ O (n)$. No deterministic algorithm that outperforms the na{\"\i}ve $ O (n)$ one was reported up to this date. The only progress in this direction is due to Ivkovi{\'c} and Lloyd, who in 1993 devised a deterministic algorithm with an amortized update time of $ O ((n + m)^{\sqrt {2} / 2})$, where $m$ is the number of edges. In this article, we show the first deterministic fully dynamic algorithm that outperforms the trivial one. Specifically, we provide a deterministic worst-case update time of $ O (\sqrt {m})$. Moreover, our algorithm maintains a matching, which in fact is a $ 3 / 2$-approximate maximum cardinality matching (MCM). We remark that no fully dynamic algorithm for maintaining $ (2 - \epsilon)$-approximate MCM improving upon the na{\"\i}ve $ O (n)$ was known prior to this work, even allowing amortized time bounds and randomization. For low arboricity graphs (e.g., planar graphs and graphs excluding fixed minors), we devise another simple deterministic algorithm with sublogarithmic update time. Specifically, it maintains a fully dynamic maximal matching with amortized update time of $ O (\log n / \log \log n)$. This result addresses an open question of Onak and Rubinfeld [2010]. We also show a deterministic algorithm with optimal space usage, which for arbitrary graphs maintains a maximal matching in amortized $ O (\sqrt {m})$ time and uses only $ O (n + m)$ space.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Patrascu:2016:IRL, author = "Mihai P{\u{a}}tra{\c{s}}cu and Mikkel Thorup", title = "On the $k$-Independence Required by Linear Probing and Minwise Independence", journal = j-TALG, volume = "12", number = "1", pages = "8:1--8:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2716317", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/hash.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show that linear probing requires $5$-independent hash functions for expected constant-time performance, matching an upper bound of Pagh et al. [2009]. More precisely, we construct a random $4$-independent hash function yielding expected logarithmic search time for certain keys. For $ (1 + \varepsilon)$-approximate minwise independence, we show that $ \Omega (\lg \frac {1}{\varepsilon })$-independent hash functions are required, matching an upper bound of Indyk [2001]. We also show that the very fast $2$-independent multiply-shift scheme of Dietzfelbinger [1996] fails badly in both applications.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{DeCarliSilva:2016:SSP, author = "Marcel K. {De Carli Silva} and Nicholas J. A. Harvey and Cristiane M. Sato", title = "Sparse Sums of Positive Semidefinite Matrices", journal = j-TALG, volume = "12", number = "1", pages = "9:1--9:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2746241", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Many fast graph algorithms begin by preprocessing the graph to improve its sparsity. A common form of this is spectral sparsification, which involves removing and reweighting the edges of the graph while approximately preserving its spectral properties. This task has a more general linear algebraic formulation in terms of approximating sums of rank-one matrices. This article considers a more general task of approximating sums of symmetric, positive semidefinite matrices of arbitrary rank. We present two deterministic, polynomial time algorithms for solving this problem. The first algorithm applies the pessimistic estimators of Wigderson and Xiao, and the second involves an extension of the method of Batson, Spielman, and Srivastava. These algorithms have several applications, including sparsifiers of hypergraphs, sparse solutions to semidefinite programs, sparsifiers of unique games, and graph sparsifiers with various auxiliary constraints.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gupta:2016:RMO, author = "Anupam Gupta and Viswanath Nagarajan and R. Ravi", title = "Robust and {MaxMin} Optimization under Matroid and Knapsack Uncertainty Sets", journal = j-TALG, volume = "12", number = "1", pages = "10:1--10:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2746226", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider the following problem: given a set system $ (U, \Omega) $ and an edge-weighted graph $ G = (U, E) $ on the same universe $U$, find the set $ A \in \Omega $ such that the Steiner tree cost with terminals $A$ is as large as possible --- ``which set in $ \Omega $ is the most difficult to connect up?'' This is an example of a max-min problem: find the set $ A \in \Omega $ such that the value of some minimization (covering) problem is as large as possible. In this article, we show that for certain covering problems that admit good deterministic online algorithms, we can give good algorithms for max-min optimization when the set system $ \Omega $ is given by a $p$-system or knapsack constraints or both. This result is similar to results for constrained maximization of submodular functions. Although many natural covering problems are not even approximately submodular, we show that one can use properties of the online algorithm as a surrogate for submodularity. Moreover, we give stronger connections between max-min optimization and two-stage robust optimization, and hence give improved algorithms for robust versions of various covering problems, for cases where the uncertainty sets are given by $p$-systems and knapsack constraints.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Georgiadis:2016:DTC, author = "Loukas Georgiadis and Robert E. Tarjan", title = "Dominator Tree Certification and Divergent Spanning Trees", journal = j-TALG, volume = "12", number = "1", pages = "11:1--11:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2764913", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "How does one verify that the output of a complicated program is correct? One can formally prove that the program is correct, but this may be beyond the power of existing methods. Alternatively, one can check that the output produced for a particular input satisfies the desired input--output relation by running a checker on the input--output pair. Then one only needs to prove the correctness of the checker. For some problems, however, even such a checker may be too complicated to formally verify. There is a third alternative: augment the original program to produce not only an output but also a correctness certificate, with the property that a very simple program (whose correctness is easy to prove) can use the certificate to verify that the input--output pair satisfies the desired input--output relation. We consider the following important instance of this general question: How does one verify that the dominator tree of a flow graph is correct? Existing fast algorithms for finding dominators are complicated, and even verifying the correctness of a dominator tree in the absence of additional information seems complicated. We define a correctness certificate for a dominator tree, show how to use it to easily verify the correctness of the tree, and show how to augment fast dominator-finding algorithms so that they produce a correctness certificate. We also relate the dominator certificate problem to the problem of finding divergent spanning trees in a flow graph, and we develop algorithms to find such trees. All our algorithms run in linear time. Previous algorithms apply just to the special case of only trivial dominators, and they take at least quadratic time.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Weimann:2016:ADP, author = "Oren Weimann and Raphael Yuster", title = "Approximating the Diameter of Planar Graphs in Near Linear Time", journal = j-TALG, volume = "12", number = "1", pages = "12:1--12:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2764910", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:16 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a $ (1 + \varepsilon)$-approximation algorithm running in $ O (f (\varepsilon) \cdot n \log^4 n)$ time for finding the diameter of an undirected planar graph with n vertices and with nonnegative edge lengths.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Polacek:2016:QPL, author = "Luk{\'a}{\v{s}} Pol{\'a}{\v{c}}ek and Ola Svensson", title = "Quasi-Polynomial Local Search for Restricted Max-Min Fair Allocation", journal = j-TALG, volume = "12", number = "2", pages = "13:1--13:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2818695", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, Asadpour et al. [2012] proved that a certain configuration LP can be used to estimate the optimal value within a factor of $ 1 / (4 + \epsilon) $, for any $ \epsilon > 0 $, but at the same time it is not known how to efficiently find a solution with a comparable performance guarantee. A natural question that arises from their work is if the difference between these guarantees is inherent or results from a lack of suitable techniques. We address this problem by giving a quasi-polynomial approximation algorithm with the mentioned performance guarantee. More specifically, we modify the local search of Asadpour et al. [2012] and provide a novel analysis that lets us significantly improve the bound on its running time: from $ 2^{O (n)} $ to $ n^{O (\log n)} $. Our techniques also have the interesting property that although we use the rather complex configuration LP in the analysis, we never actually solve it and therefore the resulting algorithm is purely combinatorial.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bender:2016:NAI, author = "Michael A. Bender and Jeremy T. Fineman and Seth Gilbert and Robert E. Tarjan", title = "A New Approach to Incremental Cycle Detection and Related Problems", journal = j-TALG, volume = "12", number = "2", pages = "14:1--14:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2756553", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of detecting a cycle in a directed graph that grows by arc insertions and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two algorithms, one suited to sparse graphs, the other to dense graphs. The former takes $ O (m i n \{ m^{1 / 2}, n^{2 / 3} \} m) $ time to insert $m$ arcs into an $n$-vertex graph; the latter takes $ O(n^2 \log n)$ time. Our sparse algorithm is substantially simpler than a previous $ O (m^{3 / 2})$-time algorithm; it is also faster on graphs of sufficient density. The time bound of our dense algorithm beats the previously best time bound of $ O (n^{5 / 2})$ for dense graphs. Our algorithms rely for their efficiency on vertex numberings weakly consistent with topological order: we allow ties. Bounds on the size of the numbers give bounds on running time.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Graham:2016:AFN, author = "Ronald Graham and Linus Hamilton and Ariel Levavi and Po-Shen Loh", title = "Anarchy Is Free in Network Creation", journal = j-TALG, volume = "12", number = "2", pages = "15:1--15:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2729978", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Internet has emerged as perhaps the most important network in modern computing, but rather miraculously, it was created through the individual actions of a multitude of agents rather than by a central planning authority. This motivates the game-theoretic study of network formation, and our article considers one of the most well-studied models, originally proposed by Fabrikant et al. In the model, each of $n$ agents corresponds to a vertex, which can create edges to other vertices at a cost of $ \alpha $ each, for some parameter $ \alpha $. Every edge can be freely used by every vertex, regardless of who paid the creation cost. To reflect the desire to be close to other vertices, each agent's cost function is further augmented by the sum total of all (graph-theoretic) distances to all other vertices. Previous research proved that for many regimes of the $ (\alpha, n)$ parameter space, the total social cost (sum of all agents' costs) of every Nash equilibrium is bounded by at most a constant multiple of the optimal social cost. In algorithmic game-theoretic nomenclature, this approximation ratio is called the price of anarchy. In our article, we significantly sharpen some of those results, proving that for all constant nonintegral $ \alpha > 2$, the price of anarchy is in fact $ 1 + o (1)$; that is, not only is it bounded by a constant, but also it tends to $1$ as $ n \rightarrow \infty $. For constant integral $ \alpha \leq 2$, we show that the price of anarchy is bounded away from $1$. We provide quantitative estimates on the rates of convergence for both results.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Blasius:2016:SPO, author = "Thomas Bl{\"a}sius and Ignaz Rutter", title = "Simultaneous {PQ}-Ordering with Applications to Constrained Embedding Problems", journal = j-TALG, volume = "12", number = "2", pages = "16:1--16:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2738054", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we define and study the new problem of Simultaneous PQ-Ordering. Its input consists of a set of PQ-trees, which represent sets of circular orders of their leaves, together with a set of child-parent relations between these PQ-trees, such that the leaves of the child form a subset of the leaves of the parent. Simultaneous PQ-Ordering asks whether orders of the leaves of each of the trees can be chosen simultaneously; that is, for every child-parent relation, the order chosen for the parent is an extension of the order chosen for the child. We show that Simultaneous PQ-Ordering is NP -complete in general, and we identify a family of instances that can be solved efficiently, the 2-fixed instances. We show that this result serves as a framework for several other problems that can be formulated as instances of Simultaneous PQ-Ordering. In particular, we give linear-time algorithms for recognizing simultaneous interval graphs and extending partial interval representations. Moreover, we obtain a linear-time algorithm for Partially PQ-Constrained Planarity for biconnected graphs, which asks for a planar embedding in the presence of PQ-trees that restrict the possible orderings of edges around vertices, and a quadratic-time algorithm for Simultaneous Embedding with Fixed Edges for biconnected graphs with a connected intersection. Both results can be extended to the case where the input graphs are not necessarily biconnected but have the property that each cutvertex is contained in at most two nontrivial blocks. This includes, for example, the case where both graphs have a maximum degree of 5.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Koutis:2016:FSS, author = "Ioannis Koutis and Alex Levin and Richard Peng", title = "Faster Spectral Sparsification and Numerical Algorithms for {SDD} Matrices", journal = j-TALG, volume = "12", number = "2", pages = "17:1--17:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2743021", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study algorithms for spectral graph sparsification. The input is a graph $G$ with $n$ vertices and $m$ edges, and the output is a sparse graph $ \tilde {G}$ that approximates $G$ in an algebraic sense. Concretely, for all vectors $x$ and any $ \epsilon > 0$, the graph $ \tilde {G}$ satisfies $ (1 - \epsilon) x^T L_G^x < x^T L \tilde {G}^x \leq (1 + \epsilon) x^T L_G^x$, where $ L_G$ and $ \tilde {G}$ are the Laplacians of $G$ and $ \tilde {G}$ respectively. The first contribution of this article applies to all existing sparsification algorithms that rely on solving solving linear systems on graph Laplacians. These algorithms are the fastest known to date. Specifically, we show that less precision is required in the solution of the linear systems, leading to speedups by an $ O (\log n)$ factor. We also present faster sparsification algorithms for slightly dense graphs: --- An $ O (m \log n)$ time algorithm that generates a sparsifier with $ O (n \log^3 n / \epsilon^2)$ edges. --- An $ O (m \log \log n)$ time algorithm for graphs with more than $ n \log^5 n \log \log n$ edges. --- An $ O (m)$ algorithm for graphs with more than $ n \log^{10} n$ edges. --- An $ O (m)$ algorithm for unweighted graphs with more than $ n \log^8 n$ edges. These bounds hold up to factors that are in $ O (\poly (\log \log n))$ and are conjectured to be removable.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aumuller:2016:OPD, author = "Martin Aum{\"u}ller and Martin Dietzfelbinger", title = "Optimal Partitioning for Dual-Pivot {Quicksort}", journal = j-TALG, volume = "12", number = "2", pages = "18:1--18:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2743020", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/java2010.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Dual-pivot quicksort refers to variants of classical quicksort where in the partitioning step two pivots are used to split the input into three segments. This can be done in different ways, giving rise to different algorithms. Recently, a dual-pivot algorithm due to Yaroslavskiy received much attention, because it replaced the well-engineered quicksort algorithm in Oracle's Java 7 runtime library. Nebel and Wild (ESA 2012) analyzed this algorithm and showed that on average it uses $ 1.9 n \ln n + O (n) $ comparisons to sort an input of size $n$, beating standard quicksort, which uses $ 2 n \ln n + O (n)$ comparisons. We introduce a model that captures all dual-pivot algorithms, give a unified analysis, and identify new dual-pivot algorithms that minimize the average number of key comparisons among all possible algorithms up to a linear term. This minimum is $ 1.8 n \ln n + O (n)$. For the case that the pivots are chosen from a small sample, we include a comparison of dual-pivot quicksort and classical quicksort. Specifically, we show that dual-pivot quicksort benefits from a skewed choice of pivots. We experimentally evaluate our algorithms and compare them to Yaroslavskiy's algorithm and the recently described $3$-pivot quicksort algorithm of Kushagra et al. (ALENEX 2014).", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ajtai:2016:SSI, author = "Mikl{\'o}s Ajtai and Vitaly Feldman and Avinatan Hassidim and Jelani Nelson", title = "Sorting and Selection with Imprecise Comparisons", journal = j-TALG, volume = "12", number = "2", pages = "19:1--19:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2701427", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a simple model of imprecise comparisons: there exists some $ \delta > 0 $ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $ \delta $, then the comparison will be made correctly; when the two elements have values that are within $ \delta $, the outcome of the comparison is unpredictable. This model is inspired by both imprecision in human judgment of values and also by bounded but potentially adversarial errors in the outcomes of sporting tournaments. Our model is closely related to a number of models commonly considered in the psychophysics literature where $ \delta $ corresponds to the Just Noticeable Difference (JND) unit or difference threshold. In experimental psychology, the method of paired comparisons was proposed as a means for ranking preferences among n elements of a human subject. The method requires performing all $ (n^2) $ comparisons, then sorting elements according to the number of wins. The large number of comparisons is performed to counter the potentially faulty decision-making of the human subject, who acts as an imprecise comparator. We show that in our model the method of paired comparisons has optimal accuracy, minimizing the errors introduced by the imprecise comparisons. However, it is also wasteful because it requires all $ (^n_2) $. We show that the same optimal guarantees can be achieved using $ 4 n^{3 / 2} $ comparisons, and we prove the optimality of our method. We then explore the general tradeoff between the guarantees on the error that can be made and number of comparisons for the problems of sorting, max-finding, and selection. Our results provide strong lower bounds and close-to-optimal solutions for each of these problems.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Efrat:2016:IAA, author = "Alon Efrat and S{\'a}ndor P. Fekete and Joseph S. B. Mitchell and Valentin Polishchuk and Jukka Suomela", title = "Improved Approximation Algorithms for Relay Placement", journal = j-TALG, volume = "12", number = "2", pages = "20:1--20:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2814938", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the relay placement problem, the input is a set of sensors and a number $ r \geq 1 $, the communication range of a relay. In the one-tier version of the problem, the objective is to place a minimum number of relays so that between every pair of sensors there is a path through sensors and/or relays such that the consecutive vertices of the path are within distance $r$ if both vertices are relays and within distance $1$ otherwise. The two-tier version adds the restrictions that the path must go through relays, and not through sensors. We present a $ 3.11$-approximation algorithm for the one-tier version and a polynomial-time approximation scheme (PTAS) for the two-tier version. We also show that the one-tier version admits no PTAS, assuming P $ \not = $ NP.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kim:2016:LKS, author = "Eun Jung Kim and Alexander Langer and Christophe Paul and Felix Reidl and Peter Rossmanith and Ignasi Sau and Somnath Sikdar", title = "Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions", journal = j-TALG, volume = "12", number = "2", pages = "21:1--21:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2797140", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a linear-time algorithm to compute a decomposition scheme for graphs $G$ that have a set $ X \subseteq V (G)$, called a treewidth-modulator, such that the treewidth of $ G - X$ is bounded by a constant. Our decomposition, called a protrusion decomposition, is the cornerstone in obtaining the following two main results. Our first result is that any parameterized graph problem (with parameter $k$) that has a finite integer index and such that $Y$ es-instances have a treewidth-modulator of size $ O (k)$ admits a linear kernel on the class of $H$-topological-minor-free graphs, for any fixed graph $H$. This result partially extends previous meta-theorems on the existence of linear kernels on graphs of bounded genus and $H$-minor-free graphs. Let $F$ be a fixed finite family of graphs containing at least one planar graph. Given an $n$-vertex graph $G$ and a non-negative integer $k$, Planar-$F$-Deletion asks whether $G$ has a set $ X \subseteq V (G)$ such that $ | X | \leq k$ and $ G - X$ is $H$-minor-free for every $ H \in F$. As our second application, we present the first single-exponential algorithm to solve Planar-$F$-Deletion. Namely, our algorithm runs in time $ 2^{O (k)} \cdot n^2$, which is asymptotically optimal with respect to $k$. So far, single-exponential algorithms were only known for special cases of the family $F$.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Abraham:2016:FSD, author = "Ittai Abraham and Shiri Chechik and Cyril Gavoille and David Peleg", title = "Forbidden-Set Distance Labels for Graphs of Bounded Doubling Dimension", journal = j-TALG, volume = "12", number = "2", pages = "22:1--22:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2818694", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article proposes a forbidden-set labeling scheme for the family of unweighted graphs with doubling dimension bounded by $ \alpha $. For an $n$ -vertex graph $G$ in this family, and for any desired precision parameter $ \epsilon > 0$, the labeling scheme stores an $ O (1 + \epsilon^{-1})^{2 \alpha } \log^2 n$-bit label at each vertex. Given the labels of two end-vertices $s$ and $t$, and the labels of a set $F$ of ``forbidden'' vertices and/or edges, our scheme can compute, in $ O (1 + \epsilon^{-1})^{2 \alpha } \cdot | F |^2 \log n$ time, a $ 1 + \epsilon $ stretch approximation for the distance between $s$ and $t$ in the graph $ G \setminus F$. The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch $ 1 + \epsilon $ for graphs of bounded doubling dimension.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kortsarz:2016:SAA, author = "Guy Kortsarz and Zeev Nutov", title = "A Simplified $ 1.5$-Approximation Algorithm for Augmenting Edge-Connectivity of a Graph from $1$ to $2$", journal = j-TALG, volume = "12", number = "2", pages = "23:1--23:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2786981", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Tree Augmentation Problem (TAP) is as follows: given a connected graph $ G = (V, \varepsilon) $ and an edge set $E$ on $V$, find a minimum size subset of edges $ F \subseteq E$ such that $ (V, \varepsilon \cup F)$ is $2$-edge-connected. In the conference version [Even et al. 2001] was sketched a $ 1.5$-approximation algorithm for the problem. Since a full proof was very complex and long, the journal version was cut into two parts. The first part [Even et al. 2009] only proved ratio $ 1.8$. An attempt to simplify the second part produced an error in Even et al. [2011]. Here we give a correct, different, and self-contained proof of the ratio $ 1.5$ that is also substantially simpler and shorter than the previous proofs.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gabow:2016:MPA, author = "Harold N. Gabow", title = "The Minset-Poset Approach to Representations of Graph Connectivity", journal = j-TALG, volume = "12", number = "2", pages = "24:1--24:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2764909", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Various instances of the minimal-set poset (minset-poset for short) have been proposed in the literature, e.g., the representation of Picard and Queyranne for all st-minimum cuts of a flow network. We begin with an explanation of why this poset structure is common. We show any family of sets $F$ that can be defined by a ``labelling algorithm'' (e.g., the Ford--Fulkerson labelling algorithm for maximum network flow) has an algorithm that constructs the minset poset for $F$. We implement this algorithm to efficiently find the nodes of the poset when $F$ is the family of minimum edge cuts of an unweighted graph; we also give related algorithms to construct the entire poset for weighted graphs. The rest of the article discusses applications to edge- and vertex connectivity, both combinatorial and algorithmic, that we now describe. For digraphs, a natural interpretation of the minset poset represents all minimum edge cuts. In the special case of undirected graphs, the minset poset is proved to be a variant of the well-known cactus representation of all mincuts. We use the poset algorithms to construct the cactus representation for unweighted graphs in time $ O (m + \lambda^2 n \log (n / \lambda))$ ($ \lambda $ is the edge connectivity) improving the previous bound $ O (\lambda n^2)$ for all but the densest graphs. We also construct the cactus representation for weighted graphs in time $ O (n m \log (n^2 / m))$, the same bound as a previously known algorithm but in linear space $ O (m)$. The latter bound also holds for constructing the minset poset for any weighted digraph; the former bound also holds for constructing the nodes of that poset for any unweighted digraph. The poset is used in algorithms to increase the edge connectivity of a graph by adding the fewest edges possible. For directed and undirected graphs, weighted and unweighted, we achieve the time of the preceding two bounds, i.e., essentially the best-known bounds to compute the edge connectivity itself. Some constructions of minset posets for graph rigidity are also sketched. For vertex connectivity, the minset poset is proved to be a slight variant of the dominator tree. This leads to an algorithm to construct the dominator tree in time $ O (m)$ on a RAM. (The algorithm is included in the appendix, since other linear-time algorithms of similar simplicity have recently been presented.)", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dinitz:2016:LCI, author = "Michael Dinitz and Guy Kortsarz and Ran Raz", title = "Label Cover Instances with Large Girth and the Hardness of Approximating Basic $k$-Spanner", journal = j-TALG, volume = "12", number = "2", pages = "25:1--25:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2818375", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the well-known Label Cover problem under the additional requirement that problem instances have large girth. We show that if the girth is some $k$, the problem is roughly $ 2^{\log^{1 - \epsilon } n} / k$ hard to approximate for all constant $ \epsilon > 0$. A similar theorem was claimed by Elkin and Peleg [2000] as part of an attempt to prove hardness for the basic $k$-spanner problem, but their proof was later found to have a fundamental error. Thus, we give both the first nontrivial lower bound for the problem of Label Cover with large girth as well as the first full proof of strong hardness for the basic $k$-spanner problem, which is both the simplest problem in graph spanners and one of the few for which super-logarithmic hardness was not known. Assuming NP $ \subseteq $ BPTIME ($ 2^{\polylog (n)}$), we show (roughly) that for every $ k \geq 3$ and every constant $ \epsilon > 0$, it is hard to approximate the basic $k$-spanner problem within a factor better than $ 2^{\log (1 - \epsilon)} n / k$. This improves over the previous best lower bound of only $ \Omega (\log n) / k$ from Kortsarz [2001]. Our main technique is subsampling the edges of $2$-query probabilistically checkable proofs (PCPs), which allows us to reduce the degree of a PCP to be essentially equal to the soundness desired. This turns out to be enough to basically guarantee large girth.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aronov:2016:STN, author = "Boris Aronov and Anne Driemel and Marc {Van Kreveld} and Maarten L{\"o}ffler and Frank Staals", title = "Segmentation of Trajectories on Nonmonotone Criteria", journal = j-TALG, volume = "12", number = "2", pages = "26:1--26:??", month = feb, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2660772", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Feb 12 18:02:17 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the trajectory segmentation problem, we are given a polygonal trajectory with $n$ vertices that we have to subdivide into a minimum number of disjoint segments (subtrajectories) that all satisfy a given criterion. The problem is known to be solvable efficiently for monotone criteria: criteria with the property that if they hold on a certain segment, they also hold on every subsegment of that segment. To the best of our knowledge, no theoretical results are known for nonmonotone criteria. We present a broader study of the segmentation problem, and suggest a general framework for solving it, based on the start-stop diagram: a 2-dimensional diagram that represents all valid and invalid segments of a given trajectory. This yields two subproblems: (1) computing the start-stop diagram, and (2) finding the optimal segmentation for a given diagram. We show that (2) is NP-hard in general. However, we identify properties of the start-stop diagram that make the problem tractable and give a polynomial-time algorithm for this case. We study two concrete nonmonotone criteria that arise in practical applications in more detail. Both are based on a given univariate attribute function $f$ over the domain of the trajectory. We say a segment satisfies an outlier-tolerant criterion if the value of f lies within a certain range for at least a given percentage of the length of the segment. We say a segment satisfies a standard deviation criterion if the standard deviation of f over the length of the segment lies below a given threshold. We show that both criteria satisfy the properties that make the segmentation problem tractable. In particular, we compute an optimal segmentation of a trajectory based on the outlier-tolerant criterion in $ O (n^2 \log n + k n^2)$ time and on the standard deviation criterion in $ O (k n^2)$ time, where $n$ is the number of vertices of the input trajectory and $k$ is the number of segments in an optimal solution.", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Konjevod:2016:SFC, author = "Goran Konjevod and Andr{\'e}a W. Richa and Donglin Xia", title = "Scale-Free Compact Routing Schemes in Networks of Low Doubling Dimension", journal = j-TALG, volume = "12", number = "3", pages = "27:1--27:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2876055", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider compact routing schemes in networks of low doubling dimension, where the doubling dimension is the least value $ \alpha $ such that any ball in the network can be covered by at most $ 2^\alpha $ balls of half radius. There are two variants of routing-scheme design: (i) labeled (name-dependent) routing, in which the designer is allowed to rename the nodes so that the names (labels) can contain additional routing information, for example, topological information; and (ii) name-independent routing, which works on top of the arbitrary original node names in the network, that is, the node names are independent of the routing scheme. In this article, given any constant $ \epsilon \in (0, 1) $ and an $n$-node edge-weighted network of doubling dimension $ \alpha \in O(\log \log n)$, we present --- a $ (1 + \epsilon)$-stretch labeled compact routing scheme with $ \lceil \log n \rceil $-bit routing labels, $ O(\log^2 n / \log \log n)$-bit packet headers, and $ ((1 / \epsilon)^{O(\alpha)} \log^3 n)$-bit routing information at each node; --- a $ (9 + \epsilon)$-stretch name-independent compact routing scheme with $ O(\log^2 n / \log \log n)$-bit packet headers, and $ ((1 / \epsilon)^{O(\alpha)} \log^3 n)$-bit routing information at each node. In addition, we prove a lower bound: any name-independent routing scheme with $ o(n^{(\epsilon / 60)^2})$ bits of storage at each node has stretch no less than $ 9 - \epsilon $ for any $ \epsilon \in (0, 8)$. Therefore, our name-independent routing scheme achieves asymptotically optimal stretch with polylogarithmic storage at each node and packet headers. Note that both schemes are scale-free in the sense that their space requirements do not depend on the normalized diameter $ \Delta $ of the network. We also present a simpler nonscale-free $ (9 + \epsilon)$-stretch name-independent compact routing scheme with improved space requirements if $ \Delta $ is polynomial in $n$.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kumar:2016:DAE, author = "V. S. Anil Kumar and Madhav V. Marathe and Srinivasan Parthasarathy and Aravind Srinivasan", title = "Distributed Algorithms for End-to-End Packet Scheduling in Wireless Ad Hoc Networks", journal = j-TALG, volume = "12", number = "3", pages = "28:1--28:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2812811", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Packet scheduling is a particular challenge in wireless networks due to interference from nearby transmissions. A distance-2 interference model serves as a useful abstraction here, and we study packet routing and scheduling under this model of interference. The main focus of our work is the development of fully distributed (decentralized) protocols. We present polylogarithmic\slash constant factor approximation algorithms for various families of disk graphs (which capture the geometric nature of wireless-signal propagation), as well as near-optimal approximation algorithms for general graphs. A basic distributed coloring procedure, originally due to Luby [1993] (Journal of Computer and System Sciences, 47:250--286, 1993), underlies many of our algorithms. The work of Finocchi et al. [2002] (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2002) showed that a natural modification of this algorithm leads to improved performance. A rigorous explanation of this was left as an open question, and we prove that the modified algorithm is indeed provably better in the worst case.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2016:FCL, author = "Michael Elkin and Shay Solomon", title = "Fast Constructions of Lightweight Spanners for General Graphs", journal = j-TALG, volume = "12", number = "3", pages = "29:1--29:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2836167", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "It is long known that for every weighted undirected $n$-vertex $m$-edge graph $ G = (V, E, \omega)$, and every integer $ k \geq 1$, there exists a $ ((2 k - 1) \cdot (1 + \epsilon))$-spanner with $ O(n^{1 + 1 / k})$ edges and weight $ O(k \cdot n^{1 / k} \cdot \omega (M S T (G)))$, for an arbitrarily small constant $ \epsilon > 0$. (Here $ \omega (\MST (G))$ stands for the weight of the minimum spanning tree of $G$.) To our knowledge, the only algorithms for constructing sparse and lightweight spanners for general graphs admit high running times. Most notable in this context is the greedy algorithm of Alth{\"o}fer et al. [1993], analyzed by Chandra et al. [1992], which requires $ O(m \cdot (n^{1 + 1 / k} + n \cdot \log n))$ time. In this article, we devise an efficient algorithm for constructing sparse and lightweight spanners. Specifically, our algorithm constructs $ ((2 k - 1) \cdot (1 + \epsilon))$-spanners with $ O(k \cdot n^{1 + 1 / k})$ edges and weight $ O(k \cdot n^{1 / k}) \cdot \omega (\MST (G))$, where $ \epsilon > 0$ is an arbitrarily small constant. The running time of our algorithm is $ O(k \cdot m + \min \{ n \cdot \log n, m \cdot \alpha (n) \})$. Moreover, by slightly increasing the running time we can reduce the other parameters. These results address an open problem by Roditty and Zwick [2004].", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borradaile:2016:TEC, author = "Glencora Borradaile and Philip Klein", title = "The Two-Edge Connectivity Survivable-Network Design Problem in Planar Graphs", journal = j-TALG, volume = "12", number = "3", pages = "30:1--30:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2831235", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider the following problem: given a graph with edge costs and a subset $Q$ of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in $Q$. The problem is a failure-resilient analog of the Steiner tree problem arising, for example, in telecommunications applications. We study a more general mixed-connectivity formulation, also employed in telecommunications optimization. Given a number (or requirement) $ r (v) \in \{ 0, 1, 2 \} $ for each vertex $v$ in the graph, find a minimum-cost subgraph in which there are $ \min \{ r (u), r (v) \} $ edge-disjoint $u$-to-$v$ paths for every pair $ u, v$ of vertices. We address the problem in planar graphs, considering a popular relaxation in which the solution is allowed to use multiple copies of the input-graph edges (paying separately for each copy). The problem is max SNP-hard in general graphs and strongly NP-hard in planar graphs. We give the first polynomial-time approximation scheme in planar graphs. The running time is $ O(n \log n)$. Under the additional restriction that the requirements are only non-zero for vertices on the boundary of a single face of a planar graph, we give a polynomial-time algorithm to find the optimal solution.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Koutis:2016:LAG, author = "Ioannis Koutis and Ryan Williams", title = "Limits and Applications of Group Algebras for Parameterized Problems", journal = j-TALG, volume = "12", number = "3", pages = "31:1--31:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2885499", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The fastest known randomized algorithms for several parameterized problems use reductions to the $k$-MlD problem: detection of multilinear monomials of degree $k$ in polynomials presented as circuits. The fastest known algorithm for $k$-MlD is based on 2$^k$ evaluations of the circuit over a suitable algebra. We use communication complexity to show that it is essentially optimal within this evaluation framework. On the positive side, we give additional applications of the method: finding a copy of a given tree on $k$ nodes, a minimum set of nodes that dominate at least $t$ nodes, and an $m$-dimensional $k$-matching. In each case, we achieve a faster algorithm than what was known before. We also apply the algebraic method to problems in exact counting. Among other results, we show that a variation of it can break the trivial upper bounds for the disjoint summation problem.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Konrad:2016:ASM, author = "Christian Konrad and Adi Ros{\'e}n", title = "Approximating Semi-matchings in Streaming and in Two-Party Communication", journal = j-TALG, volume = "12", number = "3", pages = "32:1--32:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2898960", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the streaming complexity and communication complexity of approximating unweighted semi-matchings. A semi-matching in a bipartite graph $ G = (A, B, E) $ with $ n = | A | $ is a subset of edges $ S \subseteq E $ that matches all $A$ vertices to $B$ vertices with the goal usually being to do this as fairly as possible. While the term semi-matching was coined in 2003 by Harvey et al. [2003], the problem had already previously been studied in the scheduling literature under different names. We present a deterministic one-pass streaming algorithm that for any $ 0 \leq \epsilon \leq 1$ uses space $ {\tilde O}(n^{1 + \epsilon })$ and computes an $ O(n^{(1 - \epsilon) / 2})$-approximation to the semi-matching problem. Furthermore, with $ O(\log n)$ passes it is possible to compute an $ O(\log n)$-approximation with space $ {\tilde O}(n)$. In the one-way two-party communication setting, we show that for every $ \epsilon > 0$, deterministic communication protocols for computing an $ O(n^{1 / ((1 + \epsilon) c + 1)})$-approximation require a message of size more than $ c n$ bits. We present two deterministic protocols communicating $n$ and $ 2 n$ edges that compute an $ O(\sqrt n)$ and an $ O(n^{1 / 3})$-approximation, respectively. Finally, we improve on the results of Harvey et al. [2003] and prove new links between semi-matchings and matchings. While it was known that an optimal semi-matching contains a maximum matching, we show that there is a hierarchical decomposition of an optimal semi-matching into maximum matchings. A similar result holds for semi-matchings that do not admit length-two degree-minimizing paths.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Blasius:2016:OOG, author = "Thomas Bl{\"a}sius and Ignaz Rutter and Dorothea Wagner", title = "Optimal Orthogonal Graph Drawing with Convex Bend Costs", journal = j-TALG, volume = "12", number = "3", pages = "33:1--33:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2838736", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Traditionally, the quality of orthogonal planar drawings is quantified by the total number of bends or the maximum number of bends per edge. However, this neglects that, in typical applications, edges have varying importance. We consider the problem OptimalFlexDraw that is defined as follows. Given a planar graph $G$ on $n$ vertices with maximum degree 4 (4-planar graph) and for each edge $e$ a cost function cost$_e$: $ N_0 \to R$ defining costs depending on the number of bends $e$ has, compute a planar orthogonal drawing of $G$ of minimum cost. In this generality OptimalFlexDraw is NP-hard. We show that it can be solved efficiently if (1) the cost function of each edge is convex and (2) the first bend on each edge does not cause any cost. Our algorithm takes time $ O(n, \cdot, T_{\rm flow} (n))$ and $ O(n^2, \cdot, T^{\rm flow} (n))$ for biconnected and connected graphs, respectively, where $ T_{\rm flow} (n)$ denotes the time to compute a minimum-cost flow in a planar network with multiple sources and sinks. Our result is the first polynomial-time bend-optimization algorithm for general 4-planar graphs optimizing over all embeddings. Previous work considers restricted graph classes and unit costs.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fleischer:2016:SEA, author = "Lisa Fleischer and Rahul Garg and Sanjiv Kapoor and Rohit Khandekar and Amin Saberi", title = "A Simple and Efficient Algorithm for Computing Market Equilibria", journal = j-TALG, volume = "12", number = "3", pages = "34:1--34:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2905372", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a new mathematical formulation of market equilibria in exchange economies using an indirect utility function: the function of prices and income that gives the maximum utility achievable. The formulation is a convex program and can be solved when the indirect utility function is convex in prices. We illustrate that many economies, including: -Homogeneous utilities of degree $ \alpha \in [0, 1] $ in Fisher economies-this includes Linear, Leontief, Cobb--Douglas --- Resource allocation utilities like multi-commodity flows satisfy this condition and can be efficiently solved. Further, we give a natural t{\^a}tonnement type price-adjusting algorithm in these economies. Our algorithm, which is applicable to a larger class of utility functions than previously known weak gross substitutes, mimics the natural dynamics for the markets as suggested by Walras: it iteratively adjusts a good's price upward when the demand for that good under current prices exceeds its supply; and downward when its supply exceeds its demand. The algorithm computes an approximate equilibrium in a number of iterations that is independent of the number of traders and is almost linear in the number of goods.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Golovnev:2016:FIS, author = "Alexander Golovnev and Alexander S. Kulikov and Ivan Mihajlin", title = "Families with Infants: Speeding Up Algorithms for {NP}-Hard Problems Using {FFT}", journal = j-TALG, volume = "12", number = "3", pages = "35:1--35:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2847419", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Assume that a group of n people is going to an excursion and our task is to seat them into buses with several constraints each saying that a pair of people does not want to see each other in the same bus. This is a well-known graph coloring problem (with n being the number of vertices) and it can be solved in $ O*(2^n) $ time by the inclusion-exclusion principle as shown by Bj{\"o}rklund, Husfeldt, and Koivisto in 2009. Another approach to solve this problem in $ O*(2^n) $ time is to use the Fast Fourier Transform (FFT). For this, given a graph $G$ one constructs a polynomial $ P_G(x)$ of degree $ O*(2^n)$ with the following property: $G$ is $k$-colorable if and only if the coefficient of $ x^m$ (for some particular value of $m$) in the $k$-th power of $ P(x)$ is nonzero. Then, it remains to compute this coefficient using FFT. Assume now that we have additional constraints: the group of people contains several infants and these infants should be accompanied by their relatives in a bus. We show that if the number of infants is linear, then the problem can be solved in $ O*((2 - \epsilon)^n)$ time, where $ \epsilon $ is a positive constant independent of $n$. We use this approach to improve known bounds for several NP-hard problems (the traveling salesman problem, the graph coloring problem, the problem of counting perfect matchings) on graphs of bounded average degree, as well as to simplify the proofs of several known results.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hajiaghayi:2016:CFA, author = "Mohammadtaghi Hajiaghayi and Wei Hu and Jian Li and Shi Li and Barna Saha", title = "A Constant Factor Approximation Algorithm for Fault-Tolerant $k$-Median", journal = j-TALG, volume = "12", number = "3", pages = "36:1--36:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2854153", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider the fault-tolerant $k$-median problem and give the first constant factor approximation algorithm for it. In the fault-tolerant generalization of the classical $k$-median problem, each client $j$ needs to be assigned to at least $ r_j \geq 1$ distinct open facilities. The service cost of $j$ is the sum of its distances to the $ r_j$ facilities, and the $k$-median constraint restricts the number of open facilities to at most $k$. Previously, a constant factor was known only for the special case when all $ r_j$ s are the same, and alogarithmic approximation ratio was known for the general case. In addition, we present the first polynomial time algorithm for the fault-tolerant $k$-median problem on a path or an HST by showing that the corresponding LP always has an integral optimal solution. We also consider the fault-tolerant facility location problem, in which the service cost of $j$ can be a weighted sum of its distance to the $ r_j$ facilities. We give a simple constant factor approximation algorithm, generalizing several previous results that work only for nonincreasing weight vectors.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Driemel:2016:ECV, author = "Anne Driemel and Sariel Har-Peled and Benjamin Raichel", title = "On the Expected Complexity of {Voronoi} Diagrams on Terrains", journal = j-TALG, volume = "12", number = "3", pages = "37:1--37:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2846099", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate the combinatorial complexity of geodesic Voronoi diagrams on polyhedral terrains using a probabilistic analysis. Aronov et al. [2008] prove that, if one makes certain realistic input assumptions on the terrain, this complexity is $ \Theta (n + m \sqrt n) $ in the worst case, where $n$ denotes the number of triangles that define the terrain and m denotes the number of Voronoi sites. We prove that, under a relaxed set of assumptions, the Voronoi diagram has expected complexity $ O(n + m)$, given that the sites are sampled uniformly at random from the domain of the terrain (or the surface of the terrain). Furthermore, we present a construction of a terrain that implies a lower bound of $ \Omega (n m^{2 / 3})$ on the expected worst-case complexity if these assumptions on the terrain are dropped. As an additional result, we show that the expected fatness of a cell in a random planar Voronoi diagram is bounded by a constant.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Adany:2016:ANG, author = "Ron Adany and Moran Feldman and Elad Haramaty and Rohit Khandekar and Baruch Schieber and Roy Schwartz and Hadas Shachnai and Tami Tamir", title = "All-Or-Nothing Generalized Assignment with Application to Scheduling Advertising Campaigns", journal = j-TALG, volume = "12", number = "3", pages = "38:1--38:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2843944", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study a variant of the generalized assignment problem (gap), which we label all-or-nothing gap (agap). We are given a set of items, partitioned into $n$ groups, and a set of $m$ bins. Each item $l$ has size $ s_l > 0$, and utility $ a_{l j} \geq 0$ if packed in bin $j$. Each bin can accommodate at most one item from each group; the total size of the items in a bin cannot exceed its capacity. A group of items is satisfied if all of its items are packed. The goal is to find a feasible packing of a subset of the items in the bins such that the total utility from satisfied groups is maximized. We motivate the study of agap by pointing out a central application in scheduling advertising campaigns. Our main result is an $ O(1)$-approximation algorithm for agap instances arising in practice, in which each group consists of at most $ m / 2$ items. Our algorithm uses a novel reduction of agap to maximizing submodular function subject to a matroid constraint. For agap instances with a fixed number of bins, we develop a randomized polynomial time approximation scheme (PTAS), relying on a nontrivial LP relaxation of the problem. We present a $ (3 + \epsilon)$-approximation as well as PTASs for other special cases of agap, where the utility of any item does not depend on the bin in which it is packed. Finally, we derive hardness results for the different variants of agap studied in this paper.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bille:2016:STI, author = "Philip Bille and Johannes Fischer and Inge Li G{\o}rtz and Tsvi Kopelowitz and Benjamin Sach and Hjalte Wedel Vildh{\o}j", title = "Sparse Text Indexing in Small Space", journal = j-TALG, volume = "12", number = "3", pages = "39:1--39:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2836166", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this work, we present efficient algorithms for constructing sparse suffix trees, sparse suffix arrays, and sparse position heaps for b arbitrary positions of a text $T$ of length n while using only $ O(b)$ words of space during the construction. Attempts at breaking the na{\"\i}ve bound of $ \Omega (n b)$ time for constructing sparse suffix trees in $ O(b)$ space can be traced back to the origins of string indexing in 1968. First results were not obtained until 1996, but only for the case in which the $b$ suffixes were evenly spaced in $T$. In this article, there is no constraint on the locations of the suffixes. Our main contribution is to show that the sparse suffix tree (and array) can be constructed in $ O(n \log^2 b)$ time. To achieve this, we develop a technique that allows one to efficiently answer $b$ longest common prefix queries on suffixes of $T$, using only $ O(b)$ space. We expect that this technique will prove useful in many other applications in which space usage is a concern. Our first solution is Monte Carlo, and outputs the correct tree with high probability. We then give a Las Vegas algorithm, which also uses $ O(b)$ space and runs in the same time bounds with high probability when $ b = O(\sqrt n)$. Additional trade-offs between space usage and construction time for the Monte Carlo algorithm are given. Finally, we show that, at the expense of slower pattern queries, it is possible to construct sparse position heaps in $ O(n + b \log b)$ time and $ O(b)$ space.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kratsch:2016:PLC, author = "Stefan Kratsch and Geevarghese Philip and Saurabh Ray", title = "Point Line Cover: The Easy Kernel is Essentially Tight", journal = j-TALG, volume = "12", number = "3", pages = "40:1--40:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2832912", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The input to the NP-hard point line cover problem (PLC) consists of a set $P$ of $n$ points on the plane and a positive integer $k$; the question is whether there exists a set of at most $k$ lines that pass through all points in $P$. By straightforward reduction rules, one can efficiently reduce any input to one with at most $ k^2$ points. We show that this easy reduction is already essentially tight under standard assumptions. More precisely, unless the polynomial hierarchy collapses to its third level, for any $ \epsilon > 0$, there is no polynomial-time algorithm that reduces every instance (P, k) of PLC to an equivalent instance with $ O(k^2 - \varepsilon)$ points. This answers, in the negative, an open problem posed by Lokshtanov [2009]. Our proof uses the notion of a kernel from parameterized complexity, and the machinery for deriving lower bounds on the size of kernels developed by Dell and van Melkebeek [2010, 2014]. It has two main ingredients: We first show, by reduction from vertex cover, that-unless the polynomial hierarchy collapses-PLC has no kernel of total size $ O(k^2 - \varepsilon)$ bits. This does not directly imply the claimed lower bound on the number of points, since the best-known polynomial-time encoding of a PLC instance with n points requires $ \omega (n^2)$ bits. To get around this hurdle, we build on work of Alon [1986] and devise an oracle communication protocol of cost $ O(n \log n)$ for PLC. This protocol, together with the lower bound on the total size (which also holds for such protocols), yields the stated lower bound on the number of points. While a number of essentially tight polynomial lower bounds on total sizes of kernels are known, our result is --- to the best of our knowledge --- the first to show a nontrivial lower bound for structural\slash secondary parameters. It is also the first example of a lower bound for kernelization that makes use of the full power of the oracle communication protocol lower bounds that can be obtained from the work of Dell and van Melkebeek. We combine the main abstract ideas of our proof to derive a general recipe that could be used to obtain such lower bounds for other problems with unknown or insufficiently strong encodings.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cygan:2016:PHC, author = "Marek Cygan and Holger Dell and Daniel Lokshtanov and D{\'a}niel Marx and Jesper Nederlof and Yoshio Okamoto and Ramamohan Paturi and Saket Saurabh and Magnus Wahlstr{\"o}m", title = "On Problems as Hard as {CNF-SAT}", journal = j-TALG, volume = "12", number = "3", pages = "41:1--41:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2925416", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The field of exact exponential time algorithms for non-deterministic polynomial-time hard problems has thrived since the mid-2000s. While exhaustive search remains asymptotically the fastest known algorithm for some basic problems, non-trivial exponential time algorithms have been found for a myriad of problems, including Graph Coloring, Hamiltonian Path, Dominating Set, and 3-CNF-Sat. In some instances, improving these algorithms further seems to be out of reach. The CNF-Sat problem is the canonical example of a problem for which the trivial exhaustive search algorithm runs in time $ O(2^n) $, where $n$ is the number of variables in the input formula. While there exist non-trivial algorithms for CNF-Sat that run in time $ o(2^n)$, no algorithm was able to improve the growth rate $2$ to a smaller constant, and hence it is natural to conjecture that $2$ is the optimal growth rate. The strong exponential time hypothesis (SETH) by Impagliazzo and Paturi [JCSS 2001] goes a little bit further and asserts that, for every $ \epsilon < 1$, there is a (large) integer $k$ such that $k$-CNF-Sat cannot be computed in time $ 2^{ \epsilon n}$. In this article, we show that, for every $ \epsilon < 1$, the problems Hitting Set, Set Splitting, and NAE-Sat cannot be computed in time $ O(2^{ \epsilon n})$ unless SETH fails. Here $n$ is the number of elements or variables in the input. For these problems, we actually get an equivalence to SETH in a certain sense. We conjecture that SETH implies a similar statement for Set Cover and prove that, under this assumption, the fastest known algorithms for Steiner Tree, Connected Vertex Cover, Set Partitioning, and the pseudo-polynomial time algorithm for Subset Sum cannot be significantly improved. Finally, we justify our assumption about the hardness of Set Cover by showing that the parity of the number of solutions to Set Cover cannot be computed in time $ O(2^{ \epsilon n})$ for any $ \epsilon < 1$ unless SETH fails.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Deshpande:2016:AAS, author = "Amol Deshpande and Lisa Hellerstein and Devorah Kletenik", title = "Approximation Algorithms for Stochastic Submodular Set Cover with Applications to {Boolean} Function Evaluation and Min-Knapsack", journal = j-TALG, volume = "12", number = "3", pages = "42:1--42:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2876506", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a new approximation algorithm for the stochastic submodular set cover (SSSC) problem called adaptive dual greedy. We use this algorithm to obtain a 3-approximation algorithm solving the stochastic Boolean function evaluation (SBFE) problem for linear threshold formulas (LTFs). We also obtain a 3-approximation algorithm for the closely related stochastic min-knapsack problem and a 2-approximation for a variant of that problem. We prove a new approximation bound for a previous algorithm for the SSSC problem, the adaptive greedy algorithm of Golovin and Krause. We also consider an approach to approximating SBFE problems using the adaptive greedy algorithm, which we call the $Q$-value approach. This approach easily yields a new result for evaluation of CDNF (conjunctive / disjunctive normal form) formulas, and we apply variants of it to simultaneous evaluation problems and a ranking problem. However, we show that the $Q$-value approach provably cannot be used to obtain a sublinear approximation factor for the SBFE problem for LTFs or read-once disjunctive normal form formulas.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dumitrescu:2016:TSP, author = "Adrian Dumitrescu and Csaba D. T{\'o}th", title = "The Traveling Salesman Problem for Lines, Balls, and Planes", journal = j-TALG, volume = "12", number = "3", pages = "43:1--43:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2850418", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We revisit the traveling salesman problem with neighborhoods (TSPN) and propose several new approximation algorithms. These constitute either first approximations (for hyperplanes, lines, and balls in $ R^d $, for $ d \geq 3$) or improvements over previous approximations achievable in comparable times (for unit disks in the plane). (I) Given a set of n hyperplanes in $ R^d$, a traveling salesman problem (TSP) tour whose length is at most $ O(1)$ times the optimal can be computed in $ O(n)$ time when $d$ is constant. (II) Given a set of $n$ lines in $ R^d$, a TSP tour whose length is at most $ O(\log^3 n)$ times the optimal can be computed in polynomial time for all $d$. (III) Given a set of $n$ unit balls in $ R^d$, a TSP tour whose length is at most $ O(1)$ times the optimal can be computed in polynomial time when d is constant.", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cheng:2016:FAC, author = "Siu-Wing Cheng and Liam Mencel and Antoine Vigneron", title = "A Faster Algorithm for Computing Straight Skeletons", journal = j-TALG, volume = "12", number = "3", pages = "44:1--44:??", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2898961", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jun 16 09:43:08 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with $n$ vertices, among which $r$ are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in $ O(n (\log n) \log r)$ time. It improves on the previously best known algorithm for this reduction, which is randomized, and runs in expected $ O(n \sqrt h + 1 \log^2 n)$ time for a polygon with $h$ holes. Using known motorcycle graph algorithms, our result yields improved time bounds for computing straight skeletons. In particular, we can compute the straight skeleton of a nondegenerate polygon in $ O(n (\log n) \log r + r^{4 / 3 + \epsilon })$ time for any $ \epsilon > 0$. On degenerate input, our time bound increases to $ O(n (\log n) \log r + r^{17 / 11 + \epsilon })$.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2016:AAO, author = "Timothy M. Chan and Bryan T. Wilkinson", title = "Adaptive and Approximate Orthogonal Range Counting", journal = j-TALG, volume = "12", number = "4", pages = "45:1--45:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2830567", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present three new results on one of the most basic problems in geometric data structures, 2-D orthogonal range counting. All the results are in the $w$-bit word RAM model. (1) It is well known that there are linear-space data structures for 2-D orthogonal range counting with worst-case optimal query time $ O (\log n / \log \log n)$. We give an $ O (n \log \log n)$-space adaptive data structure that improves the query time to $ O (\log \log n + \log k / \log \log n)$, where $k$ is the output count. When $ k = O (1)$, our bounds match the state of the art for the 2-D orthogonal range emptiness problem [Chan et al., 2011]. (2) We give an $ O (n \log \log n)$-space data structure for approximate 2-D orthogonal range counting that can compute a $ (1 + \delta)$-factor approximation to the count in $ O (\log \log n)$ time for any fixed constant $ \delta > 0$. Again, our bounds match the state of the art for the 2-D orthogonal range emptiness problem. (3) Last, we consider the 1-D range selection problem, where a query in an array involves finding the $k$ th least element in a given subarray. This problem is closely related to 2-D 3-sided orthogonal range counting. Recently, J{\o}rgensen and Larsen [2011] presented a linear-space adaptive data structure with query time $ O (\log \log n + \log k / \log \log n)$. We give a new linear-space structure that improves the query time to $ O (1 + \log k / \log \log n)$, exactly matching the lower bound proved by J{\o}rgensen and Larsen.", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Wimmer:2016:ALP, author = "Karl Wimmer", title = "Agnostic Learning in Permutation-Invariant Domains", journal = j-TALG, volume = "12", number = "4", pages = "46:1--46:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2963169", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We generalize algorithms from computational learning theory that are successful under the uniform distribution on the Boolean hypercube $ \{ 0, 1 \}^n $ to algorithms successful on permutation-invariant distributions, distributions that stay invariant constant on permuting the coordinates in the instances. While the tools in our generalization mimic those used for the Boolean hypercube, the fact that permutation-invariant distributions are not product distributions presents a significant obstacle. We prove analogous results for permutation-invariant distributions; more generally, we work in the domain of the symmetric group. We define noise sensitivity in this setting and show that noise sensitivity has a nice combinatorial interpretation in terms of Young tableaux. The main technical innovations involve techniques from the representation theory of the symmetric group, especially the combinatorics of Young tableaux. We show that low noise sensitivity implies concentration on ``simple'' components of the Fourier spectrum and that this fact will allow us to agnostically learn halfspaces under permutation-invariant distributions to constant accuracy in roughly the same time as in the uniform distribution over the Boolean hypercube case.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ward:2016:MSF, author = "Justin Ward and Stanislav Zivn{\'y}", title = "Maximizing $k$-Submodular Functions and Beyond", journal = j-TALG, volume = "12", number = "4", pages = "47:1--47:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2850419", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the maximization problem in the value oracle model of functions defined on $k$-tuples of sets that are submodular in every orthant and r -wise monotone, where $ k \geq 2$ and $ 1 \leq r \leq k$. We give an analysis of a deterministic greedy algorithm that shows that any such function can be approximated to a factor of $ 1 / (1 + r)$. For $ r = k$, we give an analysis of a randomized greedy algorithm that shows that any such function can be approximated to a factor of $ 1 / (1 + \sqrt {k} / 2)$. In the case of $ k = r = 2$, the considered functions correspond precisely to bisubmodular functions, in which case we obtain an approximation guarantee of $ 1 / 2$. We show that, as in the case of submodular functions, this result is the best possible both in the value query model and under the assumption that NP /= RP. Extending a result of Ando et al., we show that for any $ k \geq 3$, submodularity in every orthant and pairwise monotonicity (i.e., $ r = 2$) precisely characterize $k$-submodular functions. Consequently, we obtain an approximation guarantee of $ 1 / 3$ (and thus independent of $k$) for the maximization problem of $k$-submodular functions.", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Socala:2016:TLB, author = "Arkadiusz Socala", title = "Tight Lower Bound for the Channel Assignment Problem", journal = j-TALG, volume = "12", number = "4", pages = "48:1--48:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2876505", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the complexity of the Channel Assignment problem. An open problem asks whether Channel Assignment admits an $ O (c^n) $ (times a polynomial in the bit size) time algorithm, where $n$ is a number of the vertices, for a constant $c$ independent of the weights on the edges. We answer this question in the negative. Indeed, we show that in the standard Word RAM model, there is no $ 2^{o (n \log n)}$ (times a polynomial in the bit size) time algorithm solving Channel Assignment unless the exponential time hypothesis fails. Note that the currently best known algorithm works in time $ O^*(n !) = 2^{O (n \log n)}$, so our lower bound is tight (where the $ O^*()$ notation suppresses polynomial factors).", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Swamy:2016:IAA, author = "Chaitanya Swamy", title = "Improved Approximation Algorithms for Matroid and Knapsack Median Problems and Applications", journal = j-TALG, volume = "12", number = "4", pages = "49:1--49:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2963170", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the matroid median problem [Krishnaswamy et al. 2011], wherein we are given a set of facilities with opening costs and a matroid on the facility-set, and clients with demands and connection costs, and we seek to open an independent set of facilities and assign clients to open facilities so as to minimize the sum of the facility-opening and client-connection costs. We give a simple 8-approximation algorithm for this problem based on LP-rounding, which improves upon the 16-approximation in Krishnaswamy et al. [2011]. We illustrate the power and versatility of our techniques by deriving (a) an 8-approximation for the two-matroid median problem, a generalization of matroid median that we introduce involving two matroids; and (b) a 24-approximation algorithm for matroid median with penalties, which is a vast improvement over the 360-approximation obtained in Krishnaswamy et al. [2011]. We show that a variety of seemingly disparate facility-location problems considered in the literature-data placement problem, mobile facility location, $k$-median forest, metric uniform minimum-latency Uncapacitated Facility Location (UFL)-in fact reduce to the matroid median or two-matroid median problems, and thus obtain improved approximation guarantees for all these problems. Our techniques also yield an improvement for the knapsack median problem.", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2016:LSL, author = "Michael Elkin and Seth Pettie", title = "A Linear-Size Logarithmic Stretch Path-Reporting Distance Oracle for General Graphs", journal = j-TALG, volume = "12", number = "4", pages = "50:1--50:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2888397", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Thorup and Zwick [2001a] proposed a landmark distance oracle with the following properties. Given an $n$-vertex undirected graph $ G = (V, E)$ and a parameter $ k = 1, 2, \ldots {}$, their oracle has size $ O (k n^{1 + 1 / k})$, and upon a query $ (u, v)$ it constructs a path $ \Pi $ between $u$ and $v$ of length $ \delta (u, v)$ such that $ d_G(u, v) \leq \delta (u, v) \leq (2 k - 1) d_G (u, v)$. The query time of the oracle from Thorup and Zwick [2001a] is $ O (k)$ (in addition to the length of the returned path), and it was subsequently improved to $ O (1)$ [Wulff-Nilsen 2012; Chechik 2014]. A major drawback of the oracle of Thorup and Zwick [2001a] is that its space is $ \Omega (n \cdot \log n)$. Mendel and Naor [2006] devised an oracle with space $ O (n^{1 + 1 / k})$ and stretch $ O (k)$, but their oracle can only report distance estimates and not actual paths. In this article, we devise a path-reporting distance oracle with size $ O (n^{1 + 1 / k})$, stretch $ O (k)$, and query time $ O (n^{ \epsilon })$, for an arbitrarily small constant $ \epsilon > 0$. In particular, for $ k = \log n$, our oracle provides logarithmic stretch using linear size. Another variant of our oracle has size $ O (n \log \log n)$, polylogarithmic stretch, and query time $ O (\log \log n)$. For unweighted graphs, we devise a distance oracle with multiplicative stretch $ O (1)$, additive stretch $ O (\beta (k))$, for a function $ \beta (\cdot)$, space $ O (n^{1 + 1 / k})$, and query time $ O (n^{ \epsilon })$, for an arbitrarily small constant $ \epsilon > 0$. The tradeoff between multiplicative stretch and size in these oracles is far below Erd{\H{o}}s's girth conjecture threshold (which is stretch $ 2 k - 1$ and size $ O (n^{1 + 1 / k})$). Breaking the girth conjecture tradeoff is achieved by exhibiting a tradeoff of different nature between additive stretch $ \beta (k)$ and size $ O (n^{1 + 1 / k})$. A similar type of tradeoff was exhibited by a construction of $ (1 + \epsilon, \beta)$-spanners due to Elkin and Peleg [2001]. However, so far $ (1 + \epsilon, \beta)$-spanners had no counterpart in the distance oracles' world. An important novel tool that we develop on the way to these results is a distance-preserving path-reporting oracle. We believe that this oracle is of independent interest.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Emek:2016:SCI, author = "Yuval Emek and Magn{\'u}s M. Halld{\'o}rsson and Adi Ros{\'e}n", title = "Space-Constrained Interval Selection", journal = j-TALG, volume = "12", number = "4", pages = "51:1--51:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2886102", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study streaming algorithms for the interval selection problem: finding a maximum cardinality subset of disjoint intervals on the line. A deterministic 2-approximation streaming algorithm for this problem is developed, together with an algorithm for the special case of proper intervals, achieving improved approximation ratio of $ 3 / 2 $. We complement these upper bounds by proving that they are essentially the best possible in the streaming setting: It is shown that an approximation ratio of $ 2 - \epsilon $ (or $ 3 / 2 - \epsilon $ for proper intervals) cannot be achieved unless the space is linear in the input size. In passing, we also answer an open question of Adler and Azar (J. Scheduling 2003) regarding the space complexity of constant-competitive randomized preemptive online algorithms for the same problem.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ferragina:2016:CCO, author = "Paolo Ferragina and Rossano Venturini", title = "Compressed Cache-Oblivious String {B}-Tree", journal = j-TALG, volume = "12", number = "4", pages = "52:1--52:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2903141", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we study three variants of the well-known prefix-search problem for strings, and we design solutions for the cache-oblivious model which improve the best known results. Among these contributions, we close (asymptotically) the classic problem, which asks for the detection of the set of strings that share the longest common prefix with a queried pattern by providing an I/O-optimal solution that matches the space lower bound for tries up to a constant multiplicative factor of the form $ (1 + \epsilon) $, for $ \epsilon > 0 $. Our solutions hinge upon a novel compressed storage scheme that adds the ability to decompress prefixes of the stored strings I/O-optimally to the elegant locality-preserving front coding (Bender et al. 2006) still preserving its space bounds.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{He:2016:DSP, author = "Meng He and J. Ian Munro and Gelin Zhou", title = "Data Structures for Path Queries", journal = j-TALG, volume = "12", number = "4", pages = "53:1--53:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2905368", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider a tree $T$ on $n$ nodes, each having a weight drawn from $ [1 \ldots {} \sigma]$. In this article, we study the problem of supporting various path queries over the tree $T$. The path counting query asks for the number of the nodes on a query path whose weights are in a query range, while the path reporting query requires to report these nodes. The path median query asks for the median weight on a path between two given nodes, and the path selection query returns the $k$-th smallest weight. We design succinct data structures to encode $T$ using $ n n H (W_T) + 2 n + o (n \lg \sigma)$ bits of space, such that we can support path counting queries in $ O (\lg \sigma / \lg \lg n + 1)$ time, path reporting queries in $ O ((\occ + 1)(\lg \sigma / \lg \lg n + 1))$ time, and path median and path selection queries in $ O (\lg \sigma / \lg \lg \sigma)$ time, where $ H (W_T)$ is the entropy of the multiset of the weights of the nodes in $T$ and $ \occ $ is the size of the output. Our results not only greatly improve the best known data structures [Chazelle 1987; Krizanc et al. 2005], but also match the lower bounds for path counting, median, and selection queries [P{\u{a}}trascu 2007, 2011; J{\o}rgensen and Larsen 2011] when $ \sigma = \Omega (n / \polylog (n))$.", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hajiaghayi:2016:AAM, author = "Mohammad Taghi Hajiaghayi and Rohit Khandekar and Mohammad Reza Khani and Guy Kortsarz", title = "Approximation Algorithms for Movement Repairmen", journal = j-TALG, volume = "12", number = "4", pages = "54:1--54:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2908737", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the Movement Repairmen (MR) problem, we are given a metric space $ (V, d) $ along with a set $R$ of $k$ repairmen $ r_1, r_2, \ldots {}, r_k$ with their start depots $ s_1, s_2, \ldots {}, s_k \in V$ and speeds $ v_1, v_2, \ldots {}, v_k \geq 0$, respectively, and a set $C$ of $m$ clients $ c_1, c_2, \ldots {}, c_m$ having start locations $ s'_1, s_2, \ldots {}, s'_m \in V$ and speeds $ v'_1, v_2, \ldots {}, v'_m \geq 0$, respectively. If $t$ is the earliest time a client $ c_j$ is collocated with any repairman (say, $ r_i$ ) at a node $u$, we say that the client is served by $ r_i$ at $u$ and that its latency is $t$. The objective in the (Sum-MR) problem is to plan the movements for all repairmen and clients to minimize the sum (average) of the clients' latencies. The motivation for this problem comes, for example, from Amazon Locker Delivery [Amazon 2010] and USPS gopost [Service 2010]. We give the first $ O (\log n)$-approximation algorithm for the Sum-MR problem. In order to approximate Sum-MR, we formulate an LP for the problem and bound its integrality gap. Our LP has exponentially many variables; therefore, we need a separation oracle for the dual LP. This separation oracle is an instance of the Neighborhood Prize Collecting Steiner Tree (NPCST) problem in which we want to find a tree with weight at most L collecting the maximum profit from the clients by visiting at least one node from their neighborhoods. The NPCST problem, even with the possibility to violate both the tree weight and neighborhood radii, is still very hard to approximate. We deal with this difficulty by using LP with geometrically increasing segments of the timeline, and by giving a tricriteria approximation for the problem. The rounding needs a relatively involved analysis. We give a constant approximation algorithm for Sum-MR in Euclidean Space where the speed of the clients differs by a constant factor. We also give a constant approximation for the makespan variant.", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2016:HRD, author = "T.-H. Hubert Chan and Anupam Gupta and Bruce M. Maggs and Shuheng Zhou", title = "On Hierarchical Routing in Doubling Metrics", journal = j-TALG, volume = "12", number = "4", pages = "55:1--55:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2915183", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the problem of routing in doubling metrics and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with a small amount of routing information stored at each vertex). We say that a metric $ (X, d) $ has doubling dimension $ \dim (X) $ at most $ \alpha $ if every ball can be covered by $ 2^\alpha $ balls of half its radius. (A doubling metric is one whose doubling dimension $ \dim (X) $ is a constant.) We consider the metric space induced by the shortest-path distance in an underlying undirected graph $G$. We show how to perform $ (1 + \tau)$-stretch routing on such a metric for any $ 0 < \tau \leq 1$ with routing tables of size at most $ (\alpha / \tau)^{O (\alpha)} \log \Delta \log \delta $ bits with only $ (\alpha / \tau)^{O (\alpha)} \log \Delta $ entries, where $ \Delta $ is the diameter of the graph, and $ \delta $ is the maximum degree of the graph $G$; hence, the number of routing table entries is just $ \tau^{-O(1)} \log \Delta $ for doubling metrics. These results extend and improve on those of Talwar (2004). We also give better constructions of sparse spanners for doubling metrics than those obtained from the routing tables earlier; for $ \tau > 0$, we give algorithms to construct $ (1 + \tau)$-stretch spanners for a metric $ (X, d)$ with maximum degree at most $ (2 + 1 / \tau)^{O(\dim (X))}$, matching the results of Das et al. for Euclidean metrics.", acknowledgement = ack-nhfb, articleno = "55", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Georgiadis:2016:ADT, author = "Loukas Georgiadis and Robert E. Tarjan", title = "Addendum to {``Dominator Tree Certification and Divergent Spanning Trees''}", journal = j-TALG, volume = "12", number = "4", pages = "56:1--56:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2928271", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "56", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Sen:2016:DRB, author = "Siddhartha Sen and Robert E. Tarjan and David Hong Kyun Kim", title = "Deletion Without Rebalancing in Binary Search Trees", journal = j-TALG, volume = "12", number = "4", pages = "57:1--57:??", month = sep, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2903142", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Sep 2 19:05:47 MDT 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We address the vexing issue of deletions in balanced trees. Rebalancing after a deletion is generally more complicated than rebalancing after an insertion. Textbooks neglect deletion rebalancing, and many B-tree--based database systems do not do it. We describe a relaxation of AVL trees in which rebalancing is done after insertions but not after deletions, yet worst-case access time remains logarithmic in the number of insertions. For any application of balanced trees in which the number of updates is polynomial in the tree size, our structure offers performance competitive with that of classical balanced trees. With the addition of periodic rebuilding, the performance of our structure is theoretically superior to that of many, if not all, classic balanced tree structures. Our structure needs $ \lg \lg m + 1 $ bits of balance information per node, where m is the number of insertions and $ \lg $ is the base-two logarithm, or $ \lg \lg n + O(1) $ with periodic rebuilding, where n is the number of nodes. An insertion takes up to two rotations and O(1) amortized time, not counting the time to find the insertion position. This is the same as in standard AVL trees. Using an analysis that relies on an exponential potential function, we show that rebalancing steps occur with a frequency that is exponentially small in the height of the affected node. Our techniques apply to other types of balanced trees, notably B-trees, as we show in a companion article, and particularly red-black trees, which can be viewed as a special case of B-trees.", acknowledgement = ack-nhfb, articleno = "57", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Krishnaswamy:2016:IMU, author = "Ravishankar Krishnaswamy and Maxim Sviridenko", title = "Inapproximability of the Multilevel Uncapacitated Facility Location Problem", journal = j-TALG, volume = "13", number = "1", pages = "1:1--1:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2907050", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we present improved inapproximability results for the $k$-level uncapacitated facility location problem. In particular, we show that there is no polynomial time approximation algorithm with performance guarantee better than 1.539 unless P = NP for the case when $ k = 2$. For the case of general $k$ (tending to infinity), we obtain a better hardness factor of 1.61. Interestingly, our results show that the two-level problem is computationally harder than the well-known uncapacitated facility location problem ($ k = 1$) since the best-known approximation guarantee for the latter problem is 1.488 due to Li [2013], and our inapproximability is a factor of 1.539 for the two-level problem. The only inapproximability result known before for this class of metric facility location problems is the bound of 1.463 due to Guha and Khuller [1999], which holds even for the case of $ k = 1$.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Austrin:2016:BBB, author = "Per Austrin and Siavosh Benabbas and Konstantinos Georgiou", title = "Better Balance by Being Biased: a 0.8776-Approximation for Max Bisection", journal = j-TALG, volume = "13", number = "1", pages = "2:1--2:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2907052", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Recently, Raghavendra and Tan (SODA 2012) gave a 0.85-approximation algorithm for the M ax Bisection problem. We improve their algorithm to a 0.8776-approximation. As Max Bisection is hard to approximate within $ \alpha_{GW} + \epsilon \approx 0.8786 $ under the Unique Games Conjecture (UGC), our algorithm is nearly optimal. We conjecture that Max Bisection is approximable within $ \alpha_{GW} - \epsilon $, that is, that the bisection constraint (essentially) does not make Max Cut harder. We also obtain an optimal algorithm (assuming the UGC) for the analogous variant of Max 2-Sat. Our approximation ratio for this problem exactly matches the optimal approximation ratio for Max 2-Sat, that is, $ \alpha_{LLZ} + \epsilon \approx 0.9401 $, showing that the bisection constraint does not make Max 2-Sat harder. This improves on a 0.93-approximation for this problem from Raghavendra and Tan.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2016:NNS, author = "Pankaj K. Agarwal and Boris Aronov and Sariel Har-Peled and Jeff M. Phillips and Ke Yi and Wuzhou Zhang", title = "Nearest-Neighbor Searching Under Uncertainty {II}", journal = j-TALG, volume = "13", number = "1", pages = "3:1--3:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2955098", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has a wide range of applications. In many of them, such as sensor databases, location-based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest-neighbor queries in a probabilistic framework in which the location of each input point is specified as a probability distribution function. We present efficient algorithms for (i) computing all points that are nearest neighbors of a query point with nonzero probability and (ii) estimating the probability of a point being the nearest neighbor of a query point, either exactly or within a specified additive error.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Shallue:2016:TPT, author = "Andrew Shallue", title = "Tabulating Pseudoprimes and Tabulating Liars", journal = j-TALG, volume = "13", number = "1", pages = "4:1--4:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2957759", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article explores the asymptotic complexity of two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a single fixed base a. It is now proven that tabulating up to x requires O ( x ) arithmetic operations and O ( x log x ) bits of space. The second problem is to find all strong liars and witnesses, given a fixed odd composite n. This appears to be unstudied, and a randomized algorithm is presented that requires an expected O ((log n )$^2$ + | S ( n )|) operations (here S ( n ) is the set of strong liars). Although interesting in their own right, a notable application is the search for sets of composites with no reliable witnesses.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kawarabayashi:2016:IAA, author = "Ken-Ichi Kawarabayashi and Yusuke Kobayashi", title = "An Improved Approximation Algorithm for the Edge-Disjoint Paths Problem with Congestion Two", journal = j-TALG, volume = "13", number = "1", pages = "5:1--5:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2960410", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the maximum edge-disjoint paths problem, we are given a graph and a collection of pairs of vertices, and the objective is to find the maximum number of pairs that can be routed by edge-disjoint paths. An $r$ approximation algorithm for this problem is a polynomial-time algorithm that finds at least OPT/$r$ edge-disjoint paths, where OPT denotes the maximum possible number of pairs that can be routed in a given instance. For a long time, an $ O(n^{1 / 2})$ approximation algorithm has been best known for this problem even if a congestion of two is allowed, that is, each edge is allowed to be used in at most two of the paths. In this article, we give a randomized $ O(n \frac 37 c \poly (\log n))$-approximation algorithm with congestion two. This is the first result that breaks the $ O(n^{1 / 2})$-approximation algorithm. In particular, we prove the following: (1) If we have a (randomized) polynomial-time algorithm for finding $ \Omega (O P T \frac 1 p / \polylog (n))$ edge-disjoint paths for some $ p > 1$, then we can give a randomized $ O(n^{1 / 2} \alpha)$-approximation algorithm for the edge-disjoint paths problem by using Rao-Zhou's algorithm for some $ \alpha > 0$. (2) Based on the Chekuri-Khanna-Shepherd well-linked decomposition, we show that there is a randomized algorithm for finding $ \Omega (O P T^{1 / 4} / (\log n)^{\frac 32})$ edge-disjoint paths connecting given terminal pairs with congestion two. Our framework for this algorithm is more general in the following sense. Indeed, the above two ingredients also work for the maximum edge-disjoint paths problem (with congestion one) if there is a (randomized) polynomial-time algorithm for finding $ \Omega (O P T \frac 1 p)$ edge-disjoint paths connecting given terminal pairs for some $ p > 1$.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Emek:2016:SSS, author = "Yuval Emek and Adi Ros{\'e}n", title = "Semi-Streaming Set Cover", journal = j-TALG, volume = "13", number = "1", pages = "6:1--6:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2957322", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article studies the set cover problem under the semi-streaming model. The underlying set system is formalized in terms of a hypergraph $ G = (V, E) $ whose edges arrive one by one, and the goal is to construct an edge cover $ F \subseteq E $ with the objective of minimizing the cardinality (or cost in the weighted case) of $F$. We further consider a parameterized relaxation of this problem, where, given some $ 0 \leq \epsilon < 1$, the goal is to construct an edge $ (1 - \epsilon)$-cover, namely, a subset of edges incident to all but an $ \epsilon $-fraction of the vertices (or their benefit in the weighted case). The key limitation imposed on the algorithm is that its space is limited to (poly)logarithmically many bits per vertex. Our main result is an asymptotically tight tradeoff between \epsilon and the approximation ratio: We design a semi-streaming algorithm that on input hypergraph $G$ constructs a succinct data structure $D$ such that for every $ 0 \leq \epsilon < 1$, an edge $ (1 \epsilon)$-cover that approximates the optimal edge $ (1 -)$ cover within a factor of $ f(\epsilon, n)$ can be extracted from $D$ (efficiently and with no additional space requirements), where $ f(\epsilon, n) = O (1 / \epsilon)$, if $ \epsilon > 1 / \sqrt {n}_{O (\sqrt {n})}$, otherwise. In particular, for the traditional set cover problem, we obtain an $ O(\sqrt {n})$-approximation. This algorithm is proved to be best possible by establishing a family (parameterized by $ \epsilon $) of matching lower bounds.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cohen:2016:TBS, author = "Edith Cohen and Graham Cormode and Nick Duffield and Carsten Lund", title = "On the Tradeoff between Stability and Fit", journal = j-TALG, volume = "13", number = "1", pages = "7:1--7:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2963103", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments and must decide how to respond to a new set of constraints, given that each change from the current assignment comes at a price. That is, we would like to maximize the fitness or efficiency of our system, but we need to balance it with the changeout cost from the previous state. We provide a precise formulation for this tradeoff and analyze the resulting stable extensions of some fundamental problems in measurement and analytics. Our main technical contribution is a stable extension of Probability Proportional to Size (PPS) weighted random sampling, with applications to monitoring and anomaly detection problems. We also provide a general framework that applies to top-$k$, minimum spanning tree, and assignment. In both cases, we are able to provide exact solutions and discuss efficient incremental algorithms that can find new solutions as the input changes.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aumuller:2016:HGM, author = "Martin Aum{\"u}ller and Martin Dietzfelbinger and Pascal Klaue", title = "How Good Is Multi-Pivot {Quicksort}?", journal = j-TALG, volume = "13", number = "1", pages = "8:1--8:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2963102", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Multi-Pivot Quicksort refers to variants of classical quicksort where in the partitioning step $k$ pivots are used to split the input into $ k + 1$ segments. For many years, multi-pivot quicksort was regarded as impractical, but in 2009 a two-pivot approach by Yaroslavskiy, Bentley, and Bloch was chosen as the standard sorting algorithm in Sun's Java 7. In 2014 at ALENEX, Kushagra et al. introduced an even faster algorithm that uses three pivots. This article studies what possible advantages multi-pivot quicksort might offer in general. The contributions are as follows: Natural comparison-optimal algorithms for multi-pivot quicksort are devised and analyzed. The analysis shows that the benefits of using multiple pivots with respect to the average comparison count are marginal and these strategies are inferior to simpler strategies such as the well-known median-of-$k$ approach. A substantial part of the partitioning cost is caused by rearranging elements. A rigorous analysis of an algorithm for rearranging elements in the partitioning step is carried out, observing mainly how often array cells are accessed during partitioning. The algorithm behaves best if three to five pivots are used. Experiments show that this translates into good cache behavior and is closest to predicting observed running times of multi-pivot quicksort algorithms. Finally, it is studied how choosing pivots from a sample affects sorting cost. The study is theoretical in the sense that although the findings motivate design recommendations for multipivot quicksort algorithms that lead to running-time improvements over known algorithms in an experimental setting, these improvements are small.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Georgiadis:2016:ECD, author = "Loukas Georgiadis and Giuseppe F. Italiano and Luigi Laura and Nikos Parotsidis", title = "$2$-Edge Connectivity in Directed Graphs", journal = j-TALG, volume = "13", number = "1", pages = "9:1--9:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2968448", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected graphs, surprisingly, not much has been investigated for directed graphs. In this article, we study 2-edge connectivity problems in directed graphs and, in particular, we consider the computation of the following natural relation: We say that two vertices $v$ and $w$ are $2$-edge-connected if there are two edge-disjoint paths from $v$ to $w$ and two edge-disjoint paths from $w$ to $v$. This relation partitions the vertices into blocks such that all vertices in the same block are 2-edge-connected. Differently from the undirected case, those blocks do not correspond to the 2-edge-connected components of the graph. The main result of this article is an algorithm for computing the 2-edge-connected blocks of a directed graph in linear time. Besides being asymptotically optimal, our algorithm improves significantly over previous bounds. Once the 2-edge-connected blocks are available, we can test in constant time if two vertices are 2-edge-connected. Additionally, when two query vertices $v$ and $w$ are not 2-edge-connected, we can produce in constant time a ``witness'' of this property by exhibiting an edge that is contained in all paths from $v$ to $w$ or in all paths from $w$ to $v$. We are also able to compute in linear time a sparse certificate for this relation, i.e., a subgraph of the input graph that has $ O(n)$ edges and maintains the same 2-edge-connected blocks as the input graph, where $n$ is the number of vertices.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Englert:2016:SAO, author = "Matthias Englert and Heiko R{\"o}glin and Berthold V{\"o}cking", title = "Smoothed Analysis of the $2$-Opt Algorithm for the General {TSP}", journal = j-TALG, volume = "13", number = "1", pages = "10:1--10:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2972953", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "2-Opt is a simple local search heuristic for the traveling salesperson problem that performs very well in experiments with respect to both running time and solution quality. In contrast to this, there are instances on which 2-Opt may need an exponential number of steps to reach a local optimum. To understand why 2-Opt usually finds local optima quickly in experiments, we study its expected running time in the model of smoothed analysis, which can be considered as a less-pessimistic variant of worst-case analysis in which the adversarial input is subject to a small amount of random noise. In our probabilistic input model, an adversary chooses an arbitrary graph $G$ and a probability density function for each edge according to which its length is chosen. We prove that in this model the expected number of local improvements is $ O (m n \phi c 16^{\sqrt {ln m}}) = m^{1 + o(1)} n \phi $, where $n$ and $m$ denote the number of vertices and edges of $G$, respectively, and $ \phi $ denotes an upper bound on the density functions.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Parter:2016:SFT, author = "Merav Parter and David Peleg", title = "Sparse Fault-Tolerant {BFS} Structures", journal = j-TALG, volume = "13", number = "1", pages = "11:1--11:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2976741", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A fault-tolerant structure for a network is required for continued functioning following the failure of some of the network's edges or vertices. This article considers breadth-first search (BFS) spanning trees and addresses the problem of designing a sparse fault-tolerant BFS structure (FT-BFS structure), namely, a sparse subgraph $T$ of the given network $G$ such that subsequent to the failure of a single edge or vertex, the surviving part $ T'$ of $T$ still contains a BFS spanning tree for (the surviving part of) $G$. For a source node $s$, a target node $t$, and an edge $ e \in G$, the shortest $s$--$t$ path $ P_{s, t, e}$ that does not go through $e$ is known as a replacement path. Thus, our FT-BFS structure contains the collection of all replacement paths $ P_{s, t, e}$ for every $ t \in V (G)$ and every failed edge $ e \in E (G)$. Our main results are as follows. We present an algorithm that for every $n$-vertex graph $G$ and source node $s$ constructs a (single edge failure) FT-BFS structure rooted at $s$ with $ O (n c \min \{ D e p t h(s), \sqrt {n} \})$ edges, where $ \Depth (s)$ is the depth of the BFS tree rooted at $s$. This result is complemented by a matching lower bound, showing that there exist $n$-vertex graphs with a source node $s$ for which any edge (or vertex) FT-BFS structure rooted at $s$ has $ \Omega (n^{3 / 2})$ edges. We then consider fault-tolerant multi-source BFS structures (FT-MBFS structures), aiming to provide (following a failure) a BFS tree rooted at each source $ s \in S$ for some subset of sources $ S \subseteq V$. Again, tight bounds are provided, showing that there exists a poly-time algorithm that for every $n$-vertex graph and source set $ S \subseteq V$ of size $ \sigma $ constructs a (single failure) FT-MBFS structure $ T *(S)$ from each source $ s_i \in S$, with $ O (\sqrt {\sigma } c n^{ 3 / 2})$ edges, and, on the other hand, there exist $n$-vertex graphs with source sets $ S \subseteq V$ of cardinality $ \sigma $, on which any FT-MBFS structure from $S$ has $ \Omega (\sqrt {\sigma } c n^{3 / 2})$ edges. Finally, we propose an $ O(\log n)$ approximation algorithm for constructing FT-BFS and FT-MBFS structures. The latter is complemented by a hardness result stating that there exists no $ \Omega (\log n)$ approximation algorithm for these problems under standard complexity assumptions. In comparison with previous constructions, our algorithm is deterministic and may improve the number of edges by a factor of up to $ \sqrt {n}$ for some instances. All our algorithms can be extended to deal with one vertex failure as well, with the same performance.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Segal-Halevi:2016:WMH, author = "Erel Segal-Halevi and Avinatan Hassidim and Yonatan Aumann", title = "Waste Makes Haste: Bounded Time Algorithms for Envy-Free Cake Cutting with Free Disposal", journal = j-TALG, volume = "13", number = "1", pages = "12:1--12:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2988232", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the classic problem of envy-free division of a heterogeneous good (``cake'') among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for three or more agents. The impossibility result, however, assumes that the entire cake must be allocated. In this article, we replace the entire-allocation requirement with a weaker partial-proportionality requirement: the piece given to each agent must be worth for it at least a certain positive fraction of the entire cake value. We prove that this version of the problem is solvable in bounded time even when the pieces must be connected. We present simple, bounded-time envy-free cake-cutting algorithms for (1) giving each of $n$ agents a connected piece with a positive value; (2) giving each of three agents a connected piece worth at least $ 1 / 3$; (3) giving each of four agents a connected piece worth at least $ 1 / 7$; (4) giving each of four agents a disconnected piece worth at least $ 1 / 4$; and (5) giving each of $n$ agents a disconnected piece worth at least $ (1 - \epsilon) / n$ for any positive $ \epsilon $.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Im:2016:MLS, author = "Sungjin Im and Viswanath Nagarajan and Ruben {Van Der Zwaan}", title = "Minimum Latency Submodular Cover", journal = j-TALG, volume = "13", number = "1", pages = "13:1--13:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2987751", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the Minimum Latency Submodular Cover (MLSC) problem, which consists of a metric $ (V, d) $ with source $ r \in V $ and $m$ monotone submodular functions $ f_1, f_2, \ldots {}, f_m \colon 2^V \to [0, 1]$. The goal is to find a path originating at $r$ that minimizes the total ``cover time'' of all functions. This generalizes well-studied problems, such as Submodular Ranking [Azar and Gamzu 2011] and the Group Steiner Tree [Garg et al. 2000]. We give a polynomial time $ O(\log 1 / \epsilon c \log^{2 + \delta } |V|)$-approximation algorithm for MLSC, where $ \epsilon > 0$ is the smallest non-zero marginal increase of any $ \{ f_i^m_{i = 1} \} $ and $ \delta > 0$ is any constant. We also consider the Latency Covering Steiner Tree (LCST) problem, which is the special case of MLSC where the $ f_i$'s are multi-coverage functions. This is a common generalization of the Latency Group Steiner Tree [Gupta et al. 2010; Chakrabarty and Swamy 2011] and Generalized Min-sum Set Cover [Azar et al. 2009; Bansal et al. 2010] problems. We obtain an $ O(\log^2 | V |)$-approximation algorithm for LCST. Finally, we study a natural stochastic extension of the Submodular Ranking problem and obtain an adaptive algorithm with an $ O (\log 1 / \epsilon)$-approximation ratio, which is best possible. This result also generalizes some previously studied stochastic optimization problems, such as Stochastic Set Cover [Goemans and Vondr{\'a}k 2006] and Shared Filter Evaluation [Munagala et al. 2007; Liu et al. 2008].", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Krauthgamer:2016:CTA, author = "Robert Krauthgamer and Tal Wagner", title = "{Cheeger}-Type Approximation for Sparsest $ s t$-Cut", journal = j-TALG, volume = "13", number = "1", pages = "14:1--14:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2996799", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce the $ s t$-cut version of the sparsest-cut problem, where the goal is to find a cut of minimum sparsity in a graph $ G (V, E)$ among those separating two distinguished vertices $ s, t \in V$. Clearly, this problem is at least as hard as the usual (non-$ s t$) version. Our main result is a polynomial-time algorithm for the product-demands setting that produces a cut of sparsity $ O(\sqrt {\rm OPT})$, where $ {\rm OPT} \leq 1$ denotes the optimum when the total edge capacity and the total demand are assumed (by normalization) to be $1$. Our result generalizes the recent work of Trevisan [arXiv, 2013] for the non-$ s t$ version of the same problem (sparsest cut with product demands), which in turn generalizes the bound achieved by the discrete Cheeger inequality, a cornerstone of Spectral Graph Theory that has numerous applications. Indeed, Cheeger's inequality handles graph conductance, the special case of product demands that are proportional to the vertex (capacitated) degrees. Along the way, we obtain an $ O(\log | V |)$ approximation for the general-demands setting of sparsest $ s t$-cut.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lubbecke:2016:NAO, author = "Elisabeth L{\"u}bbecke and Olaf Maurer and Nicole Megow and Andreas Wiese", title = "A New Approach to Online Scheduling: Approximating the Optimal Competitive Ratio", journal = j-TALG, volume = "13", number = "1", pages = "15:1--15:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2996800", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close to the best possible competitive ratio for any online algorithm. We study the problem of scheduling jobs online to minimize the weighted sum of completion times on parallel, related, and unrelated machines, and we derive both deterministic and randomized algorithms that are almost best possible among all online algorithms of the respective settings. We also generalize our techniques to arbitrary monomial cost functions and apply them to the makespan objective. Our method relies on an abstract characterization of online algorithms combined with various simplifications and transformations. We also contribute algorithmic means to compute the actual value of the best possible competitive ratio up to an arbitrary accuracy. This strongly contrasts with nearly all previous manually obtained competitiveness results, and, most importantly, it reduces the search for the optimal competitive ratio to a question that a computer can answer. We believe that our concept can also be applied to many other problems and yields a new perspective on online algorithms in general.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Babenko:2016:AHL, author = "Maxim Babenko and Andrew V. Goldberg and Anupam Gupta and Viswanath Nagarajan", title = "Algorithms for Hub Label Optimization", journal = j-TALG, volume = "13", number = "1", pages = "16:1--16:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2996593", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the hub label optimization problem, which arises in designing fast preprocessing-based shortest-path algorithms. We give $ O(\log n)$-approximation algorithms for the objectives of minimizing the maximum label size ($ l_\infty $-norm) and simultaneously minimizing a constant number of $ l_p$ norms. Prior to this, an $ O(\log n)$-approximation algorithm was known [Cohen et al. 2003] only for minimizing the total label size ($ l_1$-norm).", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Harris:2016:LMT, author = "David G. Harris", title = "Lopsidependency in the {Moser--Tardos} Framework: Beyond the {Lopsided {Lov{\'a}sz} Local Lemma}", journal = j-TALG, volume = "13", number = "1", pages = "17:1--17:??", month = dec, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/3015762", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Dec 21 16:05:01 MST 2016", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Lopsided Lov{\'a}sz Local Lemma (LLLL) is a powerful probabilistic principle that has been used in a variety of combinatorial constructions. While this principle began as a general statement about probability spaces, it has recently been transformed into a variety of polynomial-time algorithms. The resampling algorithm of Moser and Tardos [2010] is the most well-known example of this. A variety of criteria have been shown for the LLLL; the strongest possible criterion was shown by Shearer, and other criteria that are easier to use computationally have been shown by Bissacot et al. [2011], Pegden [2014], Kolipaka and Szegedy [2011], and Kolipaka et al. [2012]. We show a new criterion for the Moser-Tardos algorithm to converge. This criterion is stronger than the LLLL criterion, and, in fact, can yield better results even than the full Shearer criterion. This is possible because it does not apply in the same generality as the original LLLL; yet, it is strong enough to cover many applications of the LLLL in combinatorics. We show a variety of new bounds and algorithms. A noteworthy application is for $k$-SAT, with bounded occurrences of variables. As shown in Gebauer et al. [2011], a $k$-SAT instance in which every variable appears $ L \leq \frac 2^k + 1 e (k + 1)$ times, is satisfiable. Although this bound is asymptotically tight (in $k$), we improve it to $ L \leq \frac 2^{k + 1} (1 - 1 / k)^k k - 1 - \frac 2 k$, which can be significantly stronger when $k$ is small. We introduce a new parallel algorithm for the LLLL. While Moser and Tardos described a simple parallel algorithm for the Lov{\'a}sz Local Lemma and described a simple sequential algorithm for a form of the Lopsided Lemma, they were not able to combine the two. Our new algorithm applies in nearly all settings in which the sequential algorithm works-this includes settings covered by our new, stronger LLLL criterion.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Andoni:2017:E, author = "Alexandr Andoni and Debmalya Panigrahi and Marcin Pilipczuk", title = "Editorial", journal = j-TALG, volume = "13", number = "2", pages = "18:1--18:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3038922", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Censor-Hillel:2017:TBV, author = "Keren Censor-Hillel and Mohsen Ghaffari and George Giakkoupis and Bernhard Haeupler and Fabian Kuhn", title = "Tight Bounds on Vertex Connectivity Under Sampling", journal = j-TALG, volume = "13", number = "2", pages = "19:1--19:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3086465", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A fundamental result by Karger [10] states that for any $ \lambda $-edge-connected graph with n nodes, independently sampling each edge with probability $ p = \Omega (\log (n) / \lambda)$ results in a graph that has edge connectivity $ \Omega (\lambda p)$, with high probability. This article proves the analogous result for vertex connectivity, when either vertices or edges are sampled. We show that for any $k$-vertex-connected graph $G$ with $n$ nodes, if each node is independently sampled with probability $ p = \Omega (\sqrt {\log (n) / k})$, then the subgraph induced by the sampled nodes has vertex connectivity $ \Omega (k p^2)$, with high probability. If edges are sampled with probability $ p = \Omega (\log (n) / k)$, then the sampled subgraph has vertex connectivity $ \Omega (k p)$, with high probability. Both bounds are existentially optimal.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chakrabarty:2017:PTP, author = "Deeparnab Chakrabarty and Kashyap Dixit and Madhav Jha and C. Seshadhri", title = "Property Testing on Product Distributions: Optimal Testers for Bounded Derivative Properties", journal = j-TALG, volume = "13", number = "2", pages = "20:1--20:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3039241", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The primary problem in property testing is to decide whether a given function satisfies a certain property or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion is the Hamming distance over the uniform distribution on the domain. This restriction to uniformity is rather limiting, and it is important to investigate distances induced by more general distributions. In this article, we provide simple and optimal testers for bounded derivative properties over arbitrary product distributions. Bounded derivative properties include fundamental properties, such as monotonicity and Lipschitz continuity. Our results subsume almost all known results (upper and lower bounds) on monotonicity and Lipschitz testing over arbitrary ranges. We prove an intimate connection between bounded derivative property testing and binary search trees (BSTs). We exhibit a tester whose query complexity is the sum of expected depths of optimal BSTs for each marginal. Furthermore, we show that this sum-of-depths is also a lower bound. A technical contribution of our work is an optimal dimension reduction theorem for all bounded derivative properties that relates the distance of a function from the property to the distance of restrictions of the function to random lines. Such a theorem has been elusive even for monotonicity, and our theorem is an exponential improvement to the previous best-known result.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{An:2017:DFL, author = "Hyung-Chan An and Ashkan Norouzi-Fard and Ola Svensson", title = "Dynamic Facility Location via Exponential Clocks", journal = j-TALG, volume = "13", number = "2", pages = "21:1--21:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/2928272", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The dynamic facility location problem is a generalization of the classic facility location problem proposed by Eisenstat, Mathieu, and Schabanel to model the dynamics of evolving social/infrastructure networks. The generalization lies in that the distance metric between clients and facilities changes over time. This leads to a trade-off between optimizing the classic objective function and the ``stability'' of the solution: There is a switching cost charged every time a client changes the facility to which it is connected. While the standard linear program (LP) relaxation for the classic problem naturally extends to this problem, traditional LP-rounding techniques do not, as they are often sensitive to small changes in the metric resulting in frequent switches. We present a new LP-rounding algorithm for facility location problems, which yields the first constant approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on the clients and facilities and connects every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP roundings for facility location problems. In particular, we use no clustering and we allow clients to connect through paths of arbitrary lengths. In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Li:2017:UCM, author = "Shi Li", title = "On Uniform Capacitated $k$-Median Beyond the Natural {LP} Relaxation", journal = j-TALG, volume = "13", number = "2", pages = "22:1--22:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/2983633", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we study the uniform capacitated $k$-median (CKM) problem. In the problem, we are given a set $F$ of potential facility locations, a set $C$ of clients, a metric $d$ over $ F \cup C$, an upper bound $k$ on the number of facilities that we can open, and an upper bound $u$ on the number of clients that each facility can serve. We need to open a subset $ S \subseteq F$ of $k$ facilities and connect clients in $C$ to facilities in $S$ so that each facility is connected by at most $u$ clients. The goal is to minimize the total connection cost over all clients. Obtaining a constant approximation algorithm for this problem is a notorious open problem; most previous works gave constant approximations by either violating the capacity constraints or the cardinality constraint. Notably, all of these algorithms are based on the natural LP relaxation for the problem. The LP relaxation has unbounded integrality gap, even when we are allowed to violate the capacity constraints or the cardinality constraint by a factor of 2 --- \epsilon . Our result is an $ \exp (O(1 / \epsilon^2))$-approximation algorithm for the problem that violates the cardinality constraint by a factor of $ 1 + \epsilon $. In other words, we find a solution that opens at most $ (1 + \epsilon) k$ facilities whose cost is at most $ \exp (O (1 / \epsilon^2))$ times the optimum solution when at most k facilities can be open. This is already beyond the capability of the natural LP relaxation, as it has unbounded integrality gap even if we are allowed to open $ (2 - \epsilon) k$ facilities. Indeed, our result is based on a novel LP for this problem. It is our hope that this LP is the first step toward a constant approximation for CKM. The version that we described is the hard capacitated version of the problem, as we can only open one facility at each location. This is as opposed to the soft capacitated version, in which we are allowed to open more than one facility at each location. The hard capacitated version is more general, since one can convert a soft capacitated instance to a hard capacitated instance by making enough copies of each facility location. We give a simple proof that in the uniform capacitated case, the soft capacitated version and the hard capacitated version are actually equivalent, up to a small constant loss in the approximation ratio.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Byrka:2017:IAM, author = "Jaroslaw Byrka and Thomas Pensyl and Bartosz Rybicki and Aravind Srinivasan and Khoa Trinh", title = "An Improved Approximation for $k$-Median and Positive Correlation in Budgeted Optimization", journal = j-TALG, volume = "13", number = "2", pages = "23:1--23:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/2981561", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Dependent rounding is a useful technique for optimization problems with hard budget constraints. This framework naturally leads to negative correlation properties. However, what if an application naturally calls for dependent rounding on the one hand and desires positive correlation on the other? More generally, we develop algorithms that guarantee the known properties of dependent rounding but also have nearly bestpossible behavior-near-independence, which generalizes positive correlation-on ``small'' subsets of the variables. The recent breakthrough of Li and Svensson for the classical $k$-median problem has to handle positive correlation in certain dependent rounding settings, and does so implicitly. We improve upon Li--Svensson's approximation ratio for $k$-median from $ 2.732 + \epsilon $ to $ 2.675 + \epsilon $ by developing an algorithm that improves upon various aspects of their work. Our dependent rounding approach helps us improve the dependence of the runtime on the parameter $ \epsilon $ from Li--Svensson's $ N^{O (1 / \epsilon^2)}$ to $ N^{O ((1 / \epsilon) \log (1 / \epsilon))}$.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bacher:2017:GRP, author = "Axel Bacher and Olivier Bodini and Hsien-Kuei Hwang and Tsung-Hsi Tsai", title = "Generating Random Permutations by Coin Tossing: Classical Algorithms, New Analysis, and Modern Implementation", journal = j-TALG, volume = "13", number = "2", pages = "24:1--24:43", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3009909", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Several simple, classical, little-known algorithms in the statistics and computer science literature for generating random permutations by coin tossing are examined, analyzed, and implemented. These algorithms are either asymptotically optimal or close to being so in terms of the expected number of times the random bits are generated. In addition to asymptotic approximations to the expected complexity, we also clarify the corresponding variances, as well as the asymptotic distributions. A brief comparative discussion with numerical computations in a multicore system is also given.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Etscheid:2017:SAL, author = "Michael Etscheid and Heiko R{\"o}glin", title = "Smoothed Analysis of Local Search for the Maximum-Cut Problem", journal = j-TALG, volume = "13", number = "2", pages = "25:1--25:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3011870", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Even though local search heuristics are the method of choice in practice for many well-studied optimization problems, most of them behave poorly in the worst case. This is, in particular, the case for the Maximum-Cut Problem, for which local search can take an exponential number of steps to terminate and the problem of computing a local optimum is PLS-complete. To narrow the gap between theory and practice, we study local search for the Maximum-Cut Problem in the framework of smoothed analysis in which inputs are subject to a small amount of random noise. We show that the smoothed number of iterations is quasi-polynomial, that is, it is bounded from above by a polynomial in $ n^{\log n} $ and $ \phi $, where $n$ denotes the number of nodes and $ \phi $ denotes the perturbation parameter. This shows that worst-case instances are fragile, and it is a first step in explaining why they are rarely observed in practice.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kaplan:2017:SMQ, author = "Haim Kaplan and Shay Mozes and Yahav Nussbaum and Micha Sharir", title = "Submatrix Maximum Queries in {Monge} Matrices and Partial {Monge} Matrices, and Their Applications", journal = j-TALG, volume = "13", number = "2", pages = "26:1--26:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3039873", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We describe a data structure for submatrix maximum queries in Monge matrices or partial Monge matrices, where a query seeks the maximum element in a contiguous submatrix of the given matrix. The structure, for an $ n \times n $ Monge matrix, takes $ O (n \log n) $ space and $ O (n \log n) $ preprocessing time, and answers queries in $ O (\log^2 n) $ time. For partial Monge matrices, the space grows by $ \alpha (n) $, the preprocessing grows by $ \alpha (n) \log n $ ($ \alpha (n) $ is the inverse Ackermann function), and the query remains $ O (\log^2 n) $. Our design exploits an interpretation of the column maxima in a Monge (partial Monge, respectively) matrix as an upper envelope of pseudo-lines (pseudo-segments, respectively). We give two applications: (1) For a planar set of $n$ points in an axis-parallel rectangle $B$, we build a data structure, in $ O (n \alpha (n) \log^4 n)$ time and $ O(n \alpha (n) \log^3 n)$ space, that returns, for a query point p, the largest-area empty axis-parallel rectangle contained in $B$ and containing $p$, in $ O (\log^4 n)$ time. This improves substantially the nearly quadratic storage and preprocessing obtained by Augustine et al. [2010]. (2) Given an $n$-node arbitrarily weighted planar digraph, with possibly negative edge weights, we build, in $ O (n \log^2 n / \log \log n)$ time, a linear-size data structure that supports edge-weight updates and graph-distance queries between arbitrary pairs of nodes in $ O(n^{2 / 3} \log^{5 / 3} n)$ time per operation. This improves a previous algorithm of Fakcharoenphol and Rao [2006]. Our data structure has already been applied in a recent maximum flow algorithm for planar graphs in Borradaile et al. [2011].", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cheng:2017:FSS, author = "Siu-Wing Cheng and Jiongxin Jin and Man-Kit Lau", title = "A Fast and Simple Surface Reconstruction Algorithm", journal = j-TALG, volume = "13", number = "2", pages = "27:1--27:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3039242", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present an algorithm for surface reconstruction from a point cloud. It runs in $ O (n \log n) $ time, where n is the number of sample points, and this is optimal in the pointer machine model. The only existing $ O (n \log n)$-time algorithm is due to Funke and Ramos, and it uses some sophisticated data structures. The key task is to extract a locally uniform subsample from the input points. Our algorithm is much simpler and it is based on a variant of the standard octree. We built a prototype that runs an implementation of our algorithm to extract a locally uniform subsample, invokes Cocone to reconstruct a surface from the subsample, and adds back the sample points absent from the subsample via edge flips. In our experiments with some nonuniform samples, the subsample extraction step is fast and effective, and the prototype gives a 51\% to 68\% speedup over using Cocone alone. The prototype also runs faster on locally uniform samples.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Grossi:2017:AOE, author = "Roberto Grossi and John Iacono and Gonzalo Navarro and Rajeev Raman and S. Rao Satti", title = "Asymptotically Optimal Encodings of Range Data Structures for Selection and Top-$k$ Queries", journal = j-TALG, volume = "13", number = "2", pages = "28:1--28:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3012939", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given an array $ A[1, n] $ of elements with a total order, we consider the problem of building a data structure that solves two queries: (a) selection queries receive a range $ [i, j] $ and an integer $k$ and return the position of the $k$ th largest element in $ A[i, j]$; (b) top-$k$ queries receive $ [i, j]$ and $k$ and return the positions of the $k$ largest elements in $ A[i, j]$. These problems can be solved in optimal time, $ O(1 + \lg k / \lg \lg n)$ and $ O(k)$, respectively, using linear-space data structures. We provide the first study of the encoding data structures for the above problems, where A cannot be accessed at query time. Several applications are interested in the relative order of the entries of A, and their positions, rather their actual values, and thus we do not need to keep A at query time. In those cases, encodings save storage space: we first show that any encoding answering such queries requires $ n \lg k - O(n + k \lg k)$ bits of space; then, we design encodings using $ O(n \lg k)$ bits, that is, asymptotically optimal up to constant factors, while preserving optimal query time.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ganian:2017:DAT, author = "Robert Ganian and M. S. Ramanujan and Stefan Szeider", title = "Discovering Archipelagos of Tractability for Constraint Satisfaction and Counting", journal = j-TALG, volume = "13", number = "2", pages = "29:1--29:??", month = may, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3014587", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon Jul 24 16:50:40 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of classes of instances for which CSP can be solved in polynomial time; such classes are often called ``islands of tractability.'' A prominent way of defining islands of tractability for CSP is to restrict the relations that may occur in the constraints to a fixed set, called a constraint language, whereas a constraint language is conservative if it contains all unary relations. Schaefer's famous Dichotomy Theorem (STOC 1978) identifies all islands of tractability in terms of tractable constraint languages over a Boolean domain of values. Since then, many extensions and generalizations of this result have been obtained. Recently, Bulatov (TOCL 2011, JACM 2013) gave a full characterization of all islands of tractability for CSP and the counting version \#CSP that are defined in terms of conservative constraint languages. This article addresses the general limit of the mentioned tractability results for CSP and \#CSP, that they only apply to instances where all constraints belong to a single tractable language (in general, the union of two tractable languages is not tractable). We show that we can overcome this limitation as long as we keep some control of how constraints over the various considered tractable languages interact with each other. For this purpose, we utilize the notion of a strong backdoor of a CSP instance, as introduced by Williams et al. (IJCAI 2003), which is a set of variables that when instantiated, moves the instance to an island of tractability, that is, to a tractable class of instances. We consider strong backdoors into scattered classes, consisting of CSP instances where each connected component belongs entirely to some class from a list of tractable classes. Figuratively speaking, a scattered class constitutes an archipelago of tractability. The main difficulty lies in finding a strong backdoor of given size k; once it is found, we can try all possible instantiations of the backdoor variables and apply the polynomial time algorithms associated with the islands of tractability on the list component-wise. Our main result is an algorithm that, given a CSP instance with n variables, finds in time f ( k ) n$^{O (1)}$ a strong backdoor into a scattered class (associated with a list of finite conservative constraint languages) of size k or correctly decides that there is not such a backdoor. This also gives the running time for solving (\#)CSP, provided that (\#)CSP is polynomial-time tractable for the considered constraint languages. Our result makes significant progress towards the main goal of the backdoor-based approach to CSPs-the identification of maximal base classes for which small backdoors can be detected efficiently.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cohavi:2017:FSS, author = "Keren Cohavi and Shahar Dobzinski", title = "Faster and Simpler Sketches of Valuation Functions", journal = j-TALG, volume = "13", number = "3", pages = "30:1--30:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3039871", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present fast algorithms for sketching valuation functions. Let $ N (| N | = n) $ be some ground set and $ v \colon 2^N \to R $ be a function. We say that $ \tilde {v} \colon 2^N \to R $ is an $ \alpha $ -sketch of $v$ if for every set $S$ we have that $ v(S) / \alpha \leq \tilde {v}(S) \leq v(S)$ and $ \tilde {v}$ can be described in $ \poly (n)$ bits. Goemans et al. [SODA'09] showed that if $v$ is submodular then there exists an $ {\~ o}(\sqrt {n})$-sketch that can be constructed using polynomially many value queries (this is essentially the best possible, as Balcan and Harvey [STOC'11] show that no submodular function admits an $ n^{1 / 3 - \epsilon }$-sketch). Based on their work, Balcan et al. [COLT'12] and Badanidiyuru et al. [SODA'12] show that if $v$ is subadditive, then there exists an $ {\~ o}(\sqrt {n})$-sketch that can be constructed using polynomially many demand queries. All previous sketches are based on complicated geometric constructions. The first step in their constructions is proving the existence of a good sketch by finding an ellipsoid that ``approximates'' $v$ well (this is done by applying John's theorem to ensure the existence of an ellipsoid that is ``close'' to the polymatroid that is associated with $v$). The second step is to show that this ellipsoid can be found efficiently, and this is done by repeatedly solving a certain convex program to obtain better approximations of John's ellipsoid. In this article, we give a significantly simpler, nongeometric proof for the existence of good sketches and utilize the proof to obtain much faster algorithms that match the previously obtained approximation bounds. Specifically, we provide an algorithm that finds $ {\~ o}(\sqrt {n})$-sketch of a submodular function with only $ {\~ o}(n^{3 / 2})$ value queries, and we provide an algorithm that finds $ {\~ o} (\sqrt {n})$-sketch of a subadditive function with $ O(n)$ demand and value queries.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Glacet:2017:TVI, author = "Christian Glacet and Avery Miller and Andrzej Pelc", title = "Time vs. Information Tradeoffs for Leader Election in Anonymous Trees", journal = j-TALG, volume = "13", number = "3", pages = "31:1--31:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3039870", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Leader election is one of the fundamental problems in distributed computing. It calls for all nodes of a network to agree on a single node, called the leader. If the nodes of the network have distinct labels, then agreeing on a single node means that all nodes have to output the label of the elected leader. If the nodes of the network are anonymous, the task of leader election is formulated as follows: every node v of the network must output a simple path, which is coded as a sequence of port numbers, such that all these paths end at a common node, the leader. In this article, we study deterministic leader election in anonymous trees. Our aim is to establish tradeoffs between the allocated time $ \tau $ and the amount of information that has to be given a priori to the nodes to enable leader election in time $ \tau $ in all trees for which leader election in this time is at all possible. Following the framework of algorithms with advice, this information (a single binary string) is provided to all nodes at the start by an oracle knowing the entire tree. The length of this string is called the size of advice. For a given time $ \tau $ allocated to leader election, we give upper and lower bounds on the minimum size of advice sufficient to perform leader election in time $ \tau $ . For most values of $ \tau $, our upper and lower bounds are either tight up to multiplicative constants, or they differ only by a logarithmic factor. Let $T$ be an $n$-node tree of diameter $ \diam \leq D$. While leader election in time diam can be performed without any advice, for time $ \diam 1$ we give tight upper and lower bounds of $ \Theta (\log D)$. For time $ \diam - 2$ we give tight upper and lower bounds of $ \Theta (\log D)$ for even values of $ \diam $, and tight upper and lower bounds of $ \Theta (\log n)$ for odd values of $ \diam $. Moving to shorter time, in the interval $ [\beta \cdot \diam, \diam - 3]$ for constant $ \beta > 1 / 2$, we prove an upper bound of $ O(n \log n / D)$ and a lower bound of $ \Omega (n / D)$, the latter being valid whenever diam is odd or when the time is at most $ \diam - 4$. Hence, with the exception of the special case when $ \diam $ is even and time is exactly $ \diam - 3$, our bounds leave only a logarithmic gap in this time interval. Finally, for time $ \alpha \cdot \diam $ for any constant $ \alpha < 1 / 2$ (except for the case of very small diameters), we again give tight upper and lower bounds, this time $ \Theta (n)$.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gilbert:2017:ASR, author = "Anna C. Gilbert and Yi Li and Ely Porat and Martin J. Strauss", title = "For-All Sparse Recovery in Near-Optimal Time", journal = j-TALG, volume = "13", number = "3", pages = "32:1--32:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3039872", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An approximate sparse recovery system in $ l_1 $ norm consists of parameters $k$, $ \epsilon $, $N$; an $m$-by-$N$ measurement $ \Phi $; and a recovery algorithm $R$. Given a vector, $x$, the system approximates $x$ by $ \widehat {x} = R (\Phi x)$, which must satisfy $ || \widehat {x} - x ||_1 \leq (1 + \epsilon) || x - x_k ||_1$. We consider the ``for all'' model, in which a single matrix $ \Phi $, possibly ``constructed'' non-explicitly using the probabilistic method, is used for all signals $x$. The best existing sublinear algorithm by Porat and Strauss [2012] uses $ O(\epsilon^{-3} k \log (N / k))$ measurements and runs in time $ O(k^{1 - \alpha } N^\alpha)$ for any constant $ \alpha > 0$. In this article, we improve the number of measurements to $ O(\epsilon^{-2} k \log (N / k))$, matching the best existing upper bound (attained by super-linear algorithms), and the runtime to $ O(k^{1 + \beta } \poly (\log N, 1 / \epsilon))$, with a modest restriction that $ k \leq N^{1 - \alpha }$ and $ \epsilon \leq (\log k / \log N)^\gamma $ for any constants $ \alpha $, $ \beta $, $ \gamma > 0$. When $ k \leq \log^c N$ for some $ c > 0$, the runtime is reduced to $ O(k \poly (N, 1 / \epsilon))$. With no restrictions on $ \epsilon $, we have an approximation recovery system with $ m = O(k / \epsilon \log (N / k)((\log N / \log k)^\gamma + 1 / \epsilon))$ measurements. The overall architecture of this algorithm is similar to that of Porat and Strauss [2012] in that we repeatedly use a weak recovery system (with varying parameters) to obtain a top-level recovery algorithm. The weak recovery system consists of a two-layer hashing procedure (or with two unbalanced expanders for a deterministic algorithm). The algorithmic innovation is a novel encoding procedure that is reminiscent of network coding and that reflects the structure of the hashing stages. The idea is to encode the signal position index $i$ by associating it with a unique message $ m_i$, which will be encoded to a longer message $ m'_i$ (in contrast to Porat and Strauss [2012] in which the encoding is simply the identity). Portions of the message $ m'_i$ correspond to repetitions of the hashing, and we use a regular expander graph to encode the linkages among these portions. The decoding or recovery algorithm consists of recovering the portions of the longer messages $ m_i$ and then decoding to the original messages $ m_i$, all the while ensuring that corruptions can be detected and/or corrected. The recovery algorithm is similar to list recovery introduced in Indyk et al. [2010] and used in Gilbert et al. [2013]. In our algorithm, the messages $ \{ m_i \} $ are independent of the hashing, which enables us to obtain a better result.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Harris:2017:AEA, author = "David G. Harris and Aravind Srinivasan", title = "Algorithmic and Enumerative Aspects of the {Moser--Tardos} Distribution", journal = j-TALG, volume = "13", number = "3", pages = "33:1--33:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3039869", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Moser and Tardos have developed a powerful algorithmic approach (henceforth MT) to the Lov{\'a}sz Local Lemma (LLL); the basic operation done in MT and its variants is a search for ``bad'' events in a current configuration. In the initial stage of MT, the variables are set independently. We examine the distributions on these variables that arise during intermediate stages of MT. We show that these configurations have a more or less ``random'' form, building further on the MT-distribution concept of Haeupler et al. in understanding the (intermediate and) output distribution of MT. This has a variety of algorithmic applications; the most important is that bad events can be found relatively quickly, improving on MT across the complexity spectrum. It makes some polynomial-time algorithms sublinear (e.g., for Latin transversals, which are of basic combinatorial interest), gives lower-degree polynomial runtimes in some settings, transforms certain superpolynomial-time algorithms into polynomial-time algorithms, and leads to Las Vegas algorithms for some coloring problems for which only Monte Carlo algorithms were known. We show that, in certain conditions when the LLL condition is violated, a variant of the MT algorithm can still produce a distribution that avoids most of the bad events. We show in some cases that this MT variant can run faster than the original MT algorithm itself and develop the first-known criterion for the case of the asymmetric LLL. This can be used to find partial Latin transversals-improving on earlier bounds of Stein (1975)-among other applications. We furthermore give applications in enumeration, showing that most applications (for which we aim for all or most of the bad events to be avoided) have large solution sets. We do this by showing that the MT distribution has large R{\'e}nyi entropy.", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cheraghchi:2017:NOD, author = "Mahdi Cheraghchi and Piotr Indyk", title = "Nearly Optimal Deterministic Algorithm for Sparse {Walsh--Hadamard} Transform", journal = j-TALG, volume = "13", number = "3", pages = "34:1--34:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3029050", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For every fixed constant $ \alpha > 0 $, we design an algorithm for computing the $k$-sparse Walsh-Hadamard transform (i.e., Discrete Fourier Transform over the Boolean cube) of an $N$-dimensional vector $ x \in R^N$ in time $ k^{1 + \alpha } (\log N)^{O(1)}$. Specifically, the algorithm is given query access to $x$ and computes a $k$-sparse $ \tilde {x} \in R^N$ satisfying $ || \tilde {x} - \hat {x} ||_1 \leq c || \hat {x} - H_k(\hat {x}) ||_1$ for an absolute constant $ c > 0$, where $ \hat {x}$ is the transform of $x$ and $ H_k(\hat {x})$ is its best $k$-sparse approximation. Our algorithm is fully deterministic and only uses nonadaptive queries to $x$ (i.e., all queries are determined and performed in parallel when the algorithm starts). An important technical tool that we use is a construction of nearly optimal and linear lossless condensers, which is a careful instantiation of the GUV condenser (Guruswami et al. [2009]). Moreover, we design a deterministic and nonadaptive $ l_1$ / $ l_1$ compressed sensing scheme based on general lossless condensers that is equipped with a fast reconstruction algorithm running in time $ k^{1 + \alpha } (\log N)^{O (1)}$ (for the GUV-based condenser) and is of independent interest. Our scheme significantly simplifies and improves an earlier expander-based construction due to Berinde, Gilbert, Indyk, Karloff, and Strauss [Berinde et al. 2008]. Our methods use linear lossless condensers in a black box fashion; therefore, any future improvement on explicit constructions of such condensers would immediately translate to improved parameters in our framework (potentially leading to $ k(\log N)^{O(1)}$ reconstruction time with a reduced exponent in the poly-logarithmic factor, and eliminating the extra parameter \alpha ). By allowing the algorithm to use randomness while still using nonadaptive queries, the runtime of the algorithm can be improved to $ {\~ o}(k \log^3 N)$.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Giannopoulou:2017:UKC, author = "Archontia C. Giannopoulou and Bart M. P. Jansen and Daniel Lokshtanov and Saket Saurabh", title = "Uniform Kernelization Complexity of Hitting Forbidden Minors", journal = j-TALG, volume = "13", number = "3", pages = "35:1--35:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3029051", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The $F$-Minor-Free Deletion problem asks, for a fixed set $F$ and an input consisting of a graph $G$ and integer $k$, whether $k$ vertices can be removed from $G$ such that the resulting graph does not contain any member of $F$ as a minor. At FOCS 2012, Fomin et al. showed that the special case when $F$ contains at least one planar graph has a kernel of size $ f(F) c k^{g(F)}$ for some functions $f$ and $g$. They left open whether this Planar $F$-Minor-Free Deletion problem has kernels whose size is uniformly polynomial, of the form $ f(F) c k^c$ for some universal constant $c$. We prove that some Planar $F$-Minor-Free Deletion problems do not have uniformly polynomial kernels (unless NP $ \subseteq $ coNP/poly), not even when parameterized by the vertex cover number. On the positive side, we consider the problem of determining whether $k$ vertices can be removed to obtain a graph of treedepth at most $ \eta $. We prove that this problem admits uniformly polynomial kernels with $ O(k^6)$ vertices for every fixed $ \eta $.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fomin:2017:RFP, author = "Fedor V. Fomin and Daniel Lokshtanov and Fahad Panolan and Saket Saurabh", title = "Representative Families of Product Families", journal = j-TALG, volume = "13", number = "3", pages = "36:1--36:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3039243", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A subfamily $ F' $ of a set family $F$ is said to $q$-represent $F$ if for every $ A \in F$ and $B$ of size $q$ such that $ A \cap B = \oslash $ there exists a set $ A' \in F'$ such that $ A' \cap B = \oslash $. Recently, we provided an algorithm that, for a given family $F$ of sets of size $p$ together with an integer $q$, efficiently computes a $q$-representative family $ F'$ of $F$ of size approximately $ (p + q \atop p)$. In this article, we consider the efficient computation of q -representative families for product families $F$. A family $F$ is a product family if there exist families $A$ and $B$ such that $ F = \{ A, \cup B \colon A \in A, B \in B, A \cap B = \oslash \} $. Our main technical contribution is an algorithm that, given $A$, $B$ and $q$, computes a $q$-representative family $ F'$ of $F$. The running time of our algorithm is sublinear in $ | F |$ for many choices of $A$, $B$, and $q$ that occur naturally in several dynamic programming algorithms. We also give an algorithm for the computation of $q$ representative families for product families $F$ in the more general setting where $q$ representation also involves independence in a matroid in addition to disjointness. This algorithm considerably outperforms the naive approach where one first computes $F$ from $A$ and $B$ and then computes the q representative family $ F'$ from $F$. We give two applications of our new algorithms for computing $q$ representative families for product families. The first is a $ 3.8408^k n^{O(1)}$ deterministic algorithm for the Multilinear Monomial Detection ($k$-MlD) problem. The second is a significant improvement of deterministic dynamic programming algorithms for ``connectivity problems'' on graphs of bounded treewidth.", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Annamalai:2017:CAR, author = "Chidambaram Annamalai and Christos Kalaitzis and Ola Svensson", title = "Combinatorial Algorithm for Restricted Max--Min Fair Allocation", journal = j-TALG, volume = "13", number = "3", pages = "37:1--37:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3070694", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the basic allocation problem of assigning resources to players to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain Configuration-LP can be used to estimate the value of the optimal allocation to within a factor of 4+ \epsilon . In contrast, however, the best-known approximation algorithm for the problem has an unspecified large constant guarantee. In this article, we significantly narrow this gap by giving a 13-approximation algorithm for the problem. Our approach develops a local search technique introduced by Haxell [13] for hypergraph matchings and later used in this context by Asadpour, Feige, and Saberi [2]. For our local search procedure to terminate in polynomial time, we introduce several new ideas, such as lazy updates and greedy players. Besides the improved approximation guarantee, the highlight of our approach is that it is purely combinatorial and uses the Configuration-LP only in the analysis.", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bender:2017:COS, author = "Michael A. Bender and Mart{\'\i}n Farach-Colton and S{\'a}ndor P. Fekete and Jeremy T. Fineman and Seth Gilbert", title = "Cost-Oblivious Storage Reallocation", journal = j-TALG, volume = "13", number = "3", pages = "38:1--38:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3070693", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Databases allocate and free blocks of storage on disk. Freed blocks introduce holes where no data is stored. Allocation systems attempt to reuse such deallocated regions in order to minimize the footprint on disk. When previously allocated blocks cannot be moved, this problem is called the memory allocation problem. The competitive ratio for this problem has matching upper and lower bounds that are logarithmic in the number of requests and in the ratio of the largest to smallest requests. This article defines the storage reallocation problem, where previously allocated blocks can be moved, or reallocated, but at some cost. This cost is determined by the allocation/reallocation cost function. The objective is to minimize the storage footprint, that is, the largest memory address containing an allocated object, while simultaneously minimizing the reallocation costs. This article gives asymptotically optimal algorithms for storage reallocation, in which the storage footprint is at most $ (1 + \epsilon) $ times optimal, and the reallocation cost is $ O((1 / \epsilon) \log (1 / \epsilon)) $ times the original allocation cost, that is, it is within a constant factor of optimal when $ \epsilon $ is a constant. The algorithms are cost oblivious, which means they achieve these bounds with no knowledge of the allocation/reallocation cost function, as long as the cost function is subadditive.", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Feldman:2017:MSS, author = "Moran Feldman", title = "Maximizing Symmetric Submodular Functions", journal = j-TALG, volume = "13", number = "3", pages = "39:1--39:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3070685", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Symmetric submodular functions are an important family of submodular functions capturing many interesting cases, including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little attention by current research, unlike similar minimization problems that have been widely studied. In this work, we identify a few submodular maximization problems for which one can get a better approximation for symmetric objectives than the state-of-the-art approximation for general submodular functions. We first consider the problem of maximizing a non-negative symmetric submodular function $ f \colon 2^N \to R^+ $ subject to a down-monotone solvable polytope $ P \subseteq [0, 1]^N $. For this problem, we describe an algorithm producing a fractional solution of value at least $ 0.432 c f ({\rm OPT}) $, where OPT is the optimal integral solution. Our second result considers the problem $ \{ \max f (S) : | S | = k \} $ for a non-negative symmetric submodular function $ f \colon 2^N \to R^+ $. For this problem, we give an approximation ratio that depends on the value $ k / | N | $ and is always at least $ 0.432 $. Our method can also be applied to non-negative non-symmetric submodular functions, in which case it produces $ 1 / e - o(1) $ approximation, improving over the best-known result for this problem. For unconstrained maximization of a non-negative symmetric submodular function, we describe a deterministic linear-time $ 1 / 2$-approximation algorithm. Finally, we give a $ [1 - (1 - 1 / k)^{k - 1}]$-approximation algorithm for Submodular Welfare with $k$ players having identical non-negative submodular utility functions and show that this is the best possible approximation ratio for the problem.", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Dinitz:2017:IAA, author = "Michael Dinitz and Guy Kortsarz and Zeev Nutov", title = "Improved Approximation Algorithm for {Steiner} $k$-Forest with Nearly Uniform Weights", journal = j-TALG, volume = "13", number = "3", pages = "40:1--40:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3077581", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the Steiner $k$-Forest problem, we are given an edge weighted graph, a collection $D$ of node pairs, and an integer $ k \leq | D |$. The goal is to find a min-weight subgraph that connects at least $k$ pairs. The best known ratio for this problem is $ \min \{ O(\sqrt n), O(\sqrt k) \} $ [Gupta et al. 2010]. In Gupta et al. [2010], it is also shown that ratio $ \rho $ for Steiner $k$-Forest implies ratio $ O(\rho \cdot l o g^2 n)$ for the related Dial-a-Ride problem. The only other algorithm known for Dial-a-Ride, besides the one resulting from Gupta et al. [2010], has ratio $ O(\sqrt n)$ [Charikar and Raghavachari 1998]. We obtain approximation ratio $ n^{0.448}$ for Steiner $k$-Forest and Dial-a-Ride with unit weights, breaking the $ O(\sqrt n)$ approximation barrier for this natural case. We also show that if the maximum edge-weight is $ O(n^\epsilon)$, then one can achieve ratio $ O(n^{(1 + \epsilon) \cdot 0.448})$, which is less than $ \sqrt n$ if $ \epsilon $ is small enough. The improvement for Dial-a-Ride is the first progress for this problem in 15 years. To prove our main result, we consider the following generalization of the Minimum $k$ Edge Subgraph (M$k$-ES) problem, which we call Min-Cost $l$-Edge-Profit Subgraph (MCl-EPS): Given a graph $ G = (V, E)$ with edge-profits $ p = \{ p_e \colon e \in E \} $ and node-costs $ c = \{ c_v \colon v \in V \} $, and a lower profit bound $l$, find a minimum node-cost subgraph of $G$ of edge-profit at least $l$. The M$k$-ES problem is a special case of MCl-EPS with unit node costs and unit edge profits. The currently best known ratio for M$k$ES is $ n^{3 - 2 \sqrt {2} + \epsilon }$ [Chlamtac et al. 2012]. We extend this ratio to MCl-EPS for general node costs and profits bounded by a polynomial in $n$, which may be of independent interest.", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Borodin:2017:MSD, author = "Allan Borodin and Aadhar Jain and Hyun Chul Lee and Yuli Ye", title = "Max-Sum Diversification, Monotone Submodular Functions, and Dynamic Updates", journal = j-TALG, volume = "13", number = "3", pages = "41:1--41:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3086464", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Result diversification is an important aspect in web-based search, document summarization, facility location, portfolio management, and other applications. Given a set of ranked results for a set of objects (e.g., web documents, facilities, etc.) with a distance between any pair, the goal is to select a subset $S$ satisfying the following three criteria: (a) the subset $S$ satisfies some constraint (e.g., bounded cardinality), (b) the subset contains results of high ``quality,'' and (c) the subset contains results that are ``diverse'' relative to the distance measure. The goal of result diversification is to produce a diversified subset while maintaining high quality as much as possible. We study a broad class of problems where the distances are a metric, where the constraint is given by independence in a matroid, where quality is determined by a monotone submodular function and diversity is defined as the sum of distances between objects in $S$. Our problem is a generalization of the max-sum diversification problem studied in Gollapudi and Sharma [2009], which in turn is a generalization of the max-sum $p$-dispersion problem studied extensively in location theory. It is NP-hard even with the triangle inequality. We propose two simple and natural algorithms: a greedy algorithm for a cardinality constraint and a local search algorithm for an arbitrary matroid constraint. We prove that both algorithms achieve constant approximation ratios.", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hansen:2017:HH, author = "Thomas Dueholm Hansen and Haim Kaplan and Robert E. Tarjan and Uri Zwick", title = "Hollow Heaps", journal = j-TALG, volume = "13", number = "3", pages = "42:1--42:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3093240", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce the hollow heap, a very simple data structure with the same amortized efficiency as the classical Fibonacci heap. All heap operations except delete and delete --- min take $ O(1) $ time, worst case as well as amortized; delete and delete --- min take $ O(\log n) $ amortized time on a heap of $n$ items. Hollow heaps are the simplest structure to achieve these bounds. Hollow heaps combine two novel ideas: the use of lazy deletion and re-insertion to do decrease --- key operations and the use of a dag (directed acyclic graph) instead of a tree or set of trees to represent a heap. Lazy deletion produces hollow nodes (nodes without items), giving the data structure its name.", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cygan:2017:TKB, author = "Marek Cygan and Fabrizio Grandoni and Danny Hermelin", title = "Tight Kernel Bounds for Problems on Graphs with Small Degeneracy", journal = j-TALG, volume = "13", number = "3", pages = "43:1--43:??", month = aug, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3108239", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 9 16:15:20 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Kernelization is a strong and widely applied technique in parameterized complexity. In a nutshell, a kernelization algorithm for a parameterized problem transforms in polynomial time a given instance of the problem into an equivalent instance whose size depends solely on the parameter. Recent years have seen major advances in the study of both upper and lower bound techniques for kernelization, and by now this area has become one of the major research threads in parameterized complexity. In this article, we consider kernelization for problems on $d$-degenerate graphs, that is, graphs such that any subgraph contains a vertex of degree at most $d$. This graph class generalizes many classes of graphs for which effective kernelization is known to exist, for example, planar graphs, $H$-minor free graphs, and $H$-topological-minor free graphs. We show that for several natural problems on $d$-degenerate graphs the best-known kernelization upper bounds are essentially tight. In particular, using intricate constructions of weak compositions, we prove that unless $ {\rm coNP} \subseteq {\rm NP} / \poly \colon $ \bullet Dominating Set has no kernels of size $ O(k^{(d - 1)(d - 3) - \epsilon })$ for any $ \epsilon > 0$. The current best upper bound is $ O(k^{(d + 1)}^2)$. \bullet Independent Dominating Set has no kernels of size $ O(k^{d - 4 - \epsilon })$ for any $ \epsilon > 0$. The current best upper bound is $ O(k^{d + 1})$. \bullet Induced Matching has no kernels of size $ O(k^{d - 3 - \epsilon })$ for any $ \epsilon > 0$. The current best upper bound is $ O(k^d)$. To the best of our knowledge, Dominating Set is the first problem where a lower bound with superlinear dependence on $d$ (in the exponent) can be proved. In the last section of the article, we also give simple kernels for Connected Vertex Cover and Capacitated Vertex Cover of size $ O(k^d)$ and $ O(k^{d + 1})$, respectively. We show that the latter problem has no kernels of size $ O(k^{d - \epsilon })$ unless $ {\rm coNP} \subseteq {\rm NP} / \poly $ by a simple reduction from $d$-Exact Set Cover (the same lower bound for Connected Vertex Cover on $d$-degenerate graphs is already known).", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } %%% NB: From volume 13 number 4 onward, no further attempts will be made %%% to repair the often badly botched mathematical text in abstracts; %%% the task is simply too time consuming. @Article{Gaspers:2017:SMC, author = "Serge Gaspers and Gregory B. Sorkin", title = "Separate, Measure and Conquer: Faster Polynomial-Space Algorithms for {Max $2$-CSP} and Counting Dominating Sets", journal = j-TALG, volume = "13", number = "4", pages = "44:1--44:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3111499", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. The method capitalizes on the existence of small balanced separators for sparse graphs, which can be exploited for branching to disconnect an instance into independent components. For this algorithm design paradigm, the challenge to date has been to obtain improvements in worst-case analyses of algorithms, compared with algorithms that are analyzed with advanced methods, notably Measure and Conquer. Our contribution is the design of a general method to integrate the advantage from the separator-branching into Measure and Conquer, for a more precise and improved running time analysis. We illustrate the method with improved algorithms for Max(r,2)-CSP and \#Dominating Set. An instance of the problem Max(r,2)-CSP, or simply Max 2-CSP, is parameterized by the domain size r (often 2), the number of variables n (vertices in the constraint graph G ), and the number of constraints m (edges in G ). When G is cubic, and omitting sub-exponential terms here for clarity, we give an algorithm running in time r$^{(1 / 5) n}$ = r$^{(2 / 15) m}$ the previous best was r$^{(1 / 4) n}$ = r$^{(1 / 6) m}$. By known results, this improvement for the cubic case results in an algorithm running in time r$^{(9 / 50) m}$ for general instances; the previous best was r$^{(19 / 100) m}$. We show that the analysis of the earlier algorithm was tight: our improvement is in the algorithm, not just the analysis. The same running time improvements hold for Max Cut, an important special case of Max 2-CSP, and for Polynomial and Ring CSP, generalizations encompassing graph bisection, the Ising model, and counting. We also give faster algorithms for \#Dominating Set, counting the dominating sets of every cardinality 0, \&ldots, n for a graph G of order n. For cubic graphs, our algorithm runs in time 3$^{(1 / 5) n}$ the previous best was 2$^{(1 / 2) n}$. For general graphs, we give an unrelated algorithm running in time 1.5183$^n$ the previous best was 1.5673$^n$. The previous best algorithms for these problems all used local transformations and were analyzed by the Measure and Conquer method. Our new algorithms capitalize on the existence of small balanced separators for cubic graphs-a non-local property-and the ability to tailor the local algorithms always to ``pivot'' on a vertex in the separator. The new algorithms perform much as the old ones until the separator is empty, at which point they gain because the remaining vertices are split into two independent problem instances that can be solved recursively. It is likely that such algorithms can be effective for other problems too, and we present their design and analysis in a general framework.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gabow:2017:DSN, author = "Harold N. Gabow", title = "A Data Structure for Nearest Common Ancestors with Linking", journal = j-TALG, volume = "13", number = "4", pages = "45:1--45:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3108240", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider a forest that evolves via link operations that make the root of one tree the child of a node in another tree. Intermixed with link operations are nca operations, which return the nearest common ancestor of two given nodes when such exists. This article shows that a sequence of m such nca and link operations on a forest of n nodes can be processed online in time O ( m \alpha ( m, n )+ n ). This was previously known only for a restricted type of link operation. The special case where a link only extends a tree by adding a new leaf occurs in Edmonds' algorithm for finding a maximum weight matching on a general graph. Incorporating our algorithm into the implementation of Edmonds' algorithm in [9] achieves time O ( n ( m + n log n )) for weighted matching, an arguably optimum asymptotic bound ( n and m are the number of vertices and edges, respectively). Our data structure also provides a simple alternative implementation of the incremental-tree set merging algorithm of Gabow and Tarjan [11].", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ramanujan:2017:LTP, author = "M. S. Ramanujan and Saket Saurabh", title = "Linear-Time Parameterized Algorithms via Skew-Symmetric Multicuts", journal = j-TALG, volume = "13", number = "4", pages = "46:1--46:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3128600", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A skew-symmetric graph ( D = ( V, A ), \sigma ) is a directed graph D with an involution \sigma on the set of vertices and arcs. Flows on skew-symmetric graphs have been used to generalize maximum flow and maximum matching problems on graphs, initially by Tutte and later by Goldberg and Karzanov. In this article, we introduce a separation problem, d-Skew-Symmetric Multicut, where we are given a skew-symmetric graph D, a family \tau of d -size subsets of vertices, and an integer k. The objective is to decide whether there is a set X \sqsubseteq A of k arcs such that every set J in the family has a vertex \upsilon such that \upsilon and \sigma ( \upsilon ) are in different strongly connected components of D '=( V, A \ ( X \cup \sigma (X))). In this work, we give an algorithm for d-Skew-Symmetric Multicut that runs in time O ((4 d )$^k$ ( m + n +l)), where m is the number of arcs in the graph, n is the number of vertices, and l is the length of the family given in the input. This problem, apart from being independently interesting, also captures the main combinatorial difficulty of numerous classical problems. Our algorithm for \& d-Skew-Symmetric Multicut paves the way for the first linear-time parameterized algorithms for several problems. We demonstrate its utility by obtaining the following linear-time parameterized algorithms: --- We show that Almost 2-SAT is a special case of 1-Skew-Symmetric Multicut, resulting in an algorithm for Almost 2-SAT that runs in time O (4$^k$ k$^4$ l), where k is the size of the solution and l is the length of the input formula. Then, using linear-time parameter-preserving reductions to Almost 2-SAT, we obtain algorithms for Odd Cycle Transversal and Edge Bipartization that run in time O (4$^k$ k$^4$ ( m + n )) and O (4$^k$ k$^5$ ( m + n )), respectively, where k is the size of the solution, and m and n are the number of edges and vertices respectively. This resolves an open problem posed by Reed et al. and improves on the earlier almost-linear-time algorithm of Kawarabayashi and Reed. --- We show that Deletion q-Horn Backdoor Set Detection is a special case of 3-Skew-Symmetric Multicut, giving us an algorithm for Deletion q-Horn Backdoor Set Detection that runs in time $ O(12^k k^5 l)$, where $k$ is the size of the solution and l is the length of the input formula. This gives the first fixed-parameter tractable algorithm for this problem answering a question posed in a work by Narayanaswamy et al. Using this result, we get an algorithm for Satisfiability that runs in time $ O(12^k k^5 l)$, where k is the size of the smallest q-Horn deletion backdoor set, with l being the length of the input formula.", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hwang:2017:EAS, author = "Hsien-Kuei Hwang and Svante Janson and Tsung-Hsi Tsai", title = "Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications", journal = j-TALG, volume = "13", number = "4", pages = "47:1--47:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3127585", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Divide-and-conquer recurrences of the form f ( n ) = f ( \lfloor \&fracn2; \rfloor ) + f ( \lceil \&fracn2; \rceil ) + g ( n ) ( n \geq 2), with g ( n ) and f (1) given, appear very frequently in the analysis of computer algorithms and related areas. While most previous methods and results focus on simpler crude approximation to the solution, we show that the solution always satisfies the simple identity f ( n ) = n P (log$_2$ n ) --- Q ( n ) under an optimum (iff) condition on g ( n ). This form is not only an identity but also an asymptotic expansion because Q ( n ) is of a smaller order than linearity. Explicit forms for the continuous periodic function P are provided. We show how our results can be easily applied to many dozens of concrete examples collected from the literature and how they can be extended in various directions. Our method of proof is surprisingly simple and elementary but leads to the strongest types of results for all examples to which our theory applies.", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bjorklund:2017:CTS, author = "Andreas Bj{\"o}rklund and Petteri Kaski and Lukasz Kowalik", title = "Counting Thin Subgraphs via Packings Faster than Meet-in-the-Middle Time", journal = j-TALG, volume = "13", number = "4", pages = "48:1--48:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3125500", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Vassilevska and Williams (STOC'09) showed how to count simple paths on k vertices and matchings on k /2 edges in an n -vertex graph in time n$^{k / 2 + O (1)}$. In the same year, two different algorithms with the same runtime were given by Koutis and Williams (ICALP'09), and Bj{\"o}rklund et al. (ESA'09), via n$^{st / 2 + O (1)}$ -time algorithms for counting t -tuples of pairwise disjoint sets drawn from a given family of s-sized subsets of an n -element universe. Shortly afterwards, Alon and Gutner (TALG'10) showed that these problems have \Omega ( n$^{ \lfloor st / 2 \rfloor }$ ) and \Omega ( n$^{ \lfloor k / 2 \rfloor }$ ) lower bounds when counting by color coding. Here, we show that one can do better-we show that the ``meet-in-the-middle'' exponent st /2 can be beaten and give an algorithm that counts in time n$^{0.45470382 st + O (1)}$ for t a multiple of three. This implies algorithms for counting occurrences of a fixed subgraph on k vertices and pathwidth $ p \ll k$ in an $n$-vertex graph in $ n^{0.45470382 k + 2 p + O (1)}$ time, improving on the three mentioned algorithms for paths and matchings, and circumventing the color-coding lower bound. We also give improved bounds for counting t-tuples of disjoint s-sets for s= 2, 3, 4. Our algorithms use fast matrix multiplication. We show an argument that this is necessary to go below the meet-in-the-middle barrier.", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fukunaga:2017:SCP, author = "Takuro Fukunaga", title = "Spider Covers for Prize-Collecting Network Activation Problem", journal = j-TALG, volume = "13", number = "4", pages = "49:1--49:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3132742", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the network activation problem, each edge in a graph is associated with an activation function that decides whether the edge is activated from weights assigned to its end nodes. The feasible solutions of the problem are node weights such that the activated edges form graphs of required connectivity, and the objective is to find a feasible solution minimizing its total weight. In this article, we consider a prize-collecting version of the network activation problem and present the first nontrivial approximation algorithms. Our algorithms are based on a new linear programming relaxation of the problem. They round optimal solutions for the relaxation by repeatedly computing node weights activating subgraphs, called spiders, which are known to be useful for approximating the network activation problem. For the problem with node-connectivity requirements, we also present a new potential function on uncrossable biset families and use it to analyze our algorithms.", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Shi:2017:DPD, author = "Elaine Shi and T.-H. Hubert Chan and Eleanor Rieffel and Dawn Song", title = "Distributed Private Data Analysis: Lower Bounds and Practical Constructions", journal = j-TALG, volume = "13", number = "4", pages = "50:1--50:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3146549", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a distributed private data analysis setting, where multiple parties each hold some sensitive data and they wish to run a protocol to learn some aggregate statistics over the distributed dataset, while protecting each user's privacy. As an initial effort, we consider a distributed summation problem. We first show a lower bound, that is, under information-theoretic differential privacy, any multi-party protocol with a small number of messages must have large additive error. We then show that by adopting a computational differential privacy notion, one can circumvent this lower bound and design practical protocols for the periodic distributed summation problem. Our construction has several desirable features. First, it works in the client-server model and requires no peer-to-peer communication among the clients. Second, our protocol is fault tolerant and can output meaningful statistics even when a subset of the participants fail to respond. Our constructions guarantee the privacy of honest parties even when a fraction of the participants may be compromised and colluding. In addition, we propose a new distributed noise addition mechanism that guarantees small total error.", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Henzinger:2017:STM, author = "Monika Henzinger and Sebastian Krinninger and Danupon Nanongkai", title = "Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks", journal = j-TALG, volume = "13", number = "4", pages = "51:1--51:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3146550", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic (1+ \epsilon )-approximation algorithms whose amortized time (over some number of link changes) is sublinear in D, the maximum diameter of the network. Our technique also leads to a deterministic (1+ \epsilon )-approximate incremental algorithm for single-source shortest paths in the sequential (usual RAM) model. Prior to our work, the state of the art was the classic exact algorithm of Even and Shiloach (1981), which is optimal under some assumptions (Roditty and Zwick 2011; Henzinger et al. 2015). Our result is the first to show that, in the incremental setting, this bound can be beaten in certain cases if some approximation is allowed.", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Amanatidis:2017:AAC, author = "Georgios Amanatidis and Evangelos Markakis and Afshin Nikzad and Amin Saberi", title = "Approximation Algorithms for Computing Maximin Share Allocations", journal = j-TALG, volume = "13", number = "4", pages = "52:1--52:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3147173", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the problem of computing maximin share allocations, a recently introduced fairness notion. Given a set of n agents and a set of goods, the maximin share of an agent is the best she can guarantee to herself, if she is allowed to partition the goods in any way she prefers, into n bundles, and then receive her least desirable bundle. The objective then is to find a partition, where each agent is guaranteed her maximin share. Such allocations do not always exist, hence we resort to approximation algorithms. Our main result is a 2/3-approximation that runs in polynomial time for any number of agents and goods. This improves upon the algorithm of Procaccia and Wang (2014), which is also a 2/3-approximation but runs in polynomial time only for a constant number of agents. To achieve this, we redesign certain parts of the algorithm in Procaccia and Wang (2014), exploiting the construction of carefully selected matchings in a bipartite graph representation of the problem. Furthermore, motivated by the apparent difficulty in establishing lower bounds, we undertake a probabilistic analysis. We prove that in randomly generated instances, maximin share allocations exist with high probability. This can be seen as a justification of previously reported experimental evidence. Finally, we provide further positive results for two special cases arising from previous works. The first is the intriguing case of three agents, where we provide an improved 7/8-approximation. The second case is when all item values belong to {0, 1, 2}, where we obtain an exact algorithm.", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Haeupler:2017:PAC, author = "Bernhard Haeupler and David G. Harris", title = "Parallel Algorithms and Concentration Bounds for the {Lov{\'a}sz} Local Lemma via Witness {DAGs}", journal = j-TALG, volume = "13", number = "4", pages = "53:1--53:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3147211", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Lov{\'a}sz Local Lemma (LLL) is a cornerstone principle in the probabilistic method of combinatorics, and a seminal algorithm of Moser and Tardos (2010) provides an efficient randomized algorithm to implement it. This can be parallelized to give an algorithm that uses polynomially many processors and runs in O (log$^3$ n ) time on an EREW PRAM, stemming from O (log n ) adaptive computations of a maximal independent set (MIS). Chung et al. (2014) developed faster local and parallel algorithms, potentially running in time O (log$^2$ n ), but these algorithms require more stringent conditions than the LLL. We give a new parallel algorithm that works under essentially the same conditions as the original algorithm of Moser and Tardos but uses only a single MIS computation, thus running in O (log$^2$ n ) time on an EREW PRAM. This can be derandomized to give an NC algorithm running in time O (log$^2$ n ) as well, speeding up a previous NC LLL algorithm of Chandrasekaran et al. (2013). We also provide improved and tighter bounds on the runtimes of the sequential and parallel resampling-based algorithms originally developed by Moser and Tardos. These apply to any problem instance in which the tighter Shearer LLL criterion is satisfied.", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Makarychev:2017:MPS, author = "Konstantin Makarychev and Maxim Sviridenko", title = "Maximizing Polynomials Subject to Assignment Constraints", journal = j-TALG, volume = "13", number = "4", pages = "54:1--54:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3147137", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the $q$-adic assignment problem. We first give an $ O(n^{(q - 1) / 2})$-approximation algorithm for the Koopmans--Beckman version of the problem, improving upon the result of Barvinok. Then, we introduce a new family of instances satisfying ``tensor triangle inequalities'' and give a constant factor approximation algorithm for them. We show that many classical optimization problems can be modeled by $q$-adic assignment problems from this family. Finally, we give several integrality gap examples for the natural LP relaxations of the problem.", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elmasry:2017:TOS, author = "Amr Elmasry", title = "Toward Optimal Self-Adjusting Heaps", journal = j-TALG, volume = "13", number = "4", pages = "55:1--55:??", month = dec, year = "2017", CODEN = "????", DOI = "https://doi.org/10.1145/3147138", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give a variant of the pairing heaps that achieves the following amortized costs: O (1) per find-min and insert, O (log log n ) per decrease-key and meld, O (log n ) per delete-min; where n is the number of elements in the resulting heap on which the operation is performed. These bounds are the best known for any self-adjusting heap and match two lower bounds, one established by Fredman and the other by Iacono and {\"O}zkan, for a family of self-adjusting heaps that generalizes the pairing heaps but do not include our variant. We further show how to reduce the amortized cost for meld to be paid by the other operations, on the expense of increasing that of delete-min to O (log n + log log N ), where N is the total number of elements in the collection of heaps of the data structure (not just the heap under consideration by the operation).", acknowledgement = ack-nhfb, articleno = "55", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chowdhury:2018:COB, author = "Rezaul A. Chowdhury and Vijaya Ramachandran", title = "Cache-Oblivious Buffer Heap and Cache-Efficient Computation of Shortest Paths in Graphs", journal = j-TALG, volume = "14", number = "1", pages = "1:1--1:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3147172", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the buffer heap, a cache-oblivious priority queue that supports Delete-Min, Delete, and a hybrid Insert / Decrease-Key operation in O (1/ B log$_2$ N / M ) amortized block transfers from main memory, where M and B are the (unknown) cache size and block size, respectively, and N is the number of elements in the queue. We introduce the notion of a slim data structure that captures the situation when only a limited portion of the cache, which we call a slim cache, is available to the data structure to retain data between data structural operations. We show that a buffer heap automatically adapts to such an environment and supports all operations in O (1/ \lambda + 1/ B log$_2$ N / \lambda ) amortized block transfers each when the size of the slim cache is \lambda . Our results provide substantial improvements over known trivial cache performance bounds for cache-oblivious priority queues with Decrease-Keys. Using the buffer heap, we present cache-oblivious implementations of Dijkstra's algorithm for undirected and directed single-source shortest path (SSSP) problems for graphs with non-negative real edge-weights. On a graph with n vertices and m edges, our algorithm for the undirected case performs O ( n + m / B log$_2$ n / M ) block transfers and for the directed case performs O (( n + m / B ) c log$_2$ n / B ) block transfers. These results give the first non-trivial cache-oblivious bounds for the SSSP problem on general graphs. For the all-pairs shortest path (APSP) problem on weighted undirected graphs, we incorporate slim buffer heaps into multi-buffer-buffer-heaps and use these to improve the cache-aware cache complexity. We also present a simple cache-oblivious APSP algorithm for unweighted undirected graphs that performs O ( m n / B log$_{M / B}$ n / B ) block transfers. This matches the cache-aware bound and is a substantial improvement over the previous cache-oblivious bound for the problem.", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Eppstein:2018:PCP, author = "David Eppstein", title = "The Parametric Closure Problem", journal = j-TALG, volume = "14", number = "1", pages = "2:1--2:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3147212", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We define the parametric closure problem, in which the input is a partially ordered set whose elements have linearly varying weights and the goal is to compute the sequence of minimum-weight downsets of the partial order as the weights vary. We give polynomial time solutions to many important special cases of this problem including semiorders, reachability orders of bounded-treewidth graphs, partial orders of bounded width, and series-parallel partial orders. Our result for series-parallel orders provides a significant generalization of a previous result of Carlson and Eppstein on bicriterion subtree problems.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lokshtanov:2018:IED, author = "Daniel Lokshtanov and Marcin Pilipczuk and Erik Jan {Van Leeuwen}", title = "Independence and Efficient Domination on {$ P_6 $}-free Graphs", journal = j-TALG, volume = "14", number = "1", pages = "3:1--3:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3147214", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the M aximum Weight Independent Set problem, the input is a graph G, every vertex has a non-negative integer weight, and the task is to find a set S of pairwise nonadjacent vertices, maximizing the total weight of the vertices in S. We give an $ n^{O(\log^2 n)} $ time algorithm for this problem on graphs excluding the path P$_6$ on 6 vertices as an induced subgraph. Currently, there is no constant k known for which Maximum Weight Independent Set on P$_k$ -free graphs becomes NP-hard, and our result implies that if such a k exists, then k {$>$} 6 unless all problems in NP can be decided in quasi-polynomial time. Using the combinatorial tools that we develop for this algorithm, we also give a polynomial-time algorithm for M aximum Weight Efficient Dominating Set on P$_6$ -free graphs. In this problem, the input is a graph G, every vertex has an integer weight, and the objective is to find a set S of maximum weight such that every vertex in G has exactly one vertex in S in its closed neighborhood or to determine that no such set exists. Prior to our work, the class of P$_6$ -free graphs was the only class of graphs defined by a single forbidden induced subgraph on which the computational complexity of Maximum Weight Efficient Dominating Set was unknown.", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Held:2018:BAC, author = "Stephan Held and Sophie Theresa Spirkl", title = "Binary Adder Circuits of Asymptotically Minimum Depth, Linear Size, and Fan-Out Two", journal = j-TALG, volume = "14", number = "1", pages = "4:1--4:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3147215", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of constructing fast and small binary adder circuits. Among widely used adders, the Kogge-Stone adder is often considered the fastest, because it computes the carry bits for two n -bit numbers (where n is a power of two) with a depth of 2 log$_2$ n logic gates, size 4 n log$_2$ n, and all fan-outs bounded by two. Fan-outs of more than two are disadvantageous in practice, because they lead to the insertion of repeaters for repowering the signal and additional depth in the physical implementation. However, the depth bound of the Kogge-Stone adder is off by a factor of two from the lower bound of log$_2$ n. Two separate constructions by Brent and Krapchenko achieve this lower bound asymptotically. Brent's construction gives neither a bound on the fan-out nor the size, while Krapchenko's adder has linear size, but can have up to linear fan-out. With a fan-out bound of two, neither construction achieves a depth of less than 2 log$_2$ n. In a further approach, Brent and Kung proposed an adder with linear size and fan-out two but twice the depth of the Kogge-Stone adder. These results are 33-43 years old and no substantial theoretical improvement for has been made since then. In this article, we integrate the individual advantages of all previous adder circuits into a new family of full adders, the first to improve on the depth bound of 2 log$_2$ n while maintaining a fan-out bound of two. Our adders achieve an asymptotically optimum logic gate depth of log$_2$ n + o (log$_2$ n ) and linear size O ( n ).", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Devanur:2018:PDG, author = "Nikhil R. Devanur and Zhiyi Huang", title = "Primal Dual Gives Almost Optimal Energy-Efficient Online Algorithms", journal = j-TALG, volume = "14", number = "1", pages = "5:1--5:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3155297", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of online scheduling of jobs on unrelated machines with dynamic speed scaling to minimize the sum of energy and weighted flow-time. We give an algorithm with an almost optimal competitive ratio for arbitrary power functions. (No earlier results handled arbitrary power functions for unrelated machines.) For power functions of the form f ( s ) = s$^{ \alpha }$ for some constant \alpha {$>$} 1, we get a competitive ratio of O ( \alpha \&frac; log \alpha ), improving upon a previous competitive ratio of O ( \alpha $^2$ ) by Anand et al. (2012), along with a matching lower bound of \Omega ( \alpha \&frac; log \alpha ). Further, in the resource augmentation model, with a 1+ \epsilon speed up, we give a 2(1\&frac; \epsilon + 1) competitive algorithm, with essentially the same techniques, improving the bound of 1 + O (1\&frac; \epsilon $^2$ ) by Gupta et al. (2010) and matching the bound of Anand et al. (2012) for the special case of fixed speed unrelated machines. Unlike the previous results most of which used an amortized local competitiveness argument or dual fitting methods, we use a primal-dual method, which is useful not only to analyze the algorithms but also to design the algorithm itself.", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fomin:2018:KCD, author = "Fedor V. Fomin and Daniel Lokshtanov and Saket Saurabh and Dimitrios M. Thilikos", title = "Kernels for (Connected) Dominating Set on Graphs with Excluded Topological Minors", journal = j-TALG, volume = "14", number = "1", pages = "6:1--6:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3155298", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give the first linear kernels for the Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a topological minor. In other words, we prove the existence of polynomial time algorithms that, for a given H -topological-minor-free graph G and a positive integer k, output an H-topological-minor-free graph G$^'$ on O ( k ) vertices such that G has a (connected) dominating set of size k if and only if G$^'$ has one. Our results extend the known classes of graphs on which the Dominating Set and Connected Dominating Set problems admit linear kernels. Prior to our work, it was known that these problems admit linear kernels on graphs excluding a fixed apex graph H as a minor. Moreover, for Dominating Set, a kernel of size k$^{c (H)}$, where c ( H ) is a constant depending on the size of H, follows from a more general result on the kernelization of Dominating Set on graphs of bounded degeneracy. Alon and Gutner explicitly asked whether one can obtain a linear kernel for Dominating Set on H -minor-free graphs. We answer this question in the affirmative and in fact prove a more general result. For Connected Dominating Set no polynomial kernel even on H minor-free graphs was known prior to our work. On the negative side, it is known that Connected Dominating Set on 2-degenerated graphs does not admit a polynomial kernel unless coNP \subseteq NP/poly. Our kernelization algorithm is based on a non-trivial combination of the following ingredients o The structural theorem of Grohe and Marx [STOC 2012] for graphs excluding a fixed graph H as a topological minor; o A novel notion of protrusions, different than the one defined in [FOCS 2009]; o Our results are based on a generic reduction rule that produces an equivalent instance (in case the input graph is H -minor-free) of the problem, with treewidth O (\&sqrt; k ). The application of this rule in a divide-and-conquer fashion, together with the new notion of protrusions, gives us the linear kernels. A protrusion in a graph [FOCS 2009] is a subgraph of constant treewidth which is separated from the rest of the graph by at most a constant number of vertices. In our variant of protrusions, instead of stipulating that the subgraph be of constant treewidth, we ask that it contains a constant number of vertices from a solution. We believe that this new take on protrusions would be useful for other graph problems and in different algorithmic settings.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lokshtanov:2018:LTP, author = "Daniel Lokshtanov and M. S. Ramanujan and Saket Saurabh", title = "Linear Time Parameterized Algorithms for Subset Feedback Vertex Set", journal = j-TALG, volume = "14", number = "1", pages = "7:1--7:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3155299", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the Subset Feedback Vertex Set (Subset FVS) problem, the input is a graph G on n vertices and m edges, a subset of vertices T, referred to as terminals, and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every cycle that contains a terminal. The study of parameterized algorithms for this generalization of the Feedback Vertex Set problem has received significant attention over the past few years. In fact, the parameterized complexity of this problem was open until 2011, when two groups independently showed that the problem is fixed parameter tractable. Using tools from graph minors,, Kawarabayashi and Kobayashi obtained an algorithm for Subset FVS running in time O ( f ( k )c n$^2$ m ) [SODA 2012, JCTB 2012]. Independently, Cygan et al. [ICALP 2011, SIDMA 2013] designed an algorithm for Subset FVS running in time 2$^{O (k log k)}$ c n$^{O (1)}$. More recently, Wahlstr{\"o}m obtained the first single exponential time algorithm for Subset FVS, running in time 4$^k$ c n$^{O (1)}$ [SODA 2014]. While the 2$^{O (k)}$ dependence on the parameter k is optimal under the Exponential Time Hypothesis, the dependence of this algorithm as well as those preceding it, on the input size is at least quadratic. In this article, we design the first linear time parameterized algorithms for Subset FVS. More precisely, we obtain the following new algorithms for Subset FVS. --- A randomized algorithm for Subset FVS running in time O (25.6$^k$ c ( n + m )). --- A deterministic algorithm for Subset FVS running in time 2 O ( k log k ) c ( n + m ). Since it is known that assuming the Exponential Time Hypothesis, Subset FVS cannot have an algorithm running in time 2$^{o (k)}$ n$^{O (1)}$, our first algorithm obtains the best possible asymptotic dependence on both the parameter as well as the input size. Both of our algorithms are based on ``cut centrality,'' in the sense that solution vertices are likely to show up in minimum size cuts between vertices sampled from carefully chosen distributions.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Duan:2018:SAW, author = "Ran Duan and Seth Pettie and Hsin-Hao Su", title = "Scaling Algorithms for Weighted Matching in General Graphs", journal = j-TALG, volume = "14", number = "1", pages = "8:1--8:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3155301", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a new scaling algorithm for maximum (or minimum) weight perfect matching on general, edge weighted graphs. Our algorithm runs in O ( m \&sqrt; n log( n N )) time, O ( m \&sqrt; n ) per scale, which matches the running time of the best cardinality matching algorithms on sparse graphs [16, 20, 36, 37]. Here, m, n, and N bound the number of edges, vertices, and magnitude, respectively, of any integer edge weight. Our result improves on a 25-year-old algorithm of Gabow and Tarjan, which runs in O ( m \&sqrt; n log n \alpha ( m, n ) log( n N )) time.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2018:RCD, author = "T.-H. Hubert Chan and Shaofeng H.-C. Jiang", title = "Reducing Curse of Dimensionality: Improved {PTAS} for {TSP} (with Neighborhoods) in Doubling Metrics", journal = j-TALG, volume = "14", number = "1", pages = "9:1--9:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3158232", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the Traveling Salesman Problem with Neighborhoods (TSPN) in doubling metrics. The goal is to find the shortest tour that visits each of a given collection of subsets (regions or neighborhoods) in the underlying metric space. We give a randomized polynomial-time approximation scheme (PTAS) when the regions are fat weakly disjoint. This notion of regions was first defined when a QPTAS was given for the problem in SODA 2010 (Chan and Elbassioni 2010). The regions are partitioned into a constant number of groups, where in each group, regions should have a common upper bound on their diameters and each region designates one point within it such that these points are far away from one another. We combine the techniques in the previous work, together with the recent PTAS for TSP (STOC 2012: Bartal, Gottlieb, and Krauthgamer 2012) to achieve a PTAS for TSPN. However, several nontrivial technical hurdles need to be overcome for applying the PTAS framework to TSPN: (1) Heuristic to detect sparse instances. In the STOC 2012 paper, a minimum spanning tree heuristic is used to estimate the portion of an optimal tour within some ball. However, for TSPN, it is not known if an optimal tour would use points inside the ball to visit regions that intersect the ball. (2) Partially cut regions in the recursion. After a sparse ball is identified by the heuristic, the PTAS framework for TSP uses dynamic programming to solve the instance restricted to the sparse ball and recurse on the remaining instance. However, for TSPN, it is an important issue to decide whether each region partially intersecting the sparse ball should be solved in the sparse instance or considered in the remaining instance. Surprisingly, we show that both issues can be resolved by conservatively making the ball in question responsible for all intersecting regions. In particular, a sophisticated charging argument is needed to bound the cost of combining tours in the recursion. Moreover, more refined procedures are used to improve the dependence of the running time on the doubling dimension k from the previous exp[( O (1))$^{k 2}$ ] (even for just TSP) to exp[2$^{O (k log k)}$ ].", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Parter:2018:FTA, author = "Merav Parter and David Peleg", title = "Fault-Tolerant Approximate {BFS} Structures", journal = j-TALG, volume = "14", number = "1", pages = "10:1--10:??", month = jan, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3022730", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sun Feb 18 07:13:58 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A fault-tolerant structure for a network is required to continue functioning following the failure of some of the network's edges or vertices. This article addresses the problem of designing a fault-tolerant ( \alpha, \beta ) approximate BFS structure (or FT-ABFS structure for short), namely, a subgraph H of the network G such that subsequent to the failure of some subset F of edges or vertices, the surviving part of H (namely, H \ F ) still contains an approximate BFS spanning tree for (the surviving part of) G, satisfying dist( s,v,H \ F ) {$<$}= \alpha c dist( s,v,G \ F )+ \beta for every v \in V. Our first result is an algorithm that given an n -vertex unweighted undirected graph G and a source s constructs a multiplicative (3,0) FT-ABFS structure rooted at s resilient to a failure of a single edge with at most 4 n edges (improving by an O (log n ) factor on the near-tight result of Baswana and Khanna (2010) for the special case of edge failures). This was recently improved to 2n edges by Bil{\`o} et al. (2014). Next, we consider the multiple edge faults case, for a constant integer f {$>$1}, we prove that there exists a (polynomial-time constructible) (3 f, f log n ) FT-ABFS structure with O ( f n ) edges that is resilient against f faults. We also show the existence of a (3 f +1,0) FT-ABFS structure with O ( f log$^f$ n c n ) edges. We then consider additive (1, \beta ) FT-ABFS structures and demonstrate an interesting dichotomy between multiplicative and additive spanners. In contrast to the linear size of ( \alpha, 0) FT-ABFS structures, we show that for every n, there exist \delta, \epsilon {$>$}0, and n -vertex graphs G with a source s for which any (1, n$^{ \delta }$ ) FT-ABFS structure rooted at s has \Omega ( n$^{7 / 6}$ - \epsilon ) edges. For the case of additive stretch 3, we show that (1,3) FT-ABFS structures admit a lower bound of \Omega ( n$^{5 / 4}$ ) edges.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2018:SSR, author = "Timothy M. Chan and J. Ian Munro and Venkatesh Raman", title = "Selection and Sorting in the {``Restore''} Model", journal = j-TALG, volume = "14", number = "2", pages = "11:1--11:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3168005", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the classical selection and sorting problems in a model where the initial permutation of the input has to be restored after completing the computation. Such algorithms are useful for designing space-efficient algorithms, when one encounters subproblems that have to be solved by subroutines. It is important that these subroutines leave the array in its original state after they finish so that the computation can be properly resumed. Algorithms in this model can also be relevant for saving communication time, in case the data is distributed among several machines and would need to be copied to further machines for execution of the subroutine. Although the requirement of the restoration is stringent compared to the classical versions of the problems, this model is more relaxed than a read-only memory where the input elements are not allowed to be moved within the input array. We first show that for a sequence of n integers, selection (finding the median or more generally the k -th smallest element for a given k ) can be done in O ( n ) time using O (lg n ) words$^1$ of extra space in this model. In contrast, no linear-time selection algorithm is known that uses polylogarithmic space in the read-only memory model. For sorting n integers in this model, we first present an O ( n lg n )-time algorithm using O (lg n ) words of extra space that outputs (in a write only tape) the given sequence in sorted order while restoring the order of the original input in the input tape. When the universe size U is polynomial in n, we give a faster O ( n )-time algorithm (analogous to radix sort) that uses O ( n$^{ \epsilon }$ ) words of extra space for an arbitrarily small constant \epsilon {$>$} 0. More generally, we show how to match the time bound of any word-RAM integer sorting algorithms using O ( n$^{ \epsilon }$ ) words of extra space. In sharp contrast, there is an \Omega ( n$^2$ / S )-time lower bound for integer sorting using O ( S ) bits of space in the read-only memory model. Extension of our results to arbitrary input types beyond integers is not possible: for ``indivisible'' input elements, we can prove the same \Omega ( n$^2$ / S ) lower bound for sorting in our model. We also describe space-efficient algorithms to count the number of inversions in a given sequence in this model. En route, we develop linear-time in-place algorithms to extract leading bits of the input array and to compress and decompress strings with low entropy; these techniques may be of independent interest.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2018:ANW, author = "T.-H. Hubert Chan and Fei Chen and Xiaowei Wu", title = "Analyzing Node-Weighted Oblivious Matching Problem via Continuous {LP} with Jump Discontinuity", journal = j-TALG, volume = "14", number = "2", pages = "12:1--12:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3168008", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We prove the first non-trivial performance ratio strictly above 0.5 for the weighted Ranking algorithm on the oblivious matching problem where nodes in a general graph can have arbitrary weights. We have discovered a new structural property of the ranking algorithm: if a node has two unmatched neighbors, then it will still be matched even when its rank is demoted to the bottom. This property allows us to form LP constraints for both the weighted and the unweighted versions of the problem. Using a new class of continuous linear programming (LP), we prove that the ratio for the weighted case is at least 0.501512, and we improve the ratio for the unweighted case to 0.526823 (from the previous best 0.523166 in SODA 2014). Unlike previous continuous LP, in which the primal solution must be continuous everywhere, our new continuous LP framework allows the monotone component of the primal function to have jump discontinuities, and the other primal components to take non-conventional forms, such as the Dirac \delta function.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lokshtanov:2018:KAG, author = "Daniel Lokshtanov and D{\'a}niel Marx and Saket Saurabh", title = "Known Algorithms on Graphs of Bounded Treewidth Are Probably Optimal", journal = j-TALG, volume = "14", number = "2", pages = "13:1--13:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3170442", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that n -variable m clause SAT cannot be solved in time (2- \epsilon )$^n$ m$^{O (1)}$, we show that for any \epsilon {$>$} 0: o Independent Set cannot be solved in time (2- \epsilon )$^{tw(G)}$ | V ( G )|$^{O (1)}$, o Dominating Set cannot be solved in time (3- \epsilon )$^{tw(G)}$ | V ( G )|$^{O (1)}$, o M ax Cut cannot be solved in time (2- \epsilon )$^{tw(G)}$ | V ( G )|$^{O (1)}$, o Odd Cycle Transversal cannot be solved in time (3- \epsilon )$^{tw(G)}$ | V ( G )|$^{O (1)}$, o For any fixed q {$>$}= 3, q -Coloring cannot be solved in time ( q - \epsilon )$^{tw (G)}$ | V ( G )|$^{O (1)}$, o Partition Into Triangles cannot be solved in time (2- \epsilon )$^{tw (G)}$ | V ( G )|$^{O (1)}$. Our lower bounds match the running times for the best known algorithms for the problems, up to the \epsilon in the base.", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lokshtanov:2018:DTL, author = "Daniel Lokshtanov and Pranabendu Misra and Fahad Panolan and Saket Saurabh", title = "Deterministic Truncation of Linear Matroids", journal = j-TALG, volume = "14", number = "2", pages = "14:1--14:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3170444", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let M =( E, I ) be a matroid of rank n. A k --- truncation of M is a matroid M$^'$ =( E, I$^'$ ) such that for any A \subseteq E, A \in \in I$^'$ if and only if | A |{$<$}= k and A \in I. Given a linear representation, A, of M, we consider the problem of finding a linear representation, A$_k$, of the k-truncation of M. A common way to compute A$_k$ is to multiply the matrix A with a random k $ \times $ n matrix, yielding a simple randomized algorithm. Thus, a natural question is whether we can compute A$_k$ deterministically. In this article, we settle this question for matrices over any field in which the field operations can be done efficiently. This includes any finite field and the field of rational numbers (Q). Our algorithms are based on the properties of the classical Wronskian determinant, and the folded Wronskian determinant, which was recently introduced by Guruswami and Kopparty [23, 24] and Forbes and Shpilka [14]. Our main conceptual contribution in this article is to show that the Wronskian determinant can also be used to obtain a representation of the truncation of a linear matroid in deterministic polynomial time. An important application of our result is a deterministic algorithm to compute representative sets over linear matroids, which derandomizes a result of Fomin et al. [11, 12]. This result derandomizes several parameterized algorithms, including an algorithm for l-Matroid Parity to which several problems, such as l-Matroid Intersection, can be reduced.", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{MUTZE:2018:ECM, author = "Torsten M{\"U}TZE and Jerri Nummenpalo", title = "Efficient Computation of Middle Levels {Gray} Codes", journal = j-TALG, volume = "14", number = "2", pages = "15:1--15:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3170443", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For any integer n {$>$}= 1, a middle levels Gray code is a cyclic listing of all bitstrings of length 2 n +1 that have either n or n +1 entries equal to 1 such that any two consecutive bitstrings in the list differ in exactly one bit. The question whether such a Gray code exists for every n {$>$}= 1 has been the subject of intensive research during the past 30 years and has been answered affirmatively only recently [T. M{\"u}tze. Proof of the middle levels conjecture. Proc. London Math. Soc., 112(4):677--713, 2016]. In this work, we provide the first efficient algorithm to compute a middle levels Gray code. For a given bitstring, our algorithm computes the next l bitstrings in the Gray code in time O ( n l (1+\&frac; n l)), which is O ( n ) on average per bitstring provided that l = \Omega ( n ).", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ahmadian:2018:AAM, author = "Sara Ahmadian and Babak Behsaz and Zachary Friggstad and Amin Jorati and Mohammad R. Salavatipour and Chaitanya Swamy", title = "Approximation Algorithms for Minimum-Load $k$-Facility Location", journal = j-TALG, volume = "14", number = "2", pages = "16:1--16:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3173047", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a facility-location problem that abstracts settings where the cost of serving the clients assigned to a facility is incurred by the facility. Formally, we consider the minimum-load k-facility location (ML k FL) problem, which is defined as follows. We have a set F of facilities, a set C of clients, and an integer k {$>$}= 0. Assigning client j to a facility f incurs a connection cost d ( f, j ). The goal is to open a set F \subseteq F of k facilities and assign each client j to a facility f ( j ) \in F so as to minimize max$_{f \in }$ F \Sigma $_{j \in C : f (j) = f}$ d ( f, j ); we call \Sigma $_{j \in C : f (j) = f}$ d ( f, j ) the load of facility f. This problem was studied under the name of min-max star cover in References [3, 7], who (among other results) gave bicriteria approximation algorithms for ML k FL for when F = C. ML k FL is rather poorly understood, and only an O ( k )-approximation is currently known for ML k FL, even for line metrics. Our main result is the first polytime approximation scheme (PTAS) for ML k FL on line metrics (note that no non-trivial true approximation of any kind was known for this metric). Complementing this, we prove that ML k FL is strongly NP -hard on line metrics. We also devise a quasi-PTAS for ML k FL on tree metrics. ML k FL turns out to be surprisingly challenging even on line metrics and resilient to attack by a variety of techniques that have been successfully applied to facility-location problems. For instance, we show that (a) even a configuration-style LP-relaxation has a bad integrality gap and (b) a multi-swap k -median style local-search heuristic has a bad locality gap. Thus, we need to devise various novel techniques to attack ML k FL. Our PTAS for line metrics consists of two main ingredients. First, we prove that there always exists a near-optimal solution possessing some nice structural properties. A novel aspect of this proof is that we first move to a mixed-integer LP (MILP) encoding of the problem and argue that a MILP-solution minimizing a certain potential function possesses the desired structure and then use a rounding algorithm for the generalized-assignment problem to ``transfer'' this structure to the rounded integer solution. Complementing this, we show that these structural properties enable one to find such a structured solution via dynamic programming.", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Goranci:2018:IEM, author = "Gramoz Goranci and Monika Henzinger and Mikkel Thorup", title = "Incremental Exact Min-Cut in Polylogarithmic Amortized Update Time", journal = j-TALG, volume = "14", number = "2", pages = "17:1--17:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3174803", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with O (log$^3$ n log log$^2$ n ) amortized time per edge insertion and O (1) query time. This result partially answers an open question posed by Thorup (2007). It also stays in sharp contrast to a polynomial conditional lower bound for the fully dynamic weighted minimum cut problem. Our algorithm is obtained by combining a sparsification technique of Kawarabayashi and Thorup (2015) or its recent improvement by Henzinger, Rao, and Wang (2017), and an exact incremental algorithm of Henzinger (1997). We also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O ( n log n / \epsilon $^2$ ) space Monte Carlo algorithm that can process a stream of edge insertions starting from an empty graph, and with high probability, the algorithm maintains a (1+ \epsilon )-approximation to the minimum cut. The algorithm has O (( \alpha ( n ) log$^3$ n )/ \epsilon $^2$ ) amortized update time and constant query time, where \alpha ( n ) stands for the inverse of Ackermann function.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Anagnostopoulos:2018:RES, author = "Evangelos Anagnostopoulos and Ioannis Z. Emiris and Ioannis Psarros", title = "Randomized Embeddings with Slack and High-Dimensional Approximate Nearest Neighbor", journal = j-TALG, volume = "14", number = "2", pages = "18:1--18:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3178540", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/hash.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Approximate nearest neighbor search ( \epsilon -ANN) in high dimensions has been mainly addressed by Locality Sensitive Hashing (LSH), which has complexity with polynomial dependence in dimension, sublinear query time, but subquadratic space requirement. We introduce a new ``low-quality'' embedding for metric spaces requiring that, for some query, there exists an approximate nearest neighbor among the pre-images of its k {$>$} 1 approximate nearest neighbors in the target space. In Euclidean spaces, we employ random projections to a dimension inversely proportional to k. Our approach extends to the decision problem with witness of checking whether there exists an approximate near neighbor; this also implies a solution for \epsilon -ANN. After dimension reduction, we store points in a uniform grid of side length \epsilon /\&sqrt; d$^'$, where d$^'$ is the reduced dimension. Given a query, we explore cells intersecting the unit ball around the query. This data structure requires linear space and query time in O ( d n$^{ \rho }$ ), \rho \approx 1- \epsilon $^2$ {i$>$}/log(1 \epsilon ), where n denotes input cardinality and d space dimension. Bounds are improved for doubling subsets via r -nets. We present our implementation for \epsilon -ANN in C++ and experiments for d {$<$}= 960, n {$<$}= 10$^6$, using synthetic and real datasets, which confirm the theoretical analysis and, typically, yield better practical performance. We compare to FALCONN, the state-of-the-art implementation of multi-probe LSH: our prototype software is essentially comparable in terms of preprocessing, query time, and storage usage.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Newman:2018:ASS, author = "Alantha Newman and Heiko R{\"o}glin and Johanna Seif", title = "The Alternating Stock Size Problem and the Gasoline Puzzle", journal = j-TALG, volume = "14", number = "2", pages = "19:1--19:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3178539", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a set S of integers whose sum is zero, consider the problem of finding a permutation of these integers such that (i) all prefix sums of the ordering are nonnegative and (ii) the maximum value of a prefix sum is minimized. Kellerer et al. call this problem the stock size problem and showed that it can be approximated to within 3/2. They also showed that an approximation ratio of 2 can be achieved via several simple algorithms. We consider a related problem, which we call the alternating stock size problem, where the numbers of positive and negative integers in the input set S are equal. The problem is the same as that shown earlier, but we are additionally required to alternate the positive and negative numbers in the output ordering. This problem also has several simple 2-approximations. We show that it can be approximated to within 1.79. Then we show that this problem is closely related to an optimization version of the gasoline puzzle due to Lov{\'a}sz, in which we want to minimize the size of the gas tank necessary to go around the track. We present a 2-approximation for this problem, using a natural linear programming relaxation whose feasible solutions are doubly stochastic matrices. Our novel rounding algorithm is based on a transformation that yields another doubly stochastic matrix with special properties, from which we can extract a suitable permutation.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hujdurovic:2018:PPB, author = "Ademir Hujdurovi{\'c} and Edin Husi{\'c} and Martin Milani{\'c} and Romeo Rizzi and Alexandru I. Tomescu", title = "Perfect Phylogenies via Branchings in Acyclic Digraphs and a Generalization of {Dilworth}'s Theorem", journal = j-TALG, volume = "14", number = "2", pages = "20:1--20:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3182178", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Motivated by applications in cancer genomics and following the work of Hajirasouliha and Raphael (WABI 2014), Hujdurovi{\'c} et al. (IEEE TCBB, 2018) introduced the minimum conflict-free row split (MCRS) problem: split each row of a given binary matrix into a bitwise OR of a set of rows so that the resulting matrix corresponds to a perfect phylogeny and has the minimum possible number of rows among all matrices with this property. Hajirasouliha and Raphael also proposed the study of a similar problem, in which the task is to minimize the number of distinct rows of the resulting matrix. Hujdurovi{\'c} et al. proved that both problems are NP-hard, gave a related characterization of transitively orientable graphs, and proposed a polynomial-time heuristic algorithm for the MCRS problem based on coloring cocomparability graphs. We give new, more transparent formulations of the two problems, showing that the problems are equivalent to two optimization problems on branchings in a derived directed acyclic graph. Building on these formulations, we obtain new results on the two problems, including (1) a strengthening of the heuristic by Hujdurovi{\'c} et al. via a new min-max result in digraphs generalizing Dilworth's theorem, which may be of independent interest; (2) APX-hardness results for both problems; (3) approximation algorithms; and (4) exponential-time algorithms solving the two problems to optimality faster than the na{\"\i}ve brute-force approach. Our work relates to several well-studied notions in combinatorial optimization: chain partitions in partially ordered sets, laminar hypergraphs, and (classical and weighted) colorings of graphs.", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bienkowski:2018:DOS, author = "Marcin Bienkowski and Tomasz Jurdzinski and Miros{\l}aw Korzeniowski and Dariusz R. Kowalski", title = "Distributed Online and Stochastic Queueing on a Multiple Access Channel", journal = j-TALG, volume = "14", number = "2", pages = "21:1--21:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3182396", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problems of online and stochastic packet queueing in a distributed system of n nodes with queues, where the communication between the nodes is done via a multiple access channel. In the online setting, in each round, an arbitrary number of packets can be injected to nodes' queues. Two measures of performance are considered: the total number of packets in all queues, called the total load, and the maximum queue size, called the maximum load. We develop a deterministic distributed algorithm that is asymptotically optimal with respect to both complexity measures, in a competitive way. More precisely, the total load of our algorithm is bigger than the total load of any other algorithm, including centralized online solutions, by only an additive term of O ( n$^2$ ), whereas the maximum queue size of our algorithm is at most n times bigger than the maximum queue size of any other algorithm, with an extra additive O ( n ). The optimality for both measures is justified by proving the corresponding lower bounds, which also separates nearly exponentially distributed solutions from the centralized ones. Next, we show that our algorithm is also stochastically stable for any expected injection rate smaller or equal to 1. This is the first solution to the stochastic queueing problem on a multiple access channel that achieves such stability for the (highest possible) rate equal to 1.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Schmid:2018:CWP, author = "Andreas Schmid and Jens M. Schmidt", title = "Computing $2$-Walks in Polynomial Time", journal = j-TALG, volume = "14", number = "2", pages = "22:1--22:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3183368", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A 2-walk of a graph is a walk visiting every vertex at least once and at most twice. By generalizing decompositions of Tutte and Thomassen, Gao, Richter, and Yu proved that every 3-connected planar graph contains a closed 2-walk such that all vertices visited twice are contained in 3-separators. This seminal result generalizes Tutte's theorem that every 4-connected planar graph is Hamiltonian, as well as Barnette's theorem that every 3-connected planar graph has a spanning tree with maximum degree at most 3. The algorithmic challenge of finding such a closed 2-walk is to overcome big overlapping subgraphs in the decomposition, which are also inherent in Tutte's and Thomassen's decompositions. We solve this problem by extending the decomposition of Gao, Richter, and Yu in such a way that all pieces into which the graph is decomposed are edge-disjoint. This implies the first polynomial-time algorithm that computes the closed 2-walk just mentioned. Its running time is O ( n$^3$ ).", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Wei:2018:TSB, author = "Zhewei Wei and Ke Yi", title = "Tight Space Bounds for Two-Dimensional Approximate Range Counting", journal = j-TALG, volume = "14", number = "2", pages = "23:1--23:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3205454", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the problem of two-dimensional orthogonal range counting with additive error. Given a set P of n points drawn from an n $ \times $ n grid and an error parameter \epsilon, the goal is to build a data structure, such that for any orthogonal range R, it can return the number of points in P \cap R with additive error \epsilon n. A well-known solution for this problem is obtained by using \epsilon -approximation, which is a subset A \subseteq P that can estimate the number of points in P \cap R with the number of points in A \cap R. It is known that an \epsilon-approximation of size O (\&frac;1 \epsilon log$^{2.5}$ \&frac;1 \epsilon ) exists for any P with respect to orthogonal ranges, and the best lower bound is \Omega (\&frac;1 \epsilon log \&frac;1 \epsilon ). The \epsilon-approximation is a rather restricted data structure, as we are not allowed to store any information other than the coordinates of the points. In this article, we explore what can be achieved without any restriction on the data structure. We first describe a simple data structure that uses O (\&frac;1 \epsilon (log$^2$ \&frac;1 \epsilon + log n )) bits and answers queries with error \epsilon n. We then prove a lower bound that any data structure that answers queries with error \epsilon n will have to use \Omega (\&frac;1 \epsilon (log$^2$ \&frac;1 \epsilon + log n )) bits. Our lower bound is information-theoretic: We show that there is a collection of 2$^{ \Omega }$ ( n log n ) point sets with large union combinatorial discrepancy and thus are hard to distinguish unless we use \Omega ( n log n ) bits.", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2018:CGH, author = "Pankaj K. Agarwal and Kyle Fox and Abhinandan Nath and Anastasios Sidiropoulos and Yusu Wang", title = "Computing the {Gromov--Hausdorff} Distance for Metric Trees", journal = j-TALG, volume = "14", number = "2", pages = "24:1--24:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3185466", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Gromov-Hausdorff (GH) distance is a natural way to measure distance between two metric spaces. We prove that it is NP-hard to approximate the GH distance better than a factor of 3 for geodesic metrics on a pair of trees. We complement this result by providing a polynomial time O (min n, \&sqrt; rn )-approximation algorithm for computing the GH distance between a pair of metric trees, where r is the ratio of the longest edge length in both trees to the shortest edge length. For metric trees with unit length edges, this yields an O (\&sqrt; n )-approximation algorithm$^1$.", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ashok:2018:EAT, author = "Pradeesha Ashok and Fedor V. Fomin and Sudeshna Kolay and Saket Saurabh and Meirav Zehavi", title = "Exact Algorithms for Terrain Guarding", journal = j-TALG, volume = "14", number = "2", pages = "25:1--25:??", month = jun, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3186897", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Jun 5 06:47:03 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a 1.5-dimensional terrain T, also known as an x-monotone polygonal chain, the Terrain Guarding problem seeks a set of points of minimum size on T that guards all of the points on T. Here, we say that a point p guards a point q if no point of the line segment pq is strictly below T. The Terrain Guarding problem has been extensively studied for over 20 years. In 2005 it was already established that this problem admits a constant-factor approximation algorithm (SODA 2005). However, only in 2010 King and Krohn (SODA 2010) finally showed that Terrain Guarding is NP-hard. In spite of the remarkable developments in approximation algorithms for Terrain Guarding, next to nothing is known about its parameterized complexity. In particular, the most intriguing open questions in this direction ask whether, if parameterized by the size k of a solution guard set, it admits a subexponential-time algorithm and whether it is fixed-parameter tractable. In this article, we answer the first question affirmatively by developing an n$^{O (\sqrt k)}$ -time algorithm for both Discrete Terrain Guarding and Continuous Terrain Guarding. We also make non-trivial progress with respect to the second question: we show that Discrete Orthogonal Terrain Guarding, a well-studied special case of Terrain Guarding, is fixed-parameter tractable.", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bhattacharyya:2018:EAS, author = "Arnab Bhattacharyya and Fabrizio Grandoni and Aleksandar Nikolov and Barna Saha and Saket Saurabh and Aravindan Vijayaraghavan and Qin Zhang", title = "Editorial: {ACM-SIAM Symposium on Discrete Algorithms (SODA) 2016} Special Issue", journal = j-TALG, volume = "14", number = "3", pages = "26:1--26:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3230647", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3230647", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Abboud:2018:SIR, author = "Amir Abboud and Arturs Backurs and Thomas Dueholm Hansen and Virginia Vassilevska Williams and Or Zamir", title = "Subtree Isomorphism Revisited", journal = j-TALG, volume = "14", number = "3", pages = "27:1--27:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3093239", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3093239", abstract = "The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms are known, but for the general case truly subquadratic algorithms remain elusive. Our first result is a reduction from the Orthogonal Vectors problem to Subtree Isomorphism, showing that a truly subquadratic algorithm for the latter refutes the Strong Exponential Time Hypothesis (SETH). In light of this conditional lower bound, we focus on natural special cases for which no truly subquadratic algorithms are known. We classify these cases against the quadratic barrier, showing in particular that: o Even for binary, rooted trees, a truly subquadratic algorithm refutes SETH. o Even for rooted trees of depth O (log log n ), where n is the total number of vertices, a truly subquadratic algorithm refutes SETH. o For every constant d, there is a constant \epsilon $_d$ > 0 and a randomized, truly subquadratic algorithm for degree- d rooted trees of depth at most (1+ \epsilon $_d$ ) log$_d$ n. In particular, there is an O (min { 2.85$^h$, n$^2$ }) algorithm for binary trees of depth h. Our reductions utilize new ``tree gadgets'' that are likely useful for future SETH-based lower bounds for problems on trees. Our upper bounds apply a folklore result from randomized decision tree complexity.", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hopkins:2018:IGD, author = "Samuel B. Hopkins and Pravesh Kothari and Aaron Henry Potechin and Prasad Raghavendra and Tselil Schramm", title = "On the Integrality Gap of Degree-4 Sum of Squares for Planted Clique", journal = j-TALG, volume = "14", number = "3", pages = "28:1--28:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3178538", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3178538", abstract = "The problem of finding large cliques in random graphs and its ``planted'' variant, where one wants to recover a clique of size \omega > log ( n ) added to an Erd{\H{o}}s-R{\'e}nyi graph G ~ G ( n, 1/2), have been intensely studied. Nevertheless, existing polynomial time algorithms can only recover planted cliques of size \omega = \Omega ( \sqrt n ). By contrast, information theoretically, one can recover planted cliques so long as \omega > log ( n ). In this work, we continue the investigation of algorithms from the Sum of Squares hierarchy for solving the planted clique problem begun by Meka, Potechin, and Wigderson [2] and Deshpande and Montanari [25]. Our main result is that degree four SoS does not recover the planted clique unless \omega > \sqrt n / polylog n, improving on the bound \omega > n$^{1 / 3}$ due to Reference [25]. An argument of Kelner shows that the this result cannot be proved using the same certificate as prior works. Rather, our proof involves constructing and analyzing a new certificate that yields the nearly tight lower bound by ``correcting'' the certificate of References [2, 25, 27].", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pagh:2018:CLS, author = "Rasmus Pagh", title = "{CoveringLSH}: Locality-Sensitive Hashing without False Negatives", journal = j-TALG, volume = "14", number = "3", pages = "29:1--29:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3155300", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/hash.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3155300", abstract = "We consider a new construction of locality-sensitive hash functions for Hamming space that is covering in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius r. The construction is efficient in the sense that the expected number of hash collisions between vectors at distance cr, for a given c >1, comes close to that of the best possible data independent LSH without the covering guarantee, namely, the seminal LSH construction of Indyk and Motwani (STOC'98). The efficiency of the new construction essentially matches their bound when the search radius is not too large-e.g., when cr = o (log ( n )/ log log n ), where n is the number of points in the dataset, and when cr = log ( n )/ k, where k is an integer constant. In general, it differs by at most a factor ln (4) in the exponent of the time bounds. As a consequence, LSH-based similarity search in Hamming space can avoid the problem of false negatives at little or no cost in efficiency.", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{CHAN:2018:IDA, author = "Timothy M. CHAN", title = "Improved Deterministic Algorithms for Linear Programming in Low Dimensions", journal = j-TALG, volume = "14", number = "3", pages = "30:1--30:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3155312", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3155312", abstract = "Chazelle and Matousek [ J. Algorithms, 1996] presented a derandomization of Clarkson's sampling-based algorithm [ J. ACM, 1995] for solving linear programs with n constraints and d variables in d$^{(7 + o (1)) d}$ n deterministic time. The time bound can be improved to d$^{(5 + o (1)) d}$ n with subsequent work by Br{\"o}nnimann, Chazelle, and Matousek [ SIAM J. Comput., 1999]. We first point out a much simpler derandomization of Clarkson's algorithm that avoids \epsilon -approximations and runs in d$^{(3 + o (1)) d}$ n time. We then describe a few additional ideas that eventually improve the deterministic time bound to d$^{(1 / 2 + o (1)) d}$ n.", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Karppa:2018:FSA, author = "Matti Karppa and Petteri Kaski and Jukka Kohonen", title = "A Faster Subquadratic Algorithm for Finding Outlier Correlations", journal = j-TALG, volume = "14", number = "3", pages = "31:1--31:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3174804", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3174804", abstract = "We study the problem of detecting outlier pairs of strongly correlated variables among a collection of n variables with otherwise weak pairwise correlations. After normalization, this task amounts to the geometric task where we are given as input a set of n vectors with unit Euclidean norm and dimension d, and for some constants 0< \tau < \rho < 1, we are asked to find all the outlier pairs of vectors whose inner product is at least \rho in absolute value, subject to the promise that all but at most q pairs of vectors have inner product at most \tau in absolute value. Improving on an algorithm of Valiant [FOCS 2012; J. ACM 2015], we present a randomized algorithm that for Boolean inputs ({ -1,1}-valued data normalized to unit Euclidean length) runs in time {\~O}(( n$^{max, { 1 - \gamma + M (\Delta \gamma, \gamma), M (1 - \gamma, 2 \Delta \gamma)}}$ + qdn$^{2 \gamma }$ ), where 0< \gamma < 1 is a constant tradeoff parameter and M ( \mu, \nu ) is the exponent to multiply an \lfloor n$^{ \mu }$ \rfloor $ \times $ \lfloor n$^{ \nu }$ \rfloor matrix with an \lfloor n$^{ \nu }$ \rfloor $ \times $ \lfloor n$^{ \mu }$ \rfloor matrix and \Delta =1/(1-log$_{ \tau }$ \rho ). As corollaries we obtain randomized algorithms that run in time {\~O}( ( n$^{2 / \omega 3 - log \tau \rho }$ + qdn$^{2 / (1 - log \tau \rho)3 = log \tau \tau \rho }$ ) and in time {\~o}( ( n$^{4 / 2 + \alpha (1 - log \tau \rho)}$ + qdn$^{2 / \alpha (1 - log \tau \rho)2 + \alpha (1 - log \tau \rho)}$ >), where 2 \leq \omega < 2.38 is the exponent for square matrix multiplication and 0.3< \alpha \leq 1 is the exponent for rectangular matrix multiplication. The notation {\~O}(s) hides polylogarithmic factors in n and d whose degree may depend on \rho and \tau. We present further corollaries for the light bulb problem and for learning sparse Boolean functions.", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Buchbinder:2018:DAS, author = "Niv Buchbinder and Moran Feldman", title = "Deterministic Algorithms for Submodular Maximization Problems", journal = j-TALG, volume = "14", number = "3", pages = "32:1--32:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3184990", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3184990", abstract = "Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area, most algorithms are randomized, and in almost all cases the approximation ratios obtained by current randomized algorithms are superior to the best results obtained by known deterministic algorithms. Derandomization of algorithms for general submodular function maximization seems hard since the access to the function is done via a value oracle. This makes it hard, for example, to apply standard derandomization techniques such as conditional expectations. Therefore, an interesting fundamental problem in this area is whether randomization is inherently necessary for obtaining good approximation ratios. In this work, we give evidence that randomization is not necessary for obtaining good algorithms by presenting a new technique for derandomization of algorithms for submodular function maximization. Our high level idea is to maintain explicitly a (small) distribution over the states of the algorithm, and carefully update it using marginal values obtained from an extreme point solution of a suitable linear formulation. We demonstrate our technique on two recent algorithms for unconstrained submodular maximization and for maximizing a submodular function subject to a cardinality constraint. In particular, for unconstrained submodular maximization we obtain an optimal deterministic 1/2-approximation showing that randomization is unnecessary for obtaining optimal results for this setting.", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chechik:2018:NOL, author = "Shiri Chechik and Christian Wulff-Nilsen", title = "Near-Optimal Light Spanners", journal = j-TALG, volume = "14", number = "3", pages = "33:1--33:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3199607", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3199607", abstract = "A spanner H of a weighted undirected graph G is a ``sparse'' subgraph that approximately preserves distances between every pair of vertices in G. We refer to H as a \delta -spanner of G for some parameter \delta {$>$}= 1 if the distance in H between every vertex pair is at most a factor \delta bigger than in G. In this case, we say that H has stretch \delta . Two main measures of the sparseness of a spanner are the size (number of edges) and the total weight (the sum of weights of the edges in the spanner). It is well-known that for any positive integer k, one can efficiently construct a (2 k --- 1)-spanner of G with O ( n$^{1 + 1 / k}$ ) edges where n is the number of vertices [2]. This size-stretch tradeoff is conjectured to be optimal based on a girth conjecture of Erd{\H{o}}s [17]. However, the current state of the art for the second measure is not yet optimal. Recently Elkin, Neiman and Solomon [ICALP 14] presented an improved analysis of the greedy algorithm, proving that the greedy algorithm admits (2 k --- 1) $ \cdot $ (1 + \epsilon ) stretch and total edge weight of O$_{ \epsilon }$ (( k / log k ) $ \cdot $ \omega ( MST ( G )) $ \cdot $ n$^{1 / k}$ ), where \omega ( MST ( G )) is the weight of a MST of G. The previous analysis by Chandra et al. [SOCG 92] admitted (2 k --- 1) $ \cdot $ (1 + \epsilon ) stretch and total edge weight of O$_{ \epsilon }$ ( k \omega ( MST ( G )) n$^{1 / k}$ ). Hence, Elkin et al. improved the weight of the spanner by a log k factor. In this article, we completely remove the k factor from the weight, presenting a spanner with (2 k --- 1) $ \cdot $ (1 + \epsilon ) stretch, O$_{ \epsilon }$ ( \omega ( MST ( G )) n$^{1 / k}$ ) total weight, and O ( n$^{1 + 1 / k}$ ) edges. Up to a (1 + \epsilon ) factor in the stretch this matches the girth conjecture of Erd{\H{o}}s [17].", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fomin:2018:FPT, author = "Fedor V. Fomin and Daniel Lokshtanov and Saket Saurabh and MichaL Pilipczuk and Marcin Wrochna", title = "Fully Polynomial-Time Parameterized Computations for Graphs and Matrices of Low Treewidth", journal = j-TALG, volume = "14", number = "3", pages = "34:1--34:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3186898", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3186898", abstract = "We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero entries. In each of the considered cases, the best known algorithms working on general graphs run in polynomial time; however, the exponent of the polynomial is large. Therefore, our main goal is to construct algorithms with running time of the form poly( k )$ \cdot $ n or poly( k )$ \cdot $ n log n, where k is the width of the tree decomposition given on the input. Such procedures would outperform the best known algorithms for the considered problems already for moderate values of the treewidth, like O ( n$^{1 / c}$ ) for a constant c. Our results include the following: --- an algorithm for computing the determinant and the rank of an n $ \times $ n matrix using O ( k$^3$ $ \cdot $ n ) time and arithmetic operations; -an algorithm for solving a system of linear equations using O ( k$^3$ $ \cdot $ n ) time and arithmetic operations; -an O ( k$^3$ $ \cdot $ n log n )-time randomized algorithm for finding the cardinality of a maximum matching in a graph; -an O ( k$^4$ $ \cdot $ n log$^2$ n )-time randomized algorithm for constructing a maximum matching in a graph; -an O ( k$^2$ $ \cdot $ n log n )-time algorithm for finding a maximum vertex flow in a directed graph. Moreover, we give an approximation algorithm for treewidth with time complexity suited to the running times as above. Namely, the algorithm, when given a graph G and integer k, runs in time O ( k$^7$ $ \cdot $ n log n ) and either correctly reports that the treewidth of G is larger than k, or constructs a tree decomposition of G of width O ( k$^2$ ). The above results stand in contrast with the recent work of Abboud et al. (SODA 2016), which shows that the existence of algorithms with similar running times is unlikely for the problems of finding the diameter and the radius of a graph of low treewidth.", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bliznets:2018:SPA, author = "Ivan Bliznets and Fedor V. Fomin and Marcin Pilipczuk and MichaL Pilipczuk", title = "Subexponential Parameterized Algorithm for Interval Completion", journal = j-TALG, volume = "14", number = "3", pages = "35:1--35:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3186896", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3186896", abstract = "In the Interval Completion problem we are given an n-vertex graph G and an integer k, and the task is to transform G by making use of at most k edge additions into an interval graph. This is a fundamental graph modification problem with applications in sparse matrix multiplication and molecular biology. The question about fixed-parameter tractability of Interval Completion was asked by Kaplan et al. [FOCS 1994; SIAM J. Comput. 1999] and was answered affirmatively more than a decade later by Villanger et al. [STOC 2007; SIAM J. Comput. 2009], who presented an algorithm with running time O ( k$^{2 k}$ n$^3$ m ). We give the first subexponential parameterized algorithm solving Interval Completion in time $k^{O (\sqrt{k})} n^{O(1)}$. This adds Interval Completion to a very small list of parameterized graph modification problems solvable in subexponential time.", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{DeBerg:2018:FAC, author = "Mark {De Berg} and Joachim Gudmundsson and Mehran Mehr", title = "Faster Algorithms for Computing Plurality Points", journal = j-TALG, volume = "14", number = "3", pages = "36:1--36:??", month = jul, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3186990", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Tue Oct 22 07:46:11 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/ft_gateway.cfm?id=3186990", abstract = "Let V be a set of n points in R$^d$, which we call voters. A point p \in R$^d$ is preferred over another point p ' \in R$^d$ by a voter \upsilon \in V if dist( \upsilon, p ) < dist( \upsilon, p '). A point p is called a plurality point if it is preferred by at least as many voters as any other point p '. We present an algorithm that decides in O ( n log n ) time whether V admits a plurality point in the L$_2$ norm and, if so, finds the (unique) plurality point. We also give efficient algorithms to compute a minimum-cost subset W \subset V such that V \ W admits a plurality point, and to compute a so-called minimum-radius plurality ball. Finally, we consider the problem in the personalized L$_1$ norm, where each point \upsilon \in V has a preference vector \langle w$_1$ ( \upsilon ) \ldots{}, w$_d$ ( \upsilon ) \rangle and the distance from \upsilon to any point p \in R$^d$ is given by \Sigma $_{i = 1}^d$ w$_i$ ( \upsilon )$ \cdot $ | x$_i$ ( \upsilon )- x$_i$ ( p )|. For this case we can compute in O ( n$^{d - 1}$ ) time the set of all plurality points of V. When all preference vectors are equal, the running time improves to O ( n ).", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Tamaki:2018:AGM, author = "Suguru Tamaki and Yuichi Yoshida", title = "Approximation Guarantees for the Minimum Linear Arrangement Problem by Higher Eigenvalues", journal = j-TALG, volume = "14", number = "4", pages = "1--13", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3228342", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3228342", abstract = "Given an n -vertex undirected graph G = ( V, E ) and positive edge weights { w e } e \in E, a linear arrangement is a permutation \pi : V \to {1, 2, \ldots{}, n }. The value of the arrangement is val( G, \pi ) := 1/n \Sigma e ={ u, v } \in E w e | \pi ( u ) - \pi ( v )|. In the minimum linear \ldots{}", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Krauthgamer:2018:CLB, author = "Robert Krauthgamer and Ohad Trabelsi", title = "Conditional Lower Bounds for All-Pairs Max-Flow", journal = j-TALG, volume = "14", number = "4", pages = "1--15", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3212510", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3212510", abstract = "We provide evidence that computing the maximum flow value between every pair of nodes in a directed graph on n nodes, m edges, and capacities in the range [1.. n ], which we call the All-Pairs Max-Flow problem, cannot be solved in time that is \ldots{}", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Barbay:2018:ACS, author = "J{\'e}r{\'e}my Barbay and Pablo P{\'e}rez-Lantero", title = "Adaptive Computation of the Swap-Insert Correction Distance", journal = j-TALG, volume = "14", number = "4", pages = "1--16", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3232057", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3232057", abstract = "The Swap-Insert Correction distance from a string S of length n to another string L of length m \geq n on the alphabet [1.. \sigma ] is the minimum number of insertions, and swaps of pairs of adjacent symbols, converting S into L. Contrarily to other correction \ldots{}", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gold:2018:DTW, author = "Omer Gold and Micha Sharir", title = "Dynamic Time Warping and Geometric Edit Distance: Breaking the Quadratic Barrier", journal = j-TALG, volume = "14", number = "4", pages = "1--17", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3230734", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3230734", abstract = "Dynamic Time Warping (DTW) and Geometric Edit Distance (GED) are basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequences of points in some metric space ( X, dist). The DTW and GED \ldots{}", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agarwal:2018:EAC, author = "Pankaj K. Agarwal and Kyle Fox and Oren Salzman", title = "An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles", journal = j-TALG, volume = "14", number = "4", pages = "1--21", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3230650", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3230650", abstract = "We study a path-planning problem amid a set O of obstacles in R 2, in which we wish to compute a short path between two points while also maintaining a high clearance from O; the clearance of a point is its distance from a nearest obstacle in O. \ldots{}", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Boissonnat:2018:ERF, author = "Jean-Daniel Boissonnat and Karthik C. S.", title = "An Efficient Representation for Filtrations of Simplicial Complexes", journal = j-TALG, volume = "14", number = "4", pages = "1--21", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3229146", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3229146", abstract = "A filtration over a simplicial complex K is an ordering of the simplices of K such that all prefixes in the ordering are subcomplexes of K. Filtrations are at the core of Persistent Homology, a major tool in Topological Data Analysis. To represent the \ldots{}", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Anagnostopoulos:2018:MAU, author = "Aris Anagnostopoulos and Fabrizio Grandoni and Stefano Leonardi and Andreas Wiese", title = "A Mazing $ 2 + \epsilon $ Approximation for Unsplittable Flow on a Path", journal = j-TALG, volume = "14", number = "4", pages = "1--23", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3242769", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3242769", abstract = "We study the problem of unsplittable flow on a path (UFP), which arises naturally in many applications such as bandwidth allocation, job scheduling, and caching. Here we are given a path with nonnegative edge capacities and a set of tasks, which are \ldots{}", acknowledgement = ack-nhfb, articleno = "55", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Esfandiari:2018:SAE, author = "Hossein Esfandiari and Mohammadtaghi Hajiaghayi and Vahid Liaghat and Morteza Monemizadeh and Krzysztof Onak", title = "Streaming Algorithms for Estimating the Matching Size in Planar Graphs and Beyond", journal = j-TALG, volume = "14", number = "4", pages = "1--23", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3230819", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3230819", abstract = "We consider the problem of estimating the size of a maximum matching when the edges are revealed in a streaming fashion. When the input graph is planar, we present a simple and elegant streaming algorithm that, with high probability, estimates the size \ldots{}", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Korman:2018:DDP, author = "Amos Korman and Yoav Rodeh", title = "The Dependent Doors Problem: an Investigation into Sequential Decisions without Feedback", journal = j-TALG, volume = "14", number = "4", pages = "1--23", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3218819", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3218819", abstract = "We introduce the dependent doors problem as an abstraction for situations in which one must perform a sequence of dependent decisions, without receiving feedback information on the effectiveness of previously made actions. Informally, the problem \ldots{}", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Angelini:2018:WPE, author = "Patrizio Angelini and Giordano {Da Lozzo} and Giuseppe {Di Battista} and Valentino {Di Donato} and Philipp Kindermann and G{\"u}nter Rote and Ignaz Rutter", title = "Windrose Planarity: Embedding Graphs with Direction-Constrained Edges", journal = j-TALG, volume = "14", number = "4", pages = "1--24", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3239561", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3239561", abstract = "Given a planar graph G and a partition of the neighbors of each vertex v in four sets $ v \nearrow $, $ v \nwarrow $, $ v \swarrow $, and $ v \searrow $, the problem Windrose Planarity asks to decide whether G admits a windrose-planar drawing, that is, a planar drawing in which (i) each neighbor u \in \ldots{}", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chen:2018:PGI, author = "Lin Chen and Guochuan Zhang", title = "Packing Groups of Items into Multiple Knapsacks", journal = j-TALG, volume = "14", number = "4", pages = "1--24", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3233524", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3233524", abstract = "We consider a natural generalization of the classical multiple knapsack problem in which instead of packing single items we are packing groups of items. In this problem, we have multiple knapsacks and a set of items partitioned into groups. Each item \ldots{}", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Harris:2018:DPA, author = "David G. Harris", title = "Deterministic Parallel Algorithms for Fooling Polylogarithmic Juntas and the {Lov{\'a}sz} Local Lemma", journal = j-TALG, volume = "14", number = "4", pages = "1--24", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3230651", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3230651", abstract = "Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low (almost-) independence. A series of papers, beginning with Luby (1993) and continuing with Berger and Rompel \ldots{}", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Aronov:2018:BPL, author = "Boris Aronov and Matthew J. Katz", title = "Batched Point Location in {SINR} Diagrams via Algebraic Tools", journal = j-TALG, volume = "14", number = "4", pages = "1--29", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3209678", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3209678", abstract = "The SINR (Signal to Interference plus Noise Ratio) model for the quality of wireless connections has been the subject of extensive recent study. It attempts to predict whether a particular transmitter is heard at a specific location, in a setting \ldots{}", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chan:2018:OSM, author = "T.-H. Hubert Chan and Zhiyi Huang and Shaofeng H.-C. Jiang and Ning Kang and Zhihao Gavin Tang", title = "Online Submodular Maximization with Free Disposal", journal = j-TALG, volume = "14", number = "4", pages = "1--29", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3242770", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3242770", abstract = "We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying matroid. In \ldots{}", acknowledgement = ack-nhfb, articleno = "56", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kannan:2018:GRV, author = "Sampath Kannan and Claire Mathieu and Hang Zhou", title = "Graph Reconstruction and Verification", journal = j-TALG, volume = "14", number = "4", pages = "1--30", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3199606", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3199606", abstract = "How efficiently can we find an unknown graph using distance or shortest path queries between its vertices? We assume that the unknown graph G is connected, unweighted, and has bounded degree. In the reconstruction problem, the goal is to find the graph \ldots{}", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cohen:2018:SSF, author = "Edith Cohen", title = "Stream Sampling Framework and Application for Frequency Cap Statistics", journal = j-TALG, volume = "14", number = "4", pages = "1--40", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3234338", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3234338", abstract = "Unaggregated data, in a streamed or distributed form, are prevalent and come from diverse sources such as interactions of users with web services and IP traffic. Data elements have keys (cookies, users, queries), and elements with different keys \ldots{}", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Pilipczuk:2018:NSS, author = "Marcin Pilipczuk and Micha{\l} Pilipczuk and Piotr Sankowski and Erik Jan {Van Leeuwen}", title = "Network Sparsification for {Steiner} Problems on Planar and Bounded-Genus Graphs", journal = j-TALG, volume = "14", number = "4", pages = "1--73", month = oct, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1145/3239560", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3239560", abstract = "We propose polynomial-time algorithms that sparsify planar and bounded-genus graphs while preserving optimal or near-optimal solutions to Steiner problems. Our main contribution is a polynomial-time algorithm that, given an unweighted undirected graph G \ldots{}", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gorain:2019:DGE, author = "Barun Gorain and Andrzej Pelc", title = "Deterministic Graph Exploration with Advice", journal = j-TALG, volume = "15", number = "1", pages = "1--17", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3280823", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3280823", abstract = "We consider the fundamental task of graph exploration. An n -node graph has unlabeled nodes, and all ports at any node of degree d are arbitrarily numbered 0, \ldots{}, d -1. A mobile agent, initially situated at some starting node v, has to visit all nodes and \ldots{}", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Adamaszek:2019:LKC, author = "Anna Adamaszek and Artur Czumaj and Matthias Englert and Harald R{\"a}cke", title = "An {$ O(\log k) $}-Competitive Algorithm for Generalized Caching", journal = j-TALG, volume = "15", number = "1", pages = "1--18", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3280826", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3280826", abstract = "In the generalized caching problem, we have a set of pages and a cache of size k. Each page p has a size w p \geq 1 and fetching cost c p for loading the page into the cache. At any point in time, the sum of the sizes of the pages stored in the cache cannot \ldots{}", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Disser:2019:SAN, author = "Yann Disser and Martin Skutella", title = "The Simplex Algorithm Is {NP-Mighty}", journal = j-TALG, volume = "15", number = "1", pages = "1--19", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3280847", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3280847", abstract = "We show that the Simplex Method, the Network Simplex Method-both with Dantzig's original pivot rule-and the Successive Shortest Path Algorithm are NP-mighty. That is, each of these algorithms can be used to solve, with polynomial overhead, any problem \ldots{}", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lokshtanov:2019:CIS, author = "Daniel Lokshtanov and Amer E. Mouawad", title = "The Complexity of Independent Set Reconfiguration on Bipartite Graphs", journal = j-TALG, volume = "15", number = "1", pages = "1--19", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3280825", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3280825", abstract = "We settle the complexity of the Independent Set Reconfiguration problem on bipartite graphs under all three commonly studied reconfiguration models. We show that under the token jumping or token addition/removal model, the problem is NP-complete. For \ldots{}", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Abrahamsen:2019:CTT, author = "Mikkel Abrahamsen and Bartosz Walczak", title = "Common Tangents of Two Disjoint Polygons in Linear Time and Constant Workspace", journal = j-TALG, volume = "15", number = "1", pages = "1--21", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3284355", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3284355", abstract = "We provide a remarkably simple algorithm to compute all (at most four) common tangents of two disjoint simple polygons. Given each polygon as a read-only array of its corners in cyclic order, the algorithm runs in linear time and constant workspace and \ldots{}", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Berenbrink:2019:IAD, author = "Petra Berenbrink and Ralf Klasing and Adrian Kosowski and Frederik Mallmann-Trenn and Przemys{\l}aw Uzna{\'n}ski", title = "Improved Analysis of Deterministic Load-Balancing Schemes", journal = j-TALG, volume = "15", number = "1", pages = "1--22", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3282435", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3282435", abstract = "We consider the problem of deterministic load balancing of tokens in the discrete model. A set of n processors is connected into a d -regular undirected network. In every timestep, each processor exchanges some of its tokens with each of its neighbors in \ldots{}", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Golebiewski:2019:EOC, author = "Zbigniew Go{\l}{\k{e}}biewski and Abram Magner and Wojciech Szpankowski", title = "Entropy and Optimal Compression of Some General Plane Trees", journal = j-TALG, volume = "15", number = "1", pages = "1--23", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3275444", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3275444", abstract = "We continue developing the information theory of structured data. In this article, we study models generating d -ary trees ( d \geq 2) and trees with unrestricted degree. We first compute the entropy which gives us the fundamental lower bound on compression \ldots{}", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Liu:2019:DFJ, author = "Zhengyang Liu and Xi Chen and Rocco A. Servedio and Ying Sheng and Jinyu Xie", title = "Distribution-free Junta Testing", journal = j-TALG, volume = "15", number = "1", pages = "1--23", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3264434", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3264434", abstract = "We study the problem of testing whether an unknown n -variable Boolean function is a k -junta in the distribution-free property testing model, where the distance between functions is measured with respect to an arbitrary and unknown probability \ldots{}", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hirai:2019:DDA, author = "Hiroshi Hirai", title = "A Dual Descent Algorithm for Node-capacitated Multiflow Problems and Its Applications", journal = j-TALG, volume = "15", number = "1", pages = "1--24", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3291531", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3291531", abstract = "In this article, we develop an O (( m log k )MSF( n,m , 1))-time algorithm to find a half-integral node-capacitated multiflow of the maximum total flow-value in a network with n nodes, m edges, and k terminals, where MSF( n ', m ', \gamma ) denotes the time complexity \ldots{}", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cygan:2019:PEM, author = "Marek Cygan and Marcin Mucha and Karol W{\k{e}}grzycki and Micha{\l} W{\l}odarczyk", title = "On Problems Equivalent to $ (\min, +)$-Convolution", journal = j-TALG, volume = "15", number = "1", pages = "1--25", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3293465", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3293465", abstract = "In recent years, significant progress has been made in explaining the apparent hardness of improving upon the naive solutions for many fundamental polynomially solvable problems. This progress has come in the form of conditional lower bounds-reductions \ldots{}", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bhattacharyya:2019:OAH, author = "Arnab Bhattacharyya and Palash Dey and David P. Woodruff", title = "An Optimal Algorithm for $ l_1$-Heavy Hitters in Insertion Streams and Related Problems", journal = j-TALG, volume = "15", number = "1", pages = "1--27", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3264427", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3264427", abstract = "We give the first optimal bounds for returning the l 1 -heavy hitters in a data stream of insertions, together with their approximate frequencies, closing a long line of work on this problem. For a stream of m items in { 1, 2, \ldots{}, n } and parameters 0 \< \epsilon \< \ldots{}", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fomin:2019:CWI, author = "Fedor V. Fomin and Petr A. Golovach and Daniel Lokshtanov and Saket Saurabh and Meirav Zehavi", title = "Clique-width {III}: {Hamiltonian} Cycle and the Odd Case of Graph Coloring", journal = j-TALG, volume = "15", number = "1", pages = "1--27", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3280824", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3280824", abstract = "MAX-CUT, EDGE DOMINATING SET, GRAPH COLORING, and HAMILTONIAN CYCLE on graphs of bounded clique-width have received significant attention as they can be formulated in MSO 2 (and, therefore, have linear-time algorithms on bounded treewidth graphs by the \ldots{}).", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Agrawal:2019:FVS, author = "Akanksha Agrawal and Daniel Lokshtanov and Pranabendu Misra and Saket Saurabh and Meirav Zehavi", title = "Feedback Vertex Set Inspired Kernel for Chordal Vertex Deletion", journal = j-TALG, volume = "15", number = "1", pages = "1--28", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3284356", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3284356", abstract = "Given a graph G and a parameter k, the Chordal Vertex Deletion (CVD) problem asks whether there exists a subset U \subseteq V ( G ) of size at most k that hits all induced cycles of size at least 4. The existence of a polynomial kernel for CVD was a well-known open \ldots{}", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Elkin:2019:EAC, author = "Michael Elkin and Ofer Neiman", title = "Efficient Algorithms for Constructing Very Sparse Spanners and Emulators", journal = j-TALG, volume = "15", number = "1", pages = "1--29", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3274651", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3274651", abstract = "Miller et al. [48] devised a distributed 1 algorithm in the CONGEST model that, given a parameter k = 1,2, \ldots{}, constructs an O ( k )-spanner of an input unweighted n -vertex graph with O ( n 1+1/ k ) expected edges in O ( k ) rounds of communication. In this article, \ldots{}", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fomin:2019:SKI, author = "Fedor V. Fomin and Tien-Nam Le and Daniel Lokshtanov and Saket Saurabh and St{\'e}phan Thomass{\'e} and Meirav Zehavi", title = "Subquadratic Kernels for Implicit $3$-Hitting Set and $3$-Set Packing Problems", journal = j-TALG, volume = "15", number = "1", pages = "1--44", month = jan, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3293466", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:44 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3293466", abstract = "We consider four well-studied NP-complete packing/covering problems on graphs: Feedback Vertex Set in Tournaments (FVST), Cluster Vertex Deletion (CVD), Triangle Packing in Tournaments (TPT) and Induced P 3 -Packing. For these four problems, kernels with \ldots{}", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Srinivasan:2019:E, author = "Aravind Srinivasan", title = "Editorial", journal = j-TALG, volume = "15", number = "2", pages = "1--1", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3325824", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3325824", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Marx:2019:ISI, author = "D{\'a}niel Marx and Virgi Vassilevska Williams and Neal E. Young", title = "Introduction to the Special Issue on {SODA 2017}", journal = j-TALG, volume = "15", number = "2", pages = "1--2", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3319426", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3319426", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Paz:2019:AMW, author = "Ami Paz and Gregory Schwartzman", title = "A $ (2 + \epsilon)$-Approximation for Maximum Weight Matching in the Semi-streaming Model", journal = j-TALG, volume = "15", number = "2", pages = "1--15", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3274668", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3274668", abstract = "We present a simple deterministic single-pass (2+ \epsilon )-approximation algorithm for the maximum weight matching problem in the semi-streaming model. This improves on the currently best known approximation ratio of (4+ \epsilon ). Our algorithm uses O ( n log 2 n ) bits \ldots{}", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kreutzer:2019:PKW, author = "Stephan Kreutzer and Roman Rabinovich and Sebastian Siebertz", title = "Polynomial Kernels and Wideness Properties of Nowhere Dense Graph Classes", journal = j-TALG, volume = "15", number = "2", pages = "1--19", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3274652", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3274652", abstract = "Nowhere dense classes of graphs [21, 22] are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness, a \ldots{}", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Makinen:2019:SDP, author = "Veli M{\"a}kinen and Alexandru I. Tomescu and Anna Kuosmanen and Topi Paavilainen and Travis Gagie and Rayan Chikhi", title = "Sparse Dynamic Programming on {DAGs} with Small Width", journal = j-TALG, volume = "15", number = "2", pages = "1--21", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3301312", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3301312", abstract = "The minimum path cover problem asks us to find a minimum-cardinality set of paths that cover all the nodes of a directed acyclic graph (DAG). We study the case when the size k of a minimum path cover is small, that is, when the DAG has a small width. \ldots{}", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Adjiashvili:2019:BAF, author = "David Adjiashvili", title = "Beating Approximation Factor Two for Weighted Tree Augmentation with Bounded Costs", journal = j-TALG, volume = "15", number = "2", pages = "1--26", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3182395", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3182395", abstract = "The Weighted Tree Augmentation Problem (WTAP) is a fundamental well-studied problem in the field of network design. Given an undirected tree G =( V, E ), an additional set of edges L \sqsubseteq V $ \times $ V disjoint from E called links and a cost vector c \in R \geq 0 L, WTAP asks \ldots{}", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bansal:2019:HKS, author = "Nikhil Bansal and Marek Eli{\'e}{\v{s}} and {\L}ukasz Je{\.z} and Grigorios Koumoutsos", title = "The $ (h, k)$-Server Problem on Bounded Depth Trees", journal = j-TALG, volume = "15", number = "2", pages = "1--26", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3301314", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3301314", abstract = "We study the k -server problem in the resource augmentation setting, i.e., when the performance of the online algorithm with k servers is compared to the offline optimal solution with h \leq k servers. The problem is very poorly understood beyond uniform \ldots{}", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Friggstad:2019:ASC, author = "Zachary Friggstad and Kamyar Khodamoradi and Mohsen Rezapour and Mohammad R. Salavatipour", title = "Approximation Schemes for Clustering with Outliers", journal = j-TALG, volume = "15", number = "2", pages = "1--26", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3301446", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3301446", abstract = "Clustering problems are well studied in a variety of fields, such as data science, operations research, and computer science. Such problems include variants of center location problems, k -median and k -means to name a few. In some cases, not all data \ldots{}", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Adjiashvili:2019:FTB, author = "David Adjiashvili and Andrea Baggio and Rico Zenklusen", title = "Firefighting on Trees Beyond Integrality Gaps", journal = j-TALG, volume = "15", number = "2", pages = "1--33", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3173046", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3173046", abstract = "The Firefighter problem and a variant of it, known as Resource Minimization for Fire Containment (RMFC), are natural models for optimal inhibition of harmful spreading processes. Despite considerable progress on several fronts, the approximability of \ldots{}", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kazda:2019:EDM, author = "Alexandr Kazda and Vladimir Kolmogorov and Michal Rol{\'{\i}}nek", title = "Even Delta-Matroids and the Complexity of Planar {Boolean} {CSPs}", journal = j-TALG, volume = "15", number = "2", pages = "1--33", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3230649", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3230649", abstract = "The main result of this article is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all \ldots{}", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Gao:2019:CFO, author = "Jiawei Gao and Russell Impagliazzo and Antonina Kolokolova and Ryan Williams", title = "Completeness for First-order Properties on Sparse Structures with Algorithmic Applications", journal = j-TALG, volume = "15", number = "2", pages = "1--35", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3196275", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3196275", abstract = "Properties definable in first-order logic are algorithmically interesting for both theoretical and pragmatic reasons. Many of the most studied algorithmic problems, such as Hitting Set and Orthogonal Vectors, are first-order, and the first-order \ldots{}", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cabello:2019:SAD, author = "Sergio Cabello", title = "Subquadratic Algorithms for the Diameter and the Sum of Pairwise Distances in Planar Graphs", journal = j-TALG, volume = "15", number = "2", pages = "1--38", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3218821", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3218821", abstract = "In this article, we show how to compute for $n$-vertex planar graphs in $O(n^{11/6} \polylog(n))$ expected time the diameter and the sum of the pairwise distances. The algorithms work for directed graphs with real weights and no negative cycles. In $O (n^{15/8} \ldots{} )$ \ldots{} ", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Ferraioli:2019:MLD, author = "Diodato Ferraioli and Carmine Ventre", title = "Metastability of the Logit Dynamics for Asymptotically Well-Behaved Potential Games", journal = j-TALG, volume = "15", number = "2", pages = "1--42", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3301315", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3301315", abstract = "Convergence rate and stability of a solution concept are classically measured in terms of {``eventually''} and {``forever,''} respectively. In the wake of recent computational criticisms to this approach, we study whether these timeframes can be updated to have \ldots{}", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hermelin:2019:DWS, author = "Danny Hermelin and Matthias Mnich and Erik Jan {Van Leeuwen} and Gerhard Woeginger", title = "Domination When the Stars Are Out", journal = j-TALG, volume = "15", number = "2", pages = "1--90", month = may, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3301445", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3301445", abstract = "We algorithmize the structural characterization for claw-free graphs by Chudnovsky and Seymour. Building on this result, we show that Dominating Set on claw-free graphs is (i) fixed-parameter tractable and (ii) even possesses a polynomial kernel. To \ldots{}", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Kannan:2019:LEF, author = "Sampath Kannan and Kevin T. Tian", title = "Locating Errors in Faulty Formulas", journal = j-TALG, volume = "15", number = "3", pages = "1--13", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3313776", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3313776", abstract = "Given a drawing of a read-once formula (called the blueprint), and a blackbox implementation with the same topology as the blueprint that purports to compute the formula, can we tell if it does? Under a fault model, where the only faults in the \ldots{}", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chakrabarty:2019:GCP, author = "Deeparnab Chakrabarty and Maryam Negahbani", title = "Generalized Center Problems with Outliers", journal = j-TALG, volume = "15", number = "3", pages = "1--14", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3338513", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3338513", abstract = "We study the F-center problem with outliers: Given a metric space ( X, d ), a general down-closed family F of subsets of X, and a parameter m, we need to locate a subset S \in F of centers such that the maximum distance among the closest m points in X to S \ldots{}", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Huang:2019:OVW, author = "Zhiyi Huang and Zhihao Gavin Tang and Xiaowei Wu and Yuhao Zhang", title = "Online Vertex-Weighted Bipartite Matching: Beating $ 1 - 1 / e $ with Random Arrivals", journal = j-TALG, volume = "15", number = "3", pages = "1--15", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3326169", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3326169", abstract = "We introduce a weighted version of the ranking algorithm by Karp et al. (STOC 1990), and we prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Our result shows that \ldots{}", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Blum:2019:SAG, author = "Avrim Blum and Sariel Har-Peled and Benjamin Raichel", title = "Sparse Approximation via Generating Point Sets", journal = j-TALG, volume = "15", number = "3", pages = "1--16", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3302249", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3302249", abstract = "For a set P of n points in the unit ball b \subseteq R d, consider the problem of finding a small subset T \subseteq P such that its convex-hull \epsilon -approximates the convex-hull of the original set. Specifically, the Hausdorff distance between the convex hull of T and the \ldots{}", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Amiri:2019:DDS, author = "Saeed Akhoondian Amiri and Stefan Schmid and Sebastian Siebertz", title = "Distributed Dominating Set Approximations beyond Planar Graphs", journal = j-TALG, volume = "15", number = "3", pages = "1--18", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3326170", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3326170", abstract = "The Minimum Dominating Set (MDS) problem is a fundamental and challenging problem in distributed computing. While it is well known that minimum dominating sets cannot be well approximated locally on general graphs, in recent years there has been much \ldots{}", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Koiliaris:2019:FPT, author = "Konstantinos Koiliaris and Chao Xu", title = "Faster Pseudopolynomial Time Algorithms for Subset Sum", journal = j-TALG, volume = "15", number = "3", pages = "1--20", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3329863", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3329863", abstract = "Given a (multi) set S of n positive integers and a target integer u, the subset sum problem is to decide if there is a subset of S that sums up to u. We present a series of new algorithms that compute and return all the realizable subset sums up to the \ldots{}", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chee:2019:DCW, author = "Yeow Meng Chee and Johan Chrisnata and Han Mao Kiah and Tuan Thanh Nguyen", title = "Deciding the Confusability of Words under Tandem Repeats in Linear Time", journal = j-TALG, volume = "15", number = "3", pages = "1--22", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3338514", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3338514", abstract = "Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2016) proposed the study of codes that correct tandem \ldots{}", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Harris:2019:LMC, author = "David G. Harris and Thomas Pensyl and Aravind Srinivasan and Khoa Trinh", title = "A Lottery Model for Center-Type Problems With Outliers", journal = j-TALG, volume = "15", number = "3", pages = "1--25", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3311953", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3311953", abstract = "In this article, we give tight approximation algorithms for the k -center and matroid center problems with outliers. Unfairness arises naturally in this setting: certain clients could always be considered as outliers. To address this issue, we introduce \ldots{}", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Jansen:2019:ASM, author = "Klaus Jansen and Marten Maack and Malin Rau", title = "Approximation Schemes for Machine Scheduling with Resource (In-)dependent Processing Times", journal = j-TALG, volume = "15", number = "3", pages = "1--28", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3302250", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3302250", abstract = "We consider two related scheduling problems: single resource-constrained scheduling on identical parallel machines and a generalization with resource-dependent processing times. In both problems, jobs require a certain amount of an additional resource \ldots{}", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Harris:2019:DCB, author = "David G. Harris", title = "Derandomized Concentration Bounds for Polynomials, and Hypergraph Maximal Independent Set", journal = j-TALG, volume = "15", number = "3", pages = "1--29", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3326171", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3326171", abstract = "A parallel algorithm for maximal independent set (MIS) in hypergraphs has been a long-standing algorithmic challenge, dating back nearly 30 years to a survey of Karp and Ramachandran (1990). The best randomized parallel algorithm for hypergraphs of \ldots{}", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Naor:2019:BFA, author = "Moni Naor and Yogev Eylon", title = "{Bloom} Filters in Adversarial Environments", journal = j-TALG, volume = "15", number = "3", pages = "1--30", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3306193", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3306193", abstract = "Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are independent of the \ldots{}", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Buchbinder:2019:OSM, author = "Niv Buchbinder and Moran Feldman and Roy Schwartz", title = "Online Submodular Maximization with Preemption", journal = j-TALG, volume = "15", number = "3", pages = "1--31", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3309764", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3309764", abstract = "Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements arrive one by \ldots{}", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bei:2019:APA, author = "Xiaohui Bei and Jugal Garg and Martin Hoefer", title = "Ascending-Price Algorithms for Unknown Markets", journal = j-TALG, volume = "15", number = "3", pages = "1--33", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3319394", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3319394", abstract = "We design a simple ascending-price algorithm to compute a (1 + \epsilon )-approximate equilibrium in Arrow--Debreu markets with weak gross substitute property. It applies to an unknown market setting without exact knowledge about the number of agents, their \ldots{}", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hirai:2019:TCB, author = "Hiroshi Hirai and Yuni Iwamasa and Kazuo Murota and Stanislav {\v{Z}}ivn{\'y}", title = "A Tractable Class of Binary {VCSPs} via {$M$}-Convex Intersection", journal = j-TALG, volume = "15", number = "3", pages = "1--41", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3329862", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3329862", abstract = "A binary VCSP is a general framework for the minimization problem of a function represented as the sum of unary and binary cost functions. An important line of VCSP research is to investigate what functions can be solved in polynomial time. Cooper and \ldots{}", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Coudert:2019:FPF, author = "David Coudert and Guillaume Ducoffe and Alexandru Popa", title = "Fully Polynomial {FPT} Algorithms for Some Classes of Bounded Clique-width Graphs", journal = j-TALG, volume = "15", number = "3", pages = "1--57", month = jul, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3310228", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:45 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3310228", abstract = "Recently, hardness results for problems in P were achieved using reasonable complexity-theoretic assumptions such as the Strong Exponential Time Hypothesis. According to these assumptions, many graph-theoretic problems do not admit truly subquadratic \ldots{}", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cairo:2019:ONA, author = "Massimo Cairo and Paul Medvedev and Nidia Obscura Acosta and Romeo Rizzi and Alexandru I. Tomescu", title = "An Optimal {$ O(n m) $} Algorithm for Enumerating All Walks Common to All Closed Edge-covering Walks of a Graph", journal = j-TALG, volume = "15", number = "4", pages = "1--17", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3341731", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3341731", abstract = "In this article, we consider the following problem. Given a directed graph G, output all walks of G that are sub-walks of all closed edge-covering walks of G. This problem was first considered by Tomescu and Medvedev (RECOMB 2016), who characterized \ldots{}", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Cygan:2019:ITT, author = "Marek Cygan and {\L}ukasz Kowalik and Arkadiusz Soca{\l}a", title = "Improving {TSP} Tours Using Dynamic Programming over Tree Decompositions", journal = j-TALG, volume = "15", number = "4", pages = "1--19", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3341730", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3341730", abstract = "Given a traveling salesman problem (TSP) tour H in graph G, a k -move is an operation that removes k edges from H and adds k edges of G so that a new tour H ' is formed. The popular k -OPT heuristic for TSP finds a local optimum by starting from an \ldots{}", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bienkowski:2019:DBF, author = "Marcin Bienkowski and Jaros{\l}aw Byrka and Marcin Mucha", title = "Dynamic Beats Fixed: On Phase-based Algorithms for File Migration", journal = j-TALG, volume = "15", number = "4", pages = "1--21", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3340296", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3340296", abstract = "We construct a deterministic 4-competitive algorithm for the online file migration problem, beating the currently best 20-year-old, 4.086-competitive Move-To-Local-Min (Mtlm) algorithm by Bartal et al. (SODA 1997). Like Mtlm, our algorithm also operates \ldots{}", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Brenner:2019:FCB, author = "Ulrich Brenner and Anna Hermann", title = "Faster Carry Bit Computation for Adder Circuits with Prescribed Arrival Times", journal = j-TALG, volume = "15", number = "4", pages = "1--23", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3340321", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3340321", abstract = "We consider the fundamental problem of constructing fast circuits for the carry bit computation in binary addition. Up to a small additive constant, the carry bit computation reduces to computing an And-Or path, i.e., a formula of type \ldots{}", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Klemz:2019:OLP, author = "Boris Klemz and G{\"u}nter Rote", title = "Ordered Level Planarity and Its Relationship to Geodesic Planarity, Bi-Monotonicity, and Variations of Level Planarity", journal = j-TALG, volume = "15", number = "4", pages = "1--25", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3359587", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3359587", abstract = "We introduce and study the problem Ordered Level Planarity, which asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a y -monotone curve. This can be interpreted \ldots{}", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Akitaya:2019:RWE, author = "Hugo A. Akitaya and Radoslav Fulek and Csaba D. T{\'o}th", title = "Recognizing Weak Embeddings of Graphs", journal = j-TALG, volume = "15", number = "4", pages = "1--27", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3344549", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3344549", abstract = "We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding \phi : G \to M of a graph G into a 2-manifold M maps the vertices in V ( G ) to distinct points and the edges in E ( G ) to interior-disjoint \ldots{}", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Heydrich:2019:FAS, author = "Sandy Heydrich and Andreas Wiese", title = "Faster Approximation Schemes for the Two-Dimensional Knapsack Problem", journal = j-TALG, volume = "15", number = "4", pages = "1--28", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3338512", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3338512", abstract = "For geometric optimization problems we often understand the computational complexity on a rough scale, but not very well on a finer scale. One example is the two-dimensional knapsack problem for squares. There is a polynomial time (1+ \epsilon )-approximation \ldots{}", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Hunkenschroder:2019:AAM, author = "Christoph Hunkenschr{\"o}der and Santosh Vempala and Adrian Vetta", title = "A $ 4 / 3$-Approximation Algorithm for the Minimum $2$-Edge Connected Subgraph Problem", journal = j-TALG, volume = "15", number = "4", pages = "1--28", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3341599", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3341599", abstract = "We present a factor 4/3 approximation algorithm for the problem of finding a minimum 2-edge connected spanning subgraph of a given undirected multigraph. The algorithm is based upon a reduction to a restricted class of graphs. In these graphs, the \ldots{}", acknowledgement = ack-nhfb, articleno = "55", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Chang:2019:ESE, author = "Yi-Jun Chang and Tsvi Kopelowitz and Seth Pettie and Ruosong Wang and Wei Zhan", title = "Exponential Separations in the Energy Complexity of Leader Election", journal = j-TALG, volume = "15", number = "4", pages = "1--31", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3341111", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3341111", abstract = "Energy is often the most constrained resource for battery-powered wireless devices, and most of the energy is often spent on transceiver usage (i.e., transmitting and receiving packets) rather than computation. In this article, we study the energy \ldots{}", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Fomin:2019:SCR, author = "Fedor V. Fomin and Petr A. Golovach and Daniel Lokshtanov and Saket Saurabh", title = "Spanning Circuits in Regular Matroids", journal = j-TALG, volume = "15", number = "4", pages = "1--38", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3355629", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3355629", abstract = "We consider the fundamental Matroid Theory problem of finding a circuit in a matroid containing a set T of given terminal elements. For graphic matroids, this corresponds to the problem of finding a simple cycle passing through a set of given terminal \ldots{}", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Bun:2019:HHS, author = "Mark Bun and Jelani Nelson and Uri Stemmer", title = "Heavy Hitters and the Structure of Local Privacy", journal = j-TALG, volume = "15", number = "4", pages = "1--40", month = oct, year = "2019", CODEN = "????", DOI = "https://doi.org/10.1145/3344722", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3344722", abstract = "We present a new locally differentially private algorithm for the heavy hitters problem that achieves optimal worst-case error as a function of all standardly considered parameters. Prior work obtained error rates that depend optimally on the number of \ldots{}", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982", } @Article{Lee:2020:ISI, author = "Yin Tat Lee and Marcin Pilipczuk and David Woodruff", title = "Introduction to the Special Issue on {SODA'18}", journal = j-TALG, volume = "16", number = "1", pages = "1:1--1:2", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3368307", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3368307", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Asathulla:2020:FAM, author = "Mudabir Kabir Asathulla and Sanjeev Khanna and Nathaniel Lahn and Sharath Raghvendra", title = "A Faster Algorithm for Minimum-cost Bipartite Perfect Matching in Planar Graphs", journal = j-TALG, volume = "16", number = "1", pages = "2:1--2:30", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3365006", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3365006", abstract = "Given a weighted planar bipartite graph G ( A \cup B, E ) where each edge has an integer edge cost, we give an {\~O}( n 4/3 log nC ) time algorithm to compute minimum-cost perfect matching; here C is the maximum edge cost in the graph. The previous best-known \ldots{}", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Blasiok:2020:OST, author = "Jaros{\l}aw B{\l}asiok", title = "Optimal Streaming and Tracking Distinct Elements with High Probability", journal = j-TALG, volume = "16", number = "1", pages = "3:1--3:28", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3309193", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3309193", abstract = "The distinct elements problem is one of the fundamental problems in streaming algorithms-given a stream of integers in the range { 1, \ldots{}, n }, we wish to provide a (1+ \epsilon ) approximation to the number of distinct elements in the input. After a long line of \ldots{}", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Hsu:2020:NAF, author = "Chloe Ching-Yun Hsu and Chris Umans", title = "A New Algorithm for Fast Generalized {DFTs}", journal = j-TALG, volume = "16", number = "1", pages = "4:1--4:20", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3301313", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3301313", abstract = "We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups G. The new algorithm uses O (| G | \omega /2 + o (1) ) operations to compute the generalized DFT over finite groups of Lie type, including the linear, \ldots{}", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Eisenbrand:2020:PRF, author = "Friedrich Eisenbrand and Robert Weismantel", title = "Proximity Results and Faster Algorithms for Integer Programming Using the {Steinitz} Lemma", journal = j-TALG, volume = "16", number = "1", pages = "5:1--5:14", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3340322", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3340322", abstract = "We consider integer programming problems in standard form max { c T x: Ax = b, x \geq 0, x \in Z n } where A \in Z m $ \times $ n, b \in Z m, and c \in Z n . We show that such an integer program can be solved in time ( m $ \cdot $ \Delta ) O ( m ) $ \cdot $ \Vert b\Vert \infty 2, where \Delta is an upper bound on each \ldots{}", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fischer:2020:TAP, author = "Manuela Fischer and Andreas Noever", title = "Tight Analysis of Parallel Randomized Greedy {MIS}", journal = j-TALG, volume = "16", number = "1", pages = "6:1--6:13", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3326165", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3326165", abstract = "We provide a tight analysis that settles the round complexity of the well-studied parallel randomized greedy MIS algorithm, thus answering the main open question of Blelloch, Fineman, and Shun [SPAA'12]. The parallel/distributed randomized greedy \ldots{}", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chan:2020:MLF, author = "Timothy M. Chan", title = "More Logarithmic-factor Speedups for {3SUM}, (median,+)-convolution, and Some Geometric {3SUM}-hard Problems", journal = j-TALG, volume = "16", number = "1", pages = "7:1--7:23", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3363541", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3363541", abstract = "This article presents an algorithm that solves the 3SUM problem for n real numbers in O (( n 2 / log 2 n )(log log n ) O (1) ) time, improving previous solutions by about a logarithmic factor. Our framework for shaving off two logarithmic factors can be applied to \ldots{}", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chang:2020:DEC, author = "Yi-Jun Chang and Qizheng He and Wenzheng Li and Seth Pettie and Jara Uitto", title = "Distributed Edge Coloring and a Special Case of the Constructive {Lov{\'a}sz} Local Lemma", journal = j-TALG, volume = "16", number = "1", pages = "8:1--8:51", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3365004", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3365004", abstract = "The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $ \Delta $. In this article, we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. Our results are as \ldots{}", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Stein:2020:SWY, author = "Clifford Stein and Mingxian Zhong", title = "Scheduling When You Do Not Know the Number of Machines", journal = j-TALG, volume = "16", number = "1", pages = "9:1--9:20", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3340320", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3340320", abstract = "Often in a scheduling problem, there is uncertainty about the jobs to be processed. The issue of uncertainty regarding the machines has been much less studied. In this article, we study a scheduling environment in which jobs first need to be grouped \ldots{}", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Brubach:2020:AAC, author = "Brian Brubach and Karthik A. Sankararaman and Aravind Srinivasan and Pan Xu", title = "Algorithms to Approximate Column-sparse Packing Problems", journal = j-TALG, volume = "16", number = "1", pages = "10:1--10:32", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3355400", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3355400", abstract = "Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for \ldots{}", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Sawada:2020:SST, author = "Joe Sawada and Aaron Williams", title = "Solving the Sigma--Tau Problem", journal = j-TALG, volume = "16", number = "1", pages = "11:1--11:17", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3359589", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3359589", abstract = "Knuth assigned the following open problem a difficulty rating of 48/50 in The Art of Computer Programming Volume 4A: For odd n \geq 3, can the permutations of { 1,2, \ldots{}, n } be ordered in a cyclic list so that each permutation is transformed into the next by \ldots{}", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fomin:2020:ASL, author = "Fedor V. Fomin and Petr A. Golovach and Daniel Lokshtanov and Fahad Panolan and Saket Saurabh", title = "Approximation Schemes for Low-rank Binary Matrix Approximation Problems", journal = j-TALG, volume = "16", number = "1", pages = "12:1--12:39", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3365653", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3365653", abstract = "We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constraints. The new constrained clustering problem generalizes a number of problems and by solving it, we obtain the \ldots{}", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Pandurangan:2020:TMO, author = "Gopal Pandurangan and Peter Robinson and Michele Scquizzato", title = "A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning Trees", journal = j-TALG, volume = "16", number = "1", pages = "13:1--13:27", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3365005", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3365005", abstract = "This article presents a randomized (Las Vegas) distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity. This algorithm runs in {\~O}( D + \sqrt n ) time and \ldots{}", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chiplunkar:2020:RMA, author = "Ashish Chiplunkar and Sundar Vishwanathan", title = "Randomized Memoryless Algorithms for the Weighted and the Generalized $k$-server Problems", journal = j-TALG, volume = "16", number = "1", pages = "14:1--14:28", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3365002", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3365002", abstract = "The weighted k -server problem is a generalization of the k -server problem wherein the cost of moving a server of weight \beta i through a distance d is \beta i $ \cdot $ d. On uniform metric spaces, this models caching with caches having different page replacement costs. \ldots{}", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Grandoni:2020:FRP, author = "Fabrizio Grandoni and Virginia Vassilevska Williams", title = "Faster Replacement Paths and Distance Sensitivity Oracles", journal = j-TALG, volume = "16", number = "1", pages = "15:1--15:25", month = jan, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3365835", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Jan 11 07:32:46 MST 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3365835", abstract = "Shortest paths computation is one of the most fundamental problems in computer science. An important variant of the problem is when edges can fail, and one needs to compute shortest paths that avoid a (failing) edge. More formally, given a source node s, \ldots{}", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Gawrychowski:2020:SMQ, author = "Pawe{\l} Gawrychowski and Shay Mozes and Oren Weimann", title = "Submatrix Maximum Queries in {Monge} and Partial {Monge} Matrices Are Equivalent to Predecessor Search", journal = j-TALG, volume = "16", number = "2", pages = "16:1--16:24", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381416", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381416", abstract = "We present an optimal data structure for submatrix maximum queries in n $ \times $ n Monge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data \ldots{}", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Belazzougui:2020:LTS, author = "Djamal Belazzougui and Fabio Cunial and Juha K{\"a}rkk{\"a}inen and Veli M{\"a}kinen", title = "Linear-time String Indexing and Analysis in Small Space", journal = j-TALG, volume = "16", number = "2", pages = "17:1--17:54", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381417", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381417", abstract = "The field of succinct data structures has flourished over the past 16 years. Starting from the compressed suffix array by Grossi and Vitter (STOC 2000) and the FM-index by Ferragina and Manzini (FOCS 2000), a number of generalizations and applications \ldots{}", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Eden:2020:TBA, author = "Talya Eden and Reut Levi and Dana Ron", title = "Testing Bounded Arboricity", journal = j-TALG, volume = "16", number = "2", pages = "18:1--18:22", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381418", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381418", abstract = "In this article, we consider the problem of testing whether a graph has bounded arboricity. The class of graphs with bounded arboricity includes many important graph families (e.g., planar graphs and randomly generated preferential attachment graphs). \ldots{}", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Abraham:2020:RST, author = "Ittai Abraham and Shiri Chechik and Michael Elkin and Arnold Filtser and Ofer Neiman", title = "{Ramsey} Spanning Trees and Their Applications", journal = j-TALG, volume = "16", number = "2", pages = "19:1--19:21", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3371039", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3371039", abstract = "The metric Ramsey problem asks for the largest subset S of a metric space that can be embedded into an ultrametric (more generally into a Hilbert space) with a given distortion. Study of this problem was motivated as a non-linear version of Dvoretzky \ldots{} $^$", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Soltan:2020:DBC, author = "Saleh Soltan and Mihalis Yannakakis and Gil Zussman", title = "Doubly Balanced Connected Graph Partitioning", journal = j-TALG, volume = "16", number = "2", pages = "20:1--20:24", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381419", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381419", abstract = "We introduce and study the doubly balanced connected graph partitioning problem: Let $ G = (V, E) $ be a connected graph with a weight (supply/demand) function $ p : V \to \{ - 1, + 1 \} $ satisfying $ p(V) = \Sigma_{j \in V p}(j) = 0 $. The objective is to partition $G$ into $ (V_1, V_2)$ \ldots{}", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fomin:2020:SAR, author = "Fedor V. Fomin and Daniel Lokshtanov and Sudeshna Kolay and Fahad Panolan and Saket Saurabh", title = "Subexponential Algorithms for Rectilinear {Steiner} Tree and Arborescence Problems", journal = j-TALG, volume = "16", number = "2", pages = "21:1--21:37", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381420", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381420", abstract = "A rectilinear Steiner tree for a set K of points in the plane is a tree that connects k using horizontal and vertical lines. In the Rectilinear Steiner Tree problem, the input is a set K ={ z$_1$, z$_2$, \ldots{}, z$_n$ } of n points in the Euclidean plane (R$^2$ ), and the \ldots{}", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Balcan:2020:CCU, author = "Maria-Florina Balcan and Nika Haghtalab and Colin White", title = "$k$-center Clustering under Perturbation Resilience", journal = j-TALG, volume = "16", number = "2", pages = "22:1--22:39", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381424", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381424", abstract = "The k -center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case instances: a 2-\ldots{}", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Backens:2020:HCA, author = "Miriam Backens and Leslie Ann Goldberg", title = "{Holant} Clones and the Approximability of Conservative {Holant} Problems", journal = j-TALG, volume = "16", number = "2", pages = "23:1--23:55", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381425", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381425", abstract = "We construct a theory of holant clones to capture the notion of expressibility in the holant framework. Their role is analogous to the role played by functional clones in the study of weighted counting Constraint Satisfaction Problems. We explore the \ldots{}", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chan:2020:UPP, author = "T.-H. Hubert Chan and Haotian Jiang and Shaofeng H.-C. Jiang", title = "A Unified {PTAS} for Prize Collecting {TSP} and {Steiner} Tree Problem in Doubling Metrics", journal = j-TALG, volume = "16", number = "2", pages = "24:1--24:23", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3378571", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3378571", abstract = "We present a unified (randomized) polynomial-time approximation scheme (PTAS) for the prize collecting traveling salesman problem (PCTSP) and the prize collecting Steiner tree problem (PCSTP) in doubling metrics. Given a metric space and a penalty \ldots{}", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bliznets:2020:LBP, author = "Ivan Bliznets and Marek Cygan and Pawe{\l} Komosa and Micha{\l} Pilipczuk and Luk{\'a}s Mach", title = "Lower Bounds for the Parameterized Complexity of Minimum Fill-in and Other Completion Problems", journal = j-TALG, volume = "16", number = "2", pages = "25:1--25:31", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381426", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381426", abstract = "In this work, we focus on several completion problems for subclasses of chordal graphs: MINIMUM FILL-IN, INTERVAL COMPLETION, PROPER INTERVAL COMPLETION, TRIVIALLY PERFECT COMPLETION, and THRESHOLD COMPLETION. In these problems, the task is to add at \ldots{}", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Onak:2020:FDM, author = "Krzysztof Onak and Baruch Schieber and Shay Solomon and Nicole Wein", title = "Fully Dynamic {MIS} in Uniformly Sparse Graphs", journal = j-TALG, volume = "16", number = "2", pages = "26:1--26:19", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3378025", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3378025", abstract = "We consider the problem of maintaining a maximal independent set in a dynamic graph subject to edge insertions and deletions. Recently, Assadi et al. (at STOC'18) showed that a maximal independent set can be maintained in sublinear (in the dynamically \ldots{})", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kociumaka:2020:LTA, author = "Tomasz Kociumaka and Marcin Kubica and Jakub Radoszewski and Wojciech Rytter and Tomasz Wale{\'n}", title = "A Linear-Time Algorithm for Seeds Computation", journal = j-TALG, volume = "16", number = "2", pages = "27:1--27:23", month = apr, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3386369", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 29 08:16:18 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3386369", abstract = "A seed in a word is a relaxed version of a period in which the occurrences of the repeating subword may overlap. Our first contribution is a linear-time algorithm computing a linear-size representation of all seeds of a word (the number of seeds might \ldots{}).", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kisfaludi-Bak:2020:NET, author = "S{\'a}ndor Kisfaludi-Bak and Jesper Nederlof and Erik Jan van Leeuwen", title = "Nearly {ETH}-tight Algorithms for Planar {Steiner} Tree with Terminals on Few Faces", journal = j-TALG, volume = "16", number = "3", pages = "28:1--28:30", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3371389", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3371389", abstract = "The STEINER TREE problem is one of the most fundamental NP-complete problems, as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights and a subset of vertices (often called terminals); the \ldots{}.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cseh:2020:CCC, author = "{\'A}gnes Cseh and Tam{\'a}s Fleiner", title = "The Complexity of Cake Cutting with Unequal Shares", journal = j-TALG, volume = "16", number = "3", pages = "29:1--29:21", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3380742", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3380742", abstract = "An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure \ldots{}", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Martins:2020:PIF, author = "Rodrigo S. V. Martins and Daniel Panario and Claudio Qureshi and Eric Schmutz", title = "Periods of Iterations of Functions with Restricted Preimage Sizes", journal = j-TALG, volume = "16", number = "3", pages = "30:1--30:28", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3378570", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3378570", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bar-On:2020:TBO, author = "Achiya Bar-On and Itai Dinur and Orr Dunkelman and Rani Hod and Nathan Keller and Eyal Ronen and Adi Shamir", title = "Tight Bounds on Online Checkpointing Algorithms", journal = j-TALG, volume = "16", number = "3", pages = "31:1--31:22", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3379543", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3379543", abstract = "The problem of online checkpointing is a classical problem with numerous applications that has been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain $k$ memorized checkpoints during a long \ldots{}", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Lokshtanov:2020:CSI, author = "Daniel Lokshtanov and Fahad Panolan and Saket Saurabh and Roohani Sharma and Meirav Zehavi", title = "Covering Small Independent Sets and Separators with Applications to Parameterized Algorithms", journal = j-TALG, volume = "16", number = "3", pages = "32:1--32:31", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3379698", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3379698", abstract = "We present two new combinatorial tools for the design of parameterized algorithms. The first is a simple linear time randomized algorithm that given as input a $d$-degenerate graph G and an integer k, outputs an independent set Y, such that for every \ldots{}", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chlamtac:2020:ASD, author = "Eden Chlamt{\'a}c and Michael Dinitz and Guy Kortsarz and Bundit Laekhanukit", title = "Approximating Spanners and Directed {Steiner} Forest: Upper and Lower Bounds", journal = j-TALG, volume = "16", number = "3", pages = "33:1--33:31", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381451", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3381451", abstract = "It was recently found that there are very close connections between the existence of additive spanners (subgraphs where all distances are preserved up to an additive stretch), distance preservers (subgraphs in which demand pairs have their distance \ldots{}).", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Grohe:2020:IIT, author = "Martin Grohe and Daniel Neuen and Pascal Schweitzer and Daniel Wiebking", title = "An Improved Isomorphism Test for Bounded-tree-width Graphs", journal = j-TALG, volume = "16", number = "3", pages = "34:1--34:31", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3382082", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3382082", abstract = "We give a new FPT algorithm testing isomorphism of $n$-vertex graphs of tree-width $k$ in time $ 2^{k \polylog (k)} n^3$, improving the FPT algorithm due to Lokshtanov, Pilipczuk, Pilipczuk, and Saurabh (FOCS 2014), which runs in time $ 2^{O(k^5 \log k)} n^5$. Based on an \ldots{}", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Berger:2020:TSO, author = "Andr{\'e} Berger and L{\'a}szl{\'o} Kozma and Matthias Mnich and Roland Vincze", title = "Time- and Space-optimal Algorithm for the Many-visits {TSP}", journal = j-TALG, volume = "16", number = "3", pages = "35:1--35:22", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3382038", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3382038", abstract = "The many-visits traveling salesperson problem (MV-TSP) asks for an optimal tour of $n$ cities that visits each city $c$ a prescribed number $ k_c$ of times. Travel costs may be asymmetric, and visiting a city twice in a row may incur a non-zero cost. The MV-TSP \ldots{}", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Blanca:2020:SLH, author = "Antonio Blanca and Zongchen Chen and Daniel Stefankovi{\`e} and Eric Vigoda", title = "Structure Learning of {$H$}-Colorings", journal = j-TALG, volume = "16", number = "3", pages = "36:1--36:28", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3382207", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3382207", abstract = "We study the following structure learning problem for $H$-colorings. For a fixed (and known) constraint graph $H$ with $q$ colors, given access to uniformly random $H$-colorings of an unknown graph $ G = (V, E)$, how many samples are required to learn the edges of \ldots{}", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Dyer:2020:RWS, author = "Martin E. Dyer and Andreas Galanis and Leslie Ann Goldberg and Mark Jerrum and Eric Vigoda", title = "Random Walks on Small World Networks", journal = j-TALG, volume = "16", number = "3", pages = "37:1--37:33", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3382208", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3382208", abstract = "We study the mixing time of random walks on small-world networks modelled as follows: starting with the 2-dimensional periodic grid, each pair of vertices $ \{ u, v \} $ with distance $ d > 1 $ is added as a ``long-range'' edge with probability proportional to $ d^{-r} $,", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Antoniadis:2020:PET, author = "Antonios Antoniadis and Krzysztof Fleszar and Ruben Hoeksma and Kevin Schewior", title = "A {PTAS} for {Euclidean} {TSP} with Hyperplane Neighborhoods", journal = j-TALG, volume = "16", number = "3", pages = "38:1--38:16", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3383466", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3383466", abstract = "In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that visits at least one point in each region. Even in the Euclidean plane, TSPN \ldots{}", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bonamy:2020:EMD, author = "Marthe Bonamy and Oscar Defrain and Marc Heinrich and Micha{\l} Pilipczuk and Jean-Florent Raymond", title = "Enumerating Minimal Dominating Sets in {Kt}-free Graphs and Variants", journal = j-TALG, volume = "16", number = "3", pages = "39:1--39:23", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3386686", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3386686", abstract = "It is a long-standing open problem whether the minimal dominating sets of a graph can be enumerated in output-polynomial time. In this article we investigate this problem in graph classes defined by forbidding an induced subgraph. In particular, we \ldots{}", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Rottenstreich:2020:CHM, author = "Ori Rottenstreich and Haim Kaplan and Avinatan Hassidim", title = "Clustering in Hypergraphs to Minimize Average Edge Service Time", journal = j-TALG, volume = "16", number = "3", pages = "40:1--40:28", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3386121", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3386121", abstract = "We study the problem of clustering the vertices of a weighted hypergraph such that on average the vertices of each edge can be covered by a small number of clusters. This problem has many applications, such as for designing medical tests, clustering \ldots{}", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Solomon:2020:IDG, author = "Shay Solomon and Nicole Wein", title = "Improved Dynamic Graph Coloring", journal = j-TALG, volume = "16", number = "3", pages = "41:1--41:24", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3392724", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jul 8 17:38:54 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/abs/10.1145/3392724", abstract = "This article studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $ n^{1 - \epsilon } $ for any $ \epsilon > 0 $, is NP-hard in static graphs, there is no hope to achieve \ldots{}", acknowledgement = ack-nhfb, articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bonnet:2020:PHA, author = "{\'E}douard Bonnet and Tillmann Miltzow", title = "Parameterized Hardness of Art Gallery Problems", journal = j-TALG, volume = "16", number = "4", pages = "42:1--42:23", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3398684", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3398684", abstract = "Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each other if the line segment between x and y is contained in P. The Point Guard Art Gallery problem asks for a minimum set S such that every point in P is visible \ldots{}", acknowledgement = ack-nhfb, articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Galvez:2020:SEO, author = "Waldo G{\'a}lvez and Jos{\'e} A. Soto and Jos{\'e} Verschae", title = "Symmetry Exploitation for Online Machine Covering with Bounded Migration", journal = j-TALG, volume = "16", number = "4", pages = "43:1--43:22", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3397535", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3397535", abstract = "Online models that allow recourse can be highly effective in situations where classical online models are too pessimistic. One such problem is the online machine covering problem on identical machines. In this setting, jobs arrive one by one and must be \ldots{}", acknowledgement = ack-nhfb, articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Baswana:2020:ASS, author = "Surender Baswana and Keerti Choudhary and Moazzam Hussain and Liam Roditty", title = "Approximate Single-Source Fault Tolerant Shortest Path", journal = j-TALG, volume = "16", number = "4", pages = "44:1--44:22", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3397532", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3397532", abstract = "Let G=(V,E) be an n -vertices m -edges directed graph with edge weights in the range [1, W ] for some parameter W, and s \epsilon V be a designated source. In this article, we address several variants of the problem of maintaining the (1+ \epsilon )-approximate shortest \ldots{}", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Alman:2020:DPP, author = "Josh Alman and Matthias Mnich and Virginia Vassilevska Williams", title = "Dynamic Parameterized Problems and Algorithms", journal = j-TALG, volume = "16", number = "4", pages = "45:1--45:46", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3395037", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3395037", abstract = "Fixed-parameter algorithms and kernelization are two powerful methods to solve NP-hard problems. Yet so far those algorithms have been largely restricted to static inputs. In this article, we provide fixed-parameter algorithms and kernelizations for \ldots{}", acknowledgement = ack-nhfb, articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chakrabarty:2020:NUC, author = "Deeparnab Chakrabarty and Prachi Goyal and Ravishankar Krishnaswamy", title = "The Non-Uniform $k$-Center Problem", journal = j-TALG, volume = "16", number = "4", pages = "46:1--46:19", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3392720", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3392720", abstract = "In this article, we introduce and study the Non-Uniform $k$-Center (NUkC) problem. Given a finite metric space $ (X, d)$ and a collection of balls of radii $ \{ r_1 \geq \ldots {} \geq r_k \} $, the NUkC problem is to find a placement of their centers in the metric space and find \ldots{}", acknowledgement = ack-nhfb, articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Eiben:2020:CPP, author = "Eduard Eiben and Iyad Kanj", title = "A Colored Path Problem and Its Applications", journal = j-TALG, volume = "16", number = "4", pages = "47:1--47:48", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3396573", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3396573", abstract = "Given a set of obstacles and two points in the plane, is there a path between the two points that does not cross more than k different obstacles? Equivalently, can we remove k obstacles so that there is an obstacle-free path between the two designated \ldots{}", acknowledgement = ack-nhfb, articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bringmann:2020:TED, author = "Karl Bringmann and Pawe{\l} Gawrychowski and Shay Mozes and Oren Weimann", title = "Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (Unless {APSP} Can)", journal = j-TALG, volume = "16", number = "4", pages = "48:1--48:22", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3381878", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3381878", abstract = "The edit distance between two rooted ordered trees with n nodes labeled from an alphabet $ \Sigma $ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well \ldots{}", acknowledgement = ack-nhfb, articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Lee:2020:MMO, author = "Euiwoong Lee and Sahil Singla", title = "Maximum Matching in the Online Batch-arrival Model", journal = j-TALG, volume = "16", number = "4", pages = "49:1--49:31", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3399676", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3399676", abstract = "Consider a two-stage matching problem, where edges of an input graph are revealed in two stages (batches) and in each stage we have to immediately and irrevocably extend our matching using the edges from that stage. The natural greedy algorithm is half \ldots{}", acknowledgement = ack-nhfb, articleno = "49", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fischer:2020:DSS, author = "Johannes Fischer and {Tomohiro I} and Dominik K{\"o}ppl", title = "Deterministic Sparse Suffix Sorting in the Restore Model", journal = j-TALG, volume = "16", number = "4", pages = "50:1--50:53", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3398681", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3398681", abstract = "Given a text T of length n, we propose a deterministic online algorithm computing the sparse suffix array and the sparse longest common prefix array of T in O( c \sqrt lg n + m lg m lg n lg$^*$ n ) time with O( m ) words of space under the premise that the space \ldots{}", acknowledgement = ack-nhfb, articleno = "50", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Agrawal:2020:PAA, author = "Akanksha Agrawal and Daniel Lokshtanov and Pranabendu Misra and Saket Saurabh and Meirav Zehavi", title = "Polylogarithmic Approximation Algorithms for Weighted-{$F$}-deletion Problems", journal = j-TALG, volume = "16", number = "4", pages = "51:1--51:38", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3389338", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3389338", acknowledgement = ack-nhfb, articleno = "51", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Beame:2020:EEI, author = "Paul Beame and Sariel Har-Peled and Sivaramakrishnan Natarajan Ramamoorthy and Cyrus Rashtchian and Makrand Sinha", title = "Edge Estimation with Independent Set Oracles", journal = j-TALG, volume = "16", number = "4", pages = "52:1--52:27", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3404867", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3404867", abstract = "We study the task of estimating the number of edges in a graph, where the access to the graph is provided via an independent set oracle. Independent set queries draw motivation from group testing and have applications to the complexity of decision \ldots{}", acknowledgement = ack-nhfb, articleno = "52", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Blomer:2020:CTS, author = "Johannes Bl{\"o}mer and Sascha Brauer and Kathrin Bujna", title = "A Complexity Theoretical Study of Fuzzy {$K$}-Means", journal = j-TALG, volume = "16", number = "4", pages = "53:1--53:25", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3409385", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3409385", abstract = "The fuzzy $K$-means problem is a popular generalization of the well-known $K$-means problem to soft clusterings. In this article, we present the first algorithmic study of the problem going beyond heuristics. Our main result is that, assuming a constant \ldots{}", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Carbonnel:2020:PWM, author = "Cl{\'e}ment Carbonnel and Miguel Romero and Stanislav Zivn{\'y}", title = "Point-Width and {Max-CSPs}", journal = j-TALG, volume = "16", number = "4", pages = "54:1--54:28", month = sep, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1145/3409447", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Sep 26 07:08:42 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3409447", abstract = "The complexity of (unbounded-arity) Max-CSPs under structural restrictions is poorly understood. The two most general hypergraph properties known to ensure tractability of Max-CSPs, \beta -acyclicity and bounded (incidence) MIM-width, are incomparable and \ldots{}", acknowledgement = ack-nhfb, articleno = "54", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Harris:2021:ORO, author = "David G. Harris", title = "Oblivious Resampling Oracles and Parallel Algorithms for the Lopsided {Lov{\'a}sz} Local Lemma", journal = j-TALG, volume = "17", number = "1", pages = "1:1--1:32", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3392035", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3392035", abstract = "The Lov{\'a}sz Local Lemma (LLL) shows that, for a collection of ``bad'' events B in a probability space that are not too likely and not too interdependent, there is a positive probability that no events in B occur. Moser and Tardos (2010) gave sequential and \ldots{}", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chan:2021:DAO, author = "Timothy M. Chan and R. Ryan Williams", title = "Deterministic {APSP}, Orthogonal Vectors, and More: Quickly Derandomizing {Razborov--Smolensky}", journal = j-TALG, volume = "17", number = "1", pages = "2:1--2:14", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3402926", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3402926", abstract = "We show how to solve all-pairs shortest paths on n nodes in deterministic $n^3 /2^{\Omega(\sqrt{\log n})}$ time, and how to count the pairs of orthogonal vectors among $n$ $0$--$1$ vectors in $d = c \log n$ dimensions in deterministic $n^{2 - 1 / O (\log c)}$ time. These running times \ldots{}", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bjelde:2021:TBO, author = "Antje Bjelde and Jan Hackfeld and Yann Disser and Christoph Hansknecht and Maarten Lipmann and Julie Mei{\ss}ner and Miriam Schl{\"O}ter and Kevin Schewior and Leen Stougie", title = "Tight Bounds for Online {TSP} on the Line", journal = j-TALG, volume = "17", number = "1", pages = "3:1--3:58", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3422362", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3422362", abstract = "We consider the online traveling salesperson problem (TSP), where requests appear online over time on the real line and need to be visited by a server initially located at the origin. We distinguish between closed and open online TSP, depending on \ldots{}", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Guo:2021:ZHP, author = "Heng Guo and Chao Liao and Pinyan Lu and Chihao Zhang", title = "Zeros of {Holant} Problems: Locations and Algorithms", journal = j-TALG, volume = "17", number = "1", pages = "4:1--4:25", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3418056", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3418056", abstract = "We present fully polynomial-time (deterministic or randomised) approximation schemes for Holant problems, defined by a non-negative constraint function satisfying a generalised second-order recurrence modulo in a couple of exceptional cases. As a \ldots{}", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{deBerg:2021:FGC, author = "Mark de Berg and Kevin Buchin and Bart M. P. Jansen and Gerhard Woeginger", title = "Fine-grained Complexity Analysis of Two Classic {TSP} Variants", journal = j-TALG, volume = "17", number = "1", pages = "5:1--5:29", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3414845", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3414845", abstract = "We analyze two classic variants of the TRAVELING SALESMAN PROBLEM (TSP) using the toolkit of fine-grained complexity. Our first set of results is motivated by the BITONIC TSP problem: given a set of n points in the plane, compute a shortest tour \ldots{}", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cygan:2021:RCM, author = "Marek Cygan and Pawe{\l} Komosa and Daniel Lokshtanov and Marcin Pilipczuk and Micha{\l} Pilipczuk and Saket Saurabh and Magnus Wahlstr{\"o}m", title = "Randomized Contractions Meet Lean Decompositions", journal = j-TALG, volume = "17", number = "1", pages = "6:1--6:30", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3426738", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3426738", abstract = "We show an algorithm that, given an $n$-vertex graph $G$ and a parameter $k$, in time $2^{O (k \log k)} n^{O(1)}$ finds a tree decomposition of $G$ with the following properties: --- every adhesion of the tree decomposition is of size at most $k$, and --- every bag of the \ldots{}", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Prezza:2021:OSE, author = "Nicola Prezza", title = "Optimal Substring Equality Queries with Applications to Sparse Text Indexing", journal = j-TALG, volume = "17", number = "1", pages = "7:1--7:23", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3426870", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3426870", abstract = "We consider the problem of encoding a string of length n from an integer alphabet of size \sigma so access, substring equality, and Longest Common Extension (LCE) queries can be answered efficiently. We describe a new space-optimal data structure supporting \ldots{}", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Christiansen:2021:OTD, author = "Anders Roy Christiansen and Mikko Berggren Ettienne and Tomasz Kociumaka and Gonzalo Navarro and Nicola Prezza", title = "Optimal-Time Dictionary-Compressed Indexes", journal = j-TALG, volume = "17", number = "1", pages = "8:1--8:39", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3426473", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3426473", abstract = "We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result, we combine several recent findings, including string \ldots{}", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Har-Peled:2021:JCP, author = "Sariel Har-Peled and Mitchell Jones", title = "Journey to the Center of the Point Set", journal = j-TALG, volume = "17", number = "1", pages = "9:1--9:21", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3431285", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3431285", abstract = "Let $P$ be a set of $n$ points in $R^d$. For a parameter $\alpha \in (0,1)$, an $\alpha$-centerpoint of $P$ is a point $p \in R^d$ such that all closed halfspaces containing $P$ also contain at least $\alpha n$ points of $P$. We revisit an algorithm of Clarkson et al. [1996] that computes \ldots{}", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Gutin:2021:RSP, author = "Gregory Gutin and Magnus Wahlstr{\"o}m and Meirav Zehavi", title = "$r$-Simple $k$-Path and Related Problems Parameterized by $ k / r$", journal = j-TALG, volume = "17", number = "1", pages = "10:1--10:64", month = jan, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3439721", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Feb 10 10:25:20 MST 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3439721", abstract = "Abasi et al. (2014) introduced the following two problems. In the $r$-Simple $k$-Path problem, given a digraph $G$ on $n$ vertices and positive integers $r$, $k$, decide whether $G$ has an $r$-simple $k$-path, which is a walk where every vertex occurs at most $r$ times and \ldots{}", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Lokshtanov:2021:AFV, author = "Daniel Lokshtanov and Pranabendu Misra and Joydeep Mukherjee and Fahad Panolan and Geevarghese Philip and Saket Saurabh", title = "$2$-Approximating Feedback Vertex Set in Tournaments", journal = j-TALG, volume = "17", number = "2", pages = "11:1--11:14", month = jun, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3446969", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jun 9 07:03:16 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3446969", abstract = "A tournament is a directed graph T such that every pair of vertices is connected by an arc. A feedback vertex set is a set S of vertices in T such that T --- S is acyclic. We consider the Feedback Vertex Set problem in tournaments. Here, the input is a \ldots{}", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chitnis:2021:PAA, author = "Rajesh Chitnis and Andreas Emil Feldmann and Pasin Manurangsi", title = "Parameterized Approximation Algorithms for Bidirected {Steiner} Network Problems", journal = j-TALG, volume = "17", number = "2", pages = "12:1--12:68", month = jun, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3447584", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jun 9 07:03:16 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3447584", abstract = "The Directed Steiner Network (DSN) problem takes as input a directed graph G =( V, E ) with non-negative edge-weights and a set D \subseteq V $ \times $ V of k demand pairs. The aim is to compute the cheapest network N \subseteq G for which there is an s\rightarrow t path for each \ldots{}", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chudnovsky:2021:FSO, author = "Maria Chudnovsky and Alex Scott and Paul Seymour", title = "Finding a Shortest Odd Hole", journal = j-TALG, volume = "17", number = "2", pages = "13:1--13:21", month = jun, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3447869", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jun 9 07:03:16 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3447869", abstract = "An odd hole in a graph is an induced cycle with odd length greater than 3. In an earlier paper (with Sophie Spirkl), solving a longstanding open problem, we gave a polynomial-time algorithm to test if a graph has an odd hole. We subsequently showed that,. \ldots{}", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chekuri:2021:NWN, author = "Chandra Chekuri and Alina Ene and Ali Vakilian", title = "Node-weighted Network Design in Planar and Minor-closed Families of Graphs", journal = j-TALG, volume = "17", number = "2", pages = "14:1--14:25", month = jun, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3447959", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jun 9 07:03:16 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3447959", abstract = "We consider node-weighted survivable network design (SNDP) in planar graphs and minor-closed families of graphs. The input consists of a node-weighted undirected graph G = ( V, E ) and integer connectivity requirements r ( uv ) for each unordered pair of \ldots{}", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Boczkowski:2021:NTP, author = "Lucas Boczkowski and Uriel Feige and Amos Korman and Yoav Rodeh", title = "Navigating in Trees with Permanently Noisy Advice", journal = j-TALG, volume = "17", number = "2", pages = "15:1--15:27", month = jun, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3448305", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jun 9 07:03:16 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3448305", abstract = "We consider a search problem on trees in which an agent starts at the root of a tree and aims to locate an adversarially placed treasure, by moving along the edges, while relying on local, partial information. Specifically, each node in the tree holds a \ldots{}", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Czumaj:2021:GSD, author = "Artur Czumaj and Peter Davies and Merav Parter", title = "Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space", journal = j-TALG, volume = "17", number = "2", pages = "16:1--16:27", month = jun, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3451992", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jun 9 07:03:16 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3451992", abstract = "The Massively Parallel Computation (MPC) model is an emerging model that distills core aspects of distributed and parallel computation, developed as a tool to solve combinatorial (typically graph) problems in systems of many machines with limited space. \ldots{}", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Halldorsson:2021:SBO, author = "Magn{\'u}s M. Halld{\'o}rsson and Tigran Tonoyan", title = "Sparse Backbone and Optimal Distributed {SINR} Algorithms", journal = j-TALG, volume = "17", number = "2", pages = "17:1--17:34", month = jun, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3452937", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jun 9 07:03:16 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3452937", abstract = "We develop randomized distributed algorithms for many of the most fundamental communication problems in wireless networks under the Signal to Interference and Noise Ratio (SINR) model of communication, including (multi-message) broadcast, local \ldots{}", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Darwish:2021:MAN, author = "Omar Darwish and Amr Elmasry and Jyrki Katajainen", title = "Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls", journal = j-TALG, volume = "17", number = "2", pages = "18:1--18:19", month = jun, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3452938", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Jun 9 07:03:16 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3452938", abstract = "We consider space-bounded computations on a random-access machine, where the input is given on a read-only random-access medium, the output is to be produced to a write-only sequential-access medium, and the available workspace allows random reads and \ldots{}", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bibak:2021:ISC, author = "Ali Bibak and Charles Carlson and Karthekeyan Chandrasekaran", title = "Improving the Smoothed Complexity of {FLIP} for Max Cut Problems", journal = j-TALG, volume = "17", number = "3", pages = "19:1--19:38", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3454125", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3454125", abstract = "Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, \ldots{}", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cohen:2021:E, author = "Edith Cohen", title = "Editorial", journal = j-TALG, volume = "17", number = "3", pages = "19e:1--19e:1", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3462270", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3462270", acknowledgement = ack-nhfb, articleno = "19e", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Coester:2021:ISP, author = "Christian Coester and Elias Koutsoupias and Philip Lazos", title = "The Infinite Server Problem", journal = j-TALG, volume = "17", number = "3", pages = "20:1--20:23", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3456632", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3456632", abstract = "We study a variant of the k -server problem, the infinite server problem, in which infinitely many servers reside initially at a particular point of the metric space and serve a sequence of requests. In the framework of competitive analysis, we show a \ldots{}", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Viola:2021:CBL, author = "Caterina Viola and Stanislav Zivn{\'y}", title = "The Combined Basic {LP} and Affine {IP} Relaxation for Promise {VCSPs} on Infinite Domains", journal = j-TALG, volume = "17", number = "3", pages = "21:1--21:23", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3458041", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3458041", abstract = "Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most recently promise CSPs. In this work, we extend an \ldots{}", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Focke:2021:CAC, author = "Jacob Focke and Leslie Ann Goldberg and Stanislav Zivn{\'y}", title = "The Complexity of Approximately Counting Retractions to Square-free Graphs", journal = j-TALG, volume = "17", number = "3", pages = "22:1--22:51", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3458040", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3458040", abstract = "A retraction is a homomorphism from a graph G to an induced subgraph H of G that is the identity on H. In a long line of research, retractions have been studied under various algorithmic settings. Recently, the problem of approximately counting \ldots{}", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Azar:2021:OSD, author = "Yossi Azar and Arun Ganesh and Rong Ge and Debmalya Panigrahi", title = "Online Service with Delay", journal = j-TALG, volume = "17", number = "3", pages = "23:1--23:31", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3459925", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3459925", abstract = "In this article, we introduce the online service with delay problem. In this problem, there are n points in a metric space that issue service requests over time, and there is a server that serves these requests. The goal is to minimize the sum of \ldots{}", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Aronov:2021:PPS, author = "Boris Aronov and Mark {De Berg} and Joachim Gudmundsson and Michael Horton", title = "On $ \beta $-Plurality Points in Spatial Voting Games", journal = j-TALG, volume = "17", number = "3", pages = "24:1--24:21", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3459097", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3459097", abstract = "Let V be a set of n points in mathcal R$^d$, called voters. A point p \in mathcal R$^d$ is a plurality point for V when the following holds: For every q \in mathcal R$^d$, the number of voters closer to p than to q is at least the number of voters closer to q than \ldots{}", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bringmann:2021:DFD, author = "Karl Bringmann and Marvin K{\"u}Nnemann and Andr{\'e} Nusser", title = "Discrete {Fr{\'e}chet} Distance under Translation: Conditional Hardness and an Improved Algorithm", journal = j-TALG, volume = "17", number = "3", pages = "25:1--25:42", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3460656", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3460656", abstract = "The discrete Fr{\'e}chet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr{\'e}chet distance under translation, which enables detection of similar movement patterns in different spatial domains. For polygonal \ldots{}", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Lokshtanov:2021:ACP, author = "Daniel Lokshtanov and Andreas Bj{\"O}rklund and Saket Saurabh and Meirav Zehavi", title = "Approximate Counting of $k$-Paths: Simpler, Deterministic, and in Polynomial Space", journal = j-TALG, volume = "17", number = "3", pages = "26:1--26:44", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3461477", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3461477", abstract = "Recently, Brand et al. [STOC 2018] gave a randomized mathcal O(4$^k$ m \epsilon $^{-2}$)-time exponential-space algorithm to approximately compute the number of paths on k vertices in a graph G up to a multiplicative error of 1 \pm \epsilon based on exterior algebra. Prior to our \ldots{}", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Brakensiek:2021:QSI, author = "Joshua Brakensiek and Venkatesan Guruswami", title = "The Quest for Strong Inapproximability Results with Perfect Completeness", journal = j-TALG, volume = "17", number = "3", pages = "27:1--27:35", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3459668", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Aug 4 07:47:50 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3459668", abstract = "The Unique Games Conjecture has pinned down the approximability of all constraint satisfaction problems (CSPs), showing that a natural semidefinite programming relaxation offers the optimal worst-case approximation ratio for any CSP. This elegant \ldots{}", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Even:2021:SRA, author = "Guy Even and Reut Levi and Moti Medina and Adi Ros{\'e}n", title = "Sublinear Random Access Generators for Preferential Attachment Graphs", journal = j-TALG, volume = "17", number = "4", pages = "28:1--28:26", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3464958", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3464958", abstract = "We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space, and randomness complexities of such samplers.\par In the standard approach, the whole graph is chosen randomly according to the randomized evolving process, stored in full, and then queries on the sampled graph are answered by simply accessing the stored graph. This may require prohibitive amounts of time, space, and random bits, especially when only a small number of queries are actually issued. Instead, we propose a setting where one generates parts of the sampled graph on-the-fly, in response to queries, and therefore requires amounts of time, space, and random bits that are a function of the actual number of queries. Yet, the responses to the queries correspond to a graph sampled from the distribution in question.\par Within this framework, we focus on two random graph models: the Barab{\'a}si--Albert Preferential Attachment model (BA-graphs) (Science, 286 (5439):509--512) (for the special case of out-degree 1) and the random recursive tree model (Theory of Probability and Mathematical Statistics, (51):1--28). We give on-the-fly generation algorithms for both models. With probability 1-1/poly(n), each and every query is answered in polylog(n) time, and the increase in space and the number of random bits consumed by any single query are both polylog(n), where n denotes the number of vertices in the graph.\par Our work thus proposes a new approach for the access to huge graphs sampled from a given distribution, and our results show that, although the BA random graph model is defined by a sequential process, efficient random access to the graph s nodes is possible. In addition to the conceptual contribution, efficient on-the-fly generation of random graphs can serve as a tool for the efficient simulation of sublinear algorithms over large BA-graphs, and the efficient estimation of their on such graphs.", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bernstein:2021:DAD, author = "Aaron Bernstein and Sebastian Forster and Monika Henzinger", title = "A Deamortization Approach for Dynamic Spanner and Dynamic Maximal Matching", journal = j-TALG, volume = "17", number = "4", pages = "29:1--29:51", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3469833", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3469833", abstract = "Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For this reason, \ldots{}", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Abboud:2021:SCH, author = "Amir Abboud and Keren Censor-Hillel and Seri Khoury and Ami Paz", title = "Smaller Cuts, Higher Lower Bounds", journal = j-TALG, volume = "17", number = "4", pages = "30:1--30:40", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3469834", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3469834", abstract = "This article proves strong lower bounds for distributed computing in the congest model, by presenting the bit-gadget: a new technique for constructing graphs with small cuts. The contribution of bit-gadgets is twofold. First, developing careful sparse \ldots{}", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Sun:2021:QMT, author = "Xiaoming Sun and David P. Woodruff and Guang Yang and Jialin Zhang", title = "Querying a Matrix through Matrix--Vector Products", journal = j-TALG, volume = "17", number = "4", pages = "31:1--31:19", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3470566", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3470566", abstract = "We consider the maximum flow problem in directed planar graphs with capacities on both vertices and arcs and with multiple sources and sinks. We present three algorithms when the capacities are integers. The first algorithm runs in O ( min \{ k$^2$ n, n log$^3$ n + \})", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Mastrolilli:2021:CIM, author = "Monaldo Mastrolilli", title = "The Complexity of the Ideal Membership Problem for Constrained Problems Over the {Boolean} Domain", journal = j-TALG, volume = "17", number = "4", pages = "32:1--32:29", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3449350", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3449350", abstract = "Given an ideal I and a polynomial f the Ideal Membership Problem (IMP) is to test if $ f \epsilon I $. This problem is a fundamental algorithmic problem with important applications and notoriously intractable. We study the complexity of the IMP for combinatorial \ldots{}", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Galvez:2021:AGK, author = "Waldo G{\'a}lvez and Fabrizio Grandoni and Salvatore Ingala and Sandy Heydrich and Arindam Khan and Andreas Wiese", title = "Approximating Geometric Knapsack via {$L$}-packings", journal = j-TALG, volume = "17", number = "4", pages = "33:1--33:67", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3473713", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3473713", abstract = "We study the two-dimensional geometric knapsack problem, in which we are given a set of n axis-aligned rectangular items, each one with an associated profit, and an axis-aligned square knapsack. The goal is to find a (non-overlapping) packing of a maximum \ldots{}", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Tarjan:2021:ZT, author = "Robert E. Tarjan and Caleb Levy and Stephen Timmel", title = "Zip Trees", journal = j-TALG, volume = "17", number = "4", pages = "34:1--34:12", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3476830", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3476830", abstract = "We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank and the tree is \ldots{}", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{An:2021:AAB, author = "Hyung-Chan An and Robert Kleinberg and David B. Shmoys", title = "Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem", journal = j-TALG, volume = "17", number = "4", pages = "35:1--35:12", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3478537", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3478537", abstract = "We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-\ldots{}) \ldots{}", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bodwin:2021:BDP, author = "Greg Bodwin and Virginia Vassilevska Williams", title = "Better Distance Preservers and Additive Spanners", journal = j-TALG, volume = "17", number = "4", pages = "36:1--36:24", month = oct, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1145/3490147", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Nov 3 10:00:35 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3490147", abstract = "We study two popular ways to sketch the shortest path distances of an input graph. The first is distance preservers, which are sparse subgraphs that agree with the distances of the original graph on a given set of demand pairs. Prior work on distance \ldots{}", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Graf:2022:AWI, author = "Alessandra Graf and David G. Harris and Penny Haxell", title = "Algorithms for Weighted Independent Transversals and Strong Colouring", journal = j-TALG, volume = "18", number = "1", pages = "1:1--1:16", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3474057", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3474057", abstract = "An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph and vertex partition, \ldots{}", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chrobak:2022:SAO, author = "Marek Chrobak and Mordecai Golin and J. Ian Munro and Neal E. Young", title = "A Simple Algorithm for Optimal Search Trees with Two-way Comparisons", journal = j-TALG, volume = "18", number = "1", pages = "2:1--2:11", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3477910", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3477910", abstract = "We present a simple O(n$^4$ ) -time algorithm for computing optimal search trees with two-way comparisons. The only previous solution to this problem, by Anderson et al., has the same running time but is significantly more complicated and is restricted to the \ldots{}", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cheng:2022:DDS, author = "Siu-Wing Cheng and Man-Kit Lau", title = "Dynamic Distribution-Sensitive Point Location", journal = j-TALG, volume = "18", number = "1", pages = "3:1--3:63", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3487403", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3487403", abstract = "We propose a dynamic data structure for the distribution-sensitive point location problem in the plane. Suppose that there is a fixed query distribution within a convex subdivision S, and we are given an oracle that can return in O (1) time the probability \ldots{}", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Hoefer:2022:IAS, author = "Martin Hoefer and Tsvi Kopelowitz", title = "Introduction to the {ACM-SIAM Symposium on Discrete Algorithms (SODA) 2019} Special Issue", journal = j-TALG, volume = "18", number = "1", pages = "4e:1--4e:2", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3508460", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3508460", acknowledgement = ack-nhfb, articleno = "4e", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Grzesik:2022:PTA, author = "Andrzej Grzesik and Tereza Klimosov{\'a} and Marcin Pilipczuk and Micha{\l} Pilipczuk", title = "Polynomial-time Algorithm for Maximum Weight Independent Set on {$ P_6 $}-free Graphs", journal = j-TALG, volume = "18", number = "1", pages = "4:1--4:57", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3414473", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3414473", abstract = "In the classic Maximum Weight Independent Set problem, we are given a graph G with a nonnegative weight function on its vertices, and the goal is to find an independent set in G of maximum possible weight. While the problem is NP-hard in general, we give \ldots{}", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cao:2022:EAT, author = "Nairen Cao and Jeremy T. Fineman and Katina Russell and Eugene Yang", title = "{I/O}-Efficient Algorithms for Topological Sort and Related Problems", journal = j-TALG, volume = "18", number = "1", pages = "5:1--5:24", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3418356", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3418356", abstract = "This article presents I/O-efficient algorithms for topologically sorting a directed acyclic graph and for the more general problem identifying and topologically sorting the strongly connected components of a directed graph G = ( V, E ). Both algorithms are \ldots{}", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Abboud:2022:SBL, author = "Amir Abboud and Karl Bringmann and Danny Hermelin and Dvir Shabtay", title = "{SETH}-based Lower Bounds for Subset Sum and Bicriteria Path", journal = j-TALG, volume = "18", number = "1", pages = "6:1--6:22", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3450524", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3450524", abstract = "Subset Sumand k -SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. An important open problem in this area is to base the hardness of one of \ldots{}", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Wei:2022:OVA, author = "Alexander Wei", title = "Optimal {Las Vegas} Approximate Near Neighbors in $ \ell_p $", journal = j-TALG, volume = "18", number = "1", pages = "7:1--7:27", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3461777", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3461777", abstract = "We show that approximate near neighbor search in high dimensions can be solved in a Las Vegas fashion (i.e., without false negatives) for l $_p$ ({1$<$}= p {$<$}= 2) while matching the performance of optimal locality-sensitive hashing. Specifically, we construct a data-\ldots{}", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Wang:2022:TBO, author = "Ruosong Wang and David P. Woodruff", title = "Tight Bounds for $ \ell_1 $ Oblivious Subspace Embeddings", journal = j-TALG, volume = "18", number = "1", pages = "8:1--8:32", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3477537", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3477537", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Wang:2022:MFP, author = "Yipu Wang", title = "Max Flows in Planar Graphs with Vertex Capacities", journal = j-TALG, volume = "18", number = "1", pages = "9:1--9:27", month = jan, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3504032", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 28 06:47:39 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3504032", abstract = "We consider the maximum flow problem in directed planar graphs with capacities on both vertices and arcs and with multiple sources and sinks. We present three algorithms when the capacities are integers. The first algorithm runs in O ( min \{ k$^2$ n, n log$^3$ n + \ldots{} \} ) \ldots{}", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bhattacharya:2022:FDC, author = "Sayan Bhattacharya and Fabrizio Grandoni and Janardhan Kulkarni and Quanquan C. Liu and Shay Solomon", title = "Fully Dynamic {$ (\Delta + 1) $}-Coloring in {$ O(1) $} Update Time", journal = j-TALG, volume = "18", number = "2", pages = "10:1--10:25", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3494539", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3494539", abstract = "The problem of $ (\Delta + 1)$-vertex coloring a graph of maximum degree $ \Delta $ has been extremely well studied over the years in various settings and models. Surprisingly, for the dynamic setting, almost nothing was known until recently. In SODA'18, Bhattacharya, \ldots{}", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bonnet:2022:VSU, author = "{\'E}douard Bonnet", title = "4 vs 7 Sparse Undirected Unweighted Diameter Is {SETH}-hard at Time $ n^{4 / 3} $", journal = j-TALG, volume = "18", number = "2", pages = "11:1--11:14", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3494540", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3494540", abstract = "We show, assuming the Strong Exponential Time Hypothesis, that for every $ \epsilon > 0 $, approximating undirected unweighted Diameter on $n$-vertex $m$-edge graphs within ratio$ 7 / 4 - \epsilon $ requires $^m{4 / 3 - o(1)}$ time, even when $ m = {\~ O}(n)$. This is the first result that conditionally rules out a near-linear time 5/3-approximation for undirected Diameter.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Haslegrave:2022:TDB, author = "John Haslegrave and Thomas Sauerwald and John Sylvester", title = "Time Dependent Biased Random Walks", journal = j-TALG, volume = "18", number = "2", pages = "12:1--12:30", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3498848", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3498848", abstract = "We study the biased random walk where at each step of a random walk a ``controller'' can, with a certain small probability, move the walk to an arbitrary neighbour. This model was introduced by Azar et al. [STOC'1992]; we extend their work to the time \ldots{}", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Marx:2022:OPA, author = "D{\'a}niel Marx and Micha{\l} Pilipczuk", title = "Optimal Parameterized Algorithms for Planar Facility Location Problems Using {Voronoi} Diagrams", journal = j-TALG, volume = "18", number = "2", pages = "13:1--13:64", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3483425", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3483425", abstract = "We study a general family of facility location problems defined on planar graphs and on the two-dimensional plane. In these problems, a subset of k objects has to be selected, satisfying certain packing (disjointness) and covering constraints. Our main \ldots{}", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cabello:2022:CIG, author = "Sergio Cabello", title = "Computing the Inverse Geodesic Length in Planar Graphs and Graphs of Bounded Treewidth", journal = j-TALG, volume = "18", number = "2", pages = "14:1--14:26", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3501303", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3501303", abstract = "The inverse geodesic length of a graph G is the sum of the inverse of the distances between all pairs of distinct vertices of G. In some domains, it is known as the Harary index or the global efficiency of the graph. We show that, if G is planar and has \ldots{}", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Wahlstrom:2022:QMM, author = "Magnus Wahlstr{\"o}m", title = "Quasipolynomial Multicut-mimicking Networks and Kernels for Multiway Cut Problems", journal = j-TALG, volume = "18", number = "2", pages = "15:1--15:19", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3501304", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3501304", abstract = "We show the existence of an exact mimicking network of k$^O$ ($^{log k}$ ) edges for minimum multicuts over a set of terminals in an undirected graph, where k is the total capacity of the terminals, i.e., the sum of the degrees of the terminal vertices. Furthermore \ldots{}", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Henzinger:2022:CTD, author = "Monika Henzinger and Pan Peng", title = "Constant-time Dynamic {$ (\Delta + 1) $}-Coloring", journal = j-TALG, volume = "18", number = "2", pages = "16:1--16:21", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3501403", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3501403", abstract = "We give a fully dynamic (Las-Vegas style) algorithm with constant expected amortized time per update that maintains a proper $ (\Delta + 1) $-vertex coloring of a graph with maximum degree at most \Delta . This improves upon the previous O (log \Delta )-time algorithm by \ldots{}", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cygan:2022:SCP, author = "Marek Cygan and Jesper Nederlof and Marcin Pilipczuk and Micha{\l} Pilipczuk and Johan M. M. {Van Rooij} and Jakub Onufry Wojtaszczyk", title = "Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time", journal = j-TALG, volume = "18", number = "2", pages = "17:1--17:31", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3506707", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3506707", abstract = "For the vast majority of local problems on graphs of small treewidth (where, by local we mean that a solution can be verified by checking separately the neighbourhood of each vertex), standard dynamic programming techniques give c$^{tw}$ | V |$^{O(1)}$ time \ldots{}", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Charalampopoulos:2022:EDO, author = "Panagiotis Charalampopoulos and Shay Mozes and Benjamin Tebeka", title = "Exact Distance Oracles for Planar Graphs with Failing Vertices", journal = j-TALG, volume = "18", number = "2", pages = "18:1--18:23", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3511541", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3511541", abstract = "We consider exact distance oracles for directed weighted planar graphs in the presence of failing vertices. Given a source vertex u, a target vertex v and a set X of k failed vertices, such an oracle returns the length of a shortest u -to- v path that \ldots{}", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Blasius:2022:ESP, author = "Thomas Bl{\"a}sius and Cedric Freiberger and Tobias Friedrich and Maximilian Katzmann and Felix Montenegro-Retana and Marianne Thieffry", title = "Efficient Shortest Paths in Scale-Free Networks with Underlying Hyperbolic Geometry", journal = j-TALG, volume = "18", number = "2", pages = "19:1--19:32", month = apr, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3516483", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Wed Apr 6 11:02:12 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3516483", abstract = "A standard approach to accelerating shortest path algorithms on networks is the bidirectional search, which explores the graph from the start and the destination, simultaneously. In practice this strategy performs particularly well on scale-free real-\ldots{}", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Gudmundsson:2022:IDM, author = "Joachim Gudmundsson and Sampson Wong", title = "Improving the Dilation of a Metric Graph by Adding Edges", journal = j-TALG, volume = "18", number = "3", pages = "20:1--20:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3517807", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3517807", abstract = "Most of the literature on spanners focuses on building the graph from scratch. This article instead focuses on adding edges to improve an existing graph. A major open problem in this field is: Given a graph embedded in a metric space, and a budget of k \ldots{}", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Sau:2022:KAM, author = "Ignasi Sau and Giannos Stamoulis and Dimitrios M. Thilikos", title = "$k$-apices of Minor-closed Graph Classes. {II}. {Parameterized} Algorithms", journal = j-TALG, volume = "18", number = "3", pages = "21:1--21:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3519028", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3519028", abstract = "Let G be a minor-closed graph class. We say that a graph G is a k -apex of G if G contains a set S of at most k vertices such that G\S belongs to G. We denote by A$_k$ ( G ) the set of all graphs that are k -apices of G. In the first paper of this series, \ldots{}", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chan:2022:NDE, author = "Pak Hay Chan and Lap Chi Lau and Aaron Schild and Sam Chiu-Wai Wong and Hong Zhou", title = "Network Design for $ s - t $ Effective Resistance", journal = j-TALG, volume = "18", number = "3", pages = "22:1--22:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3522588", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3522588", abstract = "We consider a new problem of designing a network with small s --- t effective resistance. In this problem, we are given an undirected graph G = (V,E), two designated vertices s,t \in V, and a budget k. The goal is to choose a subgraph of G with at most k edges \ldots{}", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fearnley:2022:FAF, author = "John Fearnley and D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi and Rahul Savani", title = "A Faster Algorithm for Finding {Tarski} Fixed Points", journal = j-TALG, volume = "18", number = "3", pages = "23:1--23:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3524044", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3524044", abstract = "Dang et al. have given an algorithm that can find a Tarski fixed point in a k -dimensional lattice of width n using O (log$^k$ n ) queries [ 2 ]. Multiple authors have conjectured that this algorithm is optimal [ 2, 7 ], and indeed this has been proven for two-\ldots{}", acknowledgement = ack-nhfb, articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Boffa:2022:LAD, author = "Antonio Boffa and Paolo Ferragina and Giorgio Vinciguerra", title = "A Learned Approach to Design Compressed Rank\slash Select Data Structures", journal = j-TALG, volume = "18", number = "3", pages = "24:1--24:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3524060", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3524060", abstract = "We address the problem of designing, implementing, and experimenting with compressed data structures that support rank and select queries over a dictionary of integers. We shine a new light on this classical problem by showing a connection between the \ldots{}", acknowledgement = ack-nhfb, articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Miller:2022:DLE, author = "Avery Miller and Andrzej Pelc and Ram Narayan Yadav", title = "Deterministic Leader Election in Anonymous Radio Networks", journal = j-TALG, volume = "18", number = "3", pages = "25:1--25:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3527171", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3527171", abstract = "Leader election is a fundamental task in distributed computing. It is a symmetry breaking problem, calling for one node of the network to become the leader, and for all other nodes to become non-leaders. We consider leader election in anonymous radio \ldots{}", acknowledgement = ack-nhfb, articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Agarwal:2022:MUU, author = "Pankaj K. Agarwal and Ravid Cohen and Dan Halperin and Wolfgang Mulzer", title = "Maintaining the Union of Unit Discs under Insertions with Near-Optimal Overhead", journal = j-TALG, volume = "18", number = "3", pages = "26:1--26:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3527614", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3527614", abstract = "We present efficient dynamic data structures for maintaining the union of unit discs and the lower envelope of pseudo-lines in the plane. More precisely, we present three main results in this paper: We present a linear-size data structure to maintain \ldots{}", acknowledgement = ack-nhfb, articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Neuen:2022:HIG, author = "Daniel Neuen", title = "Hypergraph Isomorphism for Groups with Restricted Composition Factors", journal = j-TALG, volume = "18", number = "3", pages = "27:1--27:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3527667", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3527667", abstract = "We consider the isomorphism problem for hypergraphs taking as input two hypergraphs over the same set of vertices V and a permutation group \Gamma over domain V, and asking whether there is a permutation \gamma \epsilon \Gamma that proves the two hypergraphs to be isomorphic. \ldots{}", acknowledgement = ack-nhfb, articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Feng:2022:RMS, author = "Weiming Feng and Heng Guo and Yitong Yin and Chihao Zhang", title = "Rapid Mixing from Spectral Independence beyond the {Boolean} Domain", journal = j-TALG, volume = "18", number = "3", pages = "28:1--28:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3531008", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3531008", abstract = "We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis Gharan [ 4 ]) from the Boolean domain to general discrete domains. This property characterises distributions with limited correlations and implies that the corresponding \ldots{}", acknowledgement = ack-nhfb, articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Jin:2022:GSI, author = "Kai Jin and Siu-Wing Cheng and Man-Kwun Chiu and Man Ting Wong", title = "A Generalization of Self-Improving Algorithms", journal = j-TALG, volume = "18", number = "3", pages = "29:1--29:??", month = jul, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3531227", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 29 07:37:10 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3531227", abstract = "Ailon et al. [SICOMP'11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances x$_1$, \ldots{}, x$_n$ follow some unknown product distribution. That is, x$_i$ is drawn independently from a fixed unknown distribution \ldots{}", acknowledgement = ack-nhfb, articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kamath:2022:ISI, author = "Gautam Kamath and Sepehr Assadi and Anne Driemel and Janardhan Kulkarni", title = "Introduction to the Special Issue on {ACM-SIAM Symposium on Discrete Algorithms (SODA) 2020}", journal = j-TALG, volume = "18", number = "4", pages = "30:1--30:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3561912", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3561912", acknowledgement = ack-nhfb, articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chen:2022:LBC, author = "Xi Chen and Tim Randolph and Rocco A. Servedio and Timothy Sun", title = "A Lower Bound on Cycle-Finding in Sparse Digraphs", journal = j-TALG, volume = "18", number = "4", pages = "31:1--31:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3417979", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3417979", abstract = "We consider the problem of finding a cycle in a sparse directed graph G that is promised to be far from acyclic, meaning that the smallest feedback arc set, i.e., a subset of edges whose deletion results in an acyclic graph, in G is large. We prove an \ldots{}", acknowledgement = ack-nhfb, articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Joseph:2022:ESL, author = "Matthew Joseph and Jieming Mao and Aaron Roth", title = "Exponential Separations in Local Privacy", journal = j-TALG, volume = "18", number = "4", pages = "32:1--32:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3459095", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3459095", abstract = "We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally differentially \ldots{}", acknowledgement = ack-nhfb, articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Abbasi-Zadeh:2022:SBR, author = "Sepehr Abbasi-Zadeh and Nikhil Bansal and Guru Guruganesh and Aleksandar Nikolov and Roy Schwartz and Mohit Singh", title = "Sticky {Brownian} Rounding and its Applications to Constraint Satisfaction Problems", journal = j-TALG, volume = "18", number = "4", pages = "33:1--33:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3459096", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3459096", abstract = "Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson [ 31 ] has been extensively studied \ldots{}", acknowledgement = ack-nhfb, articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Li:2022:DFV, author = "Jason Li and Jesper Nederlof", title = "Detecting Feedback Vertex Sets of Size $k$ in {$ O^\star (2.7 k)$} Time", journal = j-TALG, volume = "18", number = "4", pages = "34:1--34:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3504027", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3504027", abstract = "In the Feedback Vertex Set (FVS) problem, one is given an undirected graph G and an integer k, and one needs to determine whether there exists a set of k vertices that intersects all cycles of G (a so-called feedback vertex set). Feedback Vertex Set is \ldots{}", acknowledgement = ack-nhfb, articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Arya:2022:OBC, author = "Rahul Arya and Sunil Arya and Guilherme D. da Fonseca and David Mount", title = "Optimal Bound on the Combinatorial Complexity of Approximating Polytopes", journal = j-TALG, volume = "18", number = "4", pages = "35:1--35:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3559106", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3559106", abstract = "This article considers the question of how to succinctly approximate a multidimensional convex body by a polytope. Given a convex body K of unit diameter in Euclidean d -dimensional space (where d is a constant) and an error parameter \epsilon {$>$} 0, the objective \ldots{}", acknowledgement = ack-nhfb, articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chang:2022:TCS, author = "Hsien-Chih Chang and Arnaud de Mesmay", title = "Tightening Curves on Surfaces Monotonically with Applications", journal = j-TALG, volume = "18", number = "4", pages = "36:1--36:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3558097", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3558097", abstract = "We prove the first polynomial bound on the number of monotonic homotopy moves required to tighten a collection of closed curves on any compact orientable surface, where the number of crossings in the curve is not allowed to increase at any time during the \ldots{}", acknowledgement = ack-nhfb, articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Berman:2022:TTI, author = "Piotr Berman and Meiram Murzabulatov and Sofya Raskhodnikova", title = "Tolerant Testers of Image Properties", journal = j-TALG, volume = "18", number = "4", pages = "37:1--37:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3531527", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3531527", abstract = "We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property. Image processing is a particularly compelling area of applications for sublinear-\ldots{}", acknowledgement = ack-nhfb, articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Rahul:2022:GTB, author = "Saladi Rahul and Yufei Tao", title = "Generic Techniques for Building Top-$k$ Structures", journal = j-TALG, volume = "18", number = "4", pages = "38:1--38:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3546074", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3546074", abstract = "A reporting query returns the objects satisfying a predicate q from an input set. In prioritized reporting, each object carries a real-valued weight (which can be query dependent), and a query returns the objects that satisfy q and have weights at least a \ldots{}", acknowledgement = ack-nhfb, articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Jiang:2022:OAW, author = "Zhihao Jiang and Debmalya Panigrahi and Kevin Sun", title = "Online Algorithms for Weighted Paging with Predictions", journal = j-TALG, volume = "18", number = "4", pages = "39:1--39:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3548774", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3548774", abstract = "In this article, we initiate the study of the weighted paging problem with predictions. This continues the recent line of work in online algorithms with predictions, particularly that of Lykouris and Vassilvitski (ICML 2018) and Rohatgi (SODA 2020) on \ldots{}", acknowledgement = ack-nhfb, articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Agarwal:2022:DGS, author = "Pankaj Agarwal and Hsien-Chih Chang and Subhash Suri and Allen Xiao and Jie Xue", title = "Dynamic Geometric Set Cover and Hitting Set", journal = j-TALG, volume = "18", number = "4", pages = "40:1--40:??", month = oct, year = "2022", CODEN = "????", DOI = "https://doi.org/10.1145/3551639", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Nov 12 07:18:31 MST 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3551639", abstract = "We investigate dynamic versions of geometric set cover and hitting set where points and ranges may be inserted or deleted, and we want to efficiently maintain an (approximately) optimal solution for the current problem instance. While their static \ldots{}", acknowledgement = ack-nhfb, articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kantor:2023:MPS, author = "Erez Kantor and Zvi Lotker and Merav Parter and David Peleg", title = "The Minimum Principle of {SINR}: a Useful Discretization Tool for Wireless Communication", journal = j-TALG, volume = "19", number = "1", pages = "1:1--1:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3477144", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3477144", abstract = "Theoretical study of optimization problems in wireless communication often deals with tasks that concern a single point. For example, the power control problem requires computing a power assignment guaranteeing that each transmitting station s$_i$ is \ldots{}", acknowledgement = ack-nhfb, articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Gishboliner:2023:CHC, author = "Lior Gishboliner and Yevgeny Levanzov and Asaf Shapira and Raphael Yuster", title = "Counting Homomorphic Cycles in Degenerate Graphs", journal = j-TALG, volume = "19", number = "1", pages = "2:1--2:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3560820", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3560820", abstract = "Since counting subgraphs in general graphs is, by and large, a computationally demanding problem, it is natural to try and design fast algorithms for restricted families of graphs. One such family that has been extensively studied is that of graphs of \ldots{}", acknowledgement = ack-nhfb, articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Abboud:2023:SEB, author = "Amir Abboud and Fabrizio Grandoni and Virginia Vassilevska Williams", title = "Subcubic Equivalences between Graph Centrality Problems, {APSP}, and Diameter", journal = j-TALG, volume = "19", number = "1", pages = "3:1--3:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3563393", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3563393", abstract = "Measuring the importance of a node in a network is a major goal in the analysis of social networks, biological systems, transportation networks, and so forth. Different centrality measures have been proposed to capture the notion of node importance. For \ldots{}", acknowledgement = ack-nhfb, articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Buchin:2023:AMC, author = "Maike Buchin and Anne Driemel and Dennis Rohde", title = "Approximating $ (k, l)$-Median Clustering for Polygonal Curves", journal = j-TALG, volume = "19", number = "1", pages = "4:1--4:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3559764", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3559764", abstract = "In 2015, Driemel, Krivosija, and Sohler introduced the k,l -median clustering problem for polygonal curves under the Fr{\'e}chet distance. Given a set of input curves, the problem asks to find k median curves of at most l vertices each that minimize the sum of \ldots{}", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Shah:2023:RDR, author = "Rahul Shah and Cheng Sheng and Sharma Thankachan and Jeffrey Vitter", title = "Ranked Document Retrieval in External Memory", journal = j-TALG, volume = "19", number = "1", pages = "5:1--5:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3559763", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3559763", abstract = "The ranked (or top- k ) document retrieval problem is defined as follows: preprocess a collection {T$_1$, T$_2$, \ldots{}, T$_d$ } of d strings (called documents) of total length n into a data structure, such that for any given query (P,k), where P is a string (called pattern) \ldots{}", acknowledgement = ack-nhfb, articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Ito:2023:MEF, author = "Takehiro Ito and Yuni Iwamasa and Naonori Kakimura and Naoyuki Kamiyama and Yusuke Kobayashi and Shun-Ichi Maezawa and Yuta Nozaki and Yoshio Okamoto and Kenta Ozeki", title = "Monotone Edge Flips to an Orientation of Maximum Edge-Connectivity {\`a} la {Nash--Williams}", journal = j-TALG, volume = "19", number = "1", pages = "6:1--6:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3561302", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3561302", abstract = "We initiate the study of k -edge-connected orientations of undirected graphs through edge flips for k {$>$}= 2. We prove that in every orientation of an undirected 2k -edge-connected graph, there exists a sequence of edges such that flipping their directions one \ldots{}", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Har-Peled:2023:RSM, author = "Sariel Har-Peled and Manor Mendel and D{\'a}niel Ol{\'a}h", title = "Reliable Spanners for Metric Spaces", journal = j-TALG, volume = "19", number = "1", pages = "7:1--7:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3563356", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3563356", abstract = "A spanner is reliable if it can withstand large, catastrophic failures in the network. More precisely, any failure of some nodes can only cause a small damage in the remaining graph in terms of the dilation. In other words, the spanner property is \ldots{}", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bansal:2023:CAG, author = "Nikhil Bansal and Marek Eli{\'a}s and Grigorios Koumoutsos and Jesper Nederlof", title = "Competitive Algorithms for Generalized $k$-Server in Uniform Metrics", journal = j-TALG, volume = "19", number = "1", pages = "8:1--8:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3568677", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3568677", abstract = "The generalized $k$-server problem is a far-reaching extension of the $k$-server problem with several applications. Here, each server $s_i$ lies in its own metric space $M_i$. A request is a $k$-tuple $r = (r_1, r_2, \ldots{}, r_k)$, which is served by moving some server $s_i$ to the \ldots{}", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bringmann:2023:LTA, author = "Karl Bringmann and Vincent Cohen-Addad and Debarati Das", title = "A Linear-Time $ n^{0.4}$-Approximation for Longest Common Subsequence", journal = j-TALG, volume = "19", number = "1", pages = "9:1--9:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3568398", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3568398", abstract = "We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length n. The 40-year-old quadratic-time dynamic programming algorithm has recently been shown to be near-optimal by Abboud, Backurs, and Vassilevska \ldots{}", acknowledgement = ack-nhfb, articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Eberle:2023:OTM, author = "Franziska Eberle and Nicole Megow and Kevin Schewior", title = "Online Throughput Maximization on Unrelated Machines: Commitment is No Burden", journal = j-TALG, volume = "19", number = "1", pages = "10:1--10:??", month = jan, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3569582", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Mar 11 08:53:55 MST 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3569582", abstract = "We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a single or multiple possibly unrelated \ldots{}", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Agrawal:2023:PKI, author = "Akanksha Agrawal and Daniel Lokshtanov and Pranabendu Misra and Saket Saurabh and Meirav Zehavi", title = "Polynomial Kernel for Interval Vertex Deletion", journal = j-TALG, volume = "19", number = "2", pages = "11:1--11:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3571075", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3571075", abstract = "Given a graph G and an integer k, the Interval Vertex Deletion (IVD) problem asks whether there exists a subset S \subseteq V ( G ) of size at most k such that G-S is an interval graph. This problem is known to be NP-complete (according to Yannakakis at STOC 1978). \ldots{}", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Ganesh:2023:RAT, author = "Arun Ganesh and Bruce M. Maggs and Debmalya Panigrahi", title = "Robust Algorithms for {TSP} and {Steiner} Tree", journal = j-TALG, volume = "19", number = "2", pages = "12:1--12:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3570957", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3570957", abstract = "Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to minimize regret, \ldots{}", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fox:2023:MCM, author = "Kyle Fox and Debmalya Panigrahi and Fred Zhang", title = "Minimum Cut and Minimum $k$-Cut in Hypergraphs via Branching Contractions", journal = j-TALG, volume = "19", number = "2", pages = "13:1--13:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3570162", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3570162", abstract = "On hypergraphs with m hyperedges and n vertices, where p denotes the total size of the hyperedges, we provide the following results: We give an algorithm that runs in \(\widetilde{O}(mn^{2k-2})\) time for finding a minimum $k$-cut in hypergraphs of \ldots{}", acknowledgement = ack-nhfb, articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Mezei:2023:PSG, author = "Bal{\'a}zs F. Mezei and Marcin Wrochna and stanislav Zivn{\'y}", title = "{PTAS} for Sparse General-valued {CSPs}", journal = j-TALG, volume = "19", number = "2", pages = "14:1--14:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3569956", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3569956", abstract = "We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes. Baker's approach gives a PTAS on planar graphs, excluded-minor classes, \ldots{}", acknowledgement = ack-nhfb, articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Ganesh:2023:UAC, author = "Arun Ganesh and Bruce M. Maggs and Debmalya Panigrahi", title = "Universal Algorithms for Clustering Problems", journal = j-TALG, volume = "19", number = "2", pages = "15:1--15:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3572840", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3572840", abstract = "This article presents universal algorithms for clustering problems, including the widely studied k -median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must select k cluster centers \ldots{}", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Groenland:2023:APG, author = "Carla Groenland and Gwena{\"e}l Joret and Wojciech Nadara and Bartosz Walczak", title = "Approximating Pathwidth for Graphs of Small Treewidth", journal = j-TALG, volume = "19", number = "2", pages = "16:1--16:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3576044", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3576044", abstract = "We describe a polynomial-time algorithm which, given a graph G with treewidth t, approximates the pathwidth of G to within a ratio of \(O(t\sqrt {\log t})\). This is the first algorithm to achieve an f(t) -approximation for some function f. Our approach \ldots{}", acknowledgement = ack-nhfb, articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Mathieu:2023:PCV, author = "Claire Mathieu and Hang Zhou", title = "A {PTAS} for Capacitated Vehicle Routing on Trees", journal = j-TALG, volume = "19", number = "2", pages = "17:1--17:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3575799", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3575799", abstract = "We give a polynomial time approximation scheme (PTAS) for the unit demand capacitated vehicle routing problem (CVRP) on trees, for the entire range of the tour capacity. The result extends to the splittable CVRP.", acknowledgement = ack-nhfb, articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kanade:2023:CTG, author = "Varun Kanade and Frederik Mallmann-Trenn and Thomas Sauerwald", title = "On Coalescence Time in Graphs: When Is Coalescing as Fast as Meeting?", journal = j-TALG, volume = "19", number = "2", pages = "18:1--18:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3576900", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3576900", abstract = "Coalescing random walks is a fundamental distributed process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a single random \ldots{}", acknowledgement = ack-nhfb, articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Antoniadis:2023:OMA, author = "Antonios Antoniadis and Christian Coester and Marek Eli{\'a}s and Adam Polak and Bertrand Simon", title = "Online Metric Algorithms with Untrusted Predictions", journal = j-TALG, volume = "19", number = "2", pages = "19:1--19:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3582689", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3582689", abstract = "Machine-learned predictors, although achieving very good results for inputs resembling training data, cannot possibly provide perfect predictions in all situations. Still, decision-making systems that are based on such predictors need not only benefit \ldots{}", acknowledgement = ack-nhfb, articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Jayaprakash:2023:ASC, author = "Aditya Jayaprakash and Mohammad R. Salavatipour", title = "Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension", journal = j-TALG, volume = "19", number = "2", pages = "20:1--20:??", month = apr, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3582500", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Mon May 1 07:24:12 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3582500", abstract = "In this article, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. In CVRP, introduced by Dantzig and Ramser in 1959 [ 14 ], we are given a graph G=(V,E) with metric edges costs, a depot r \in V, and .", acknowledgement = ack-nhfb, articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Equi:2023:CSM, author = "Massimo Equi and Veli M{\"a}kinen and Alexandru I. Tomescu and Roberto Grossi", title = "On the Complexity of String Matching for Graphs", journal = j-TALG, volume = "19", number = "3", pages = "21:1--21:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3588334", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3588334", abstract = "Exact string matching in labeled graphs is the problem of searching paths of a graph G=(V, E) such that the concatenation of their node labels is equal to a given pattern string P [1. m ]. This basic problem can be found at the heart of more complex \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bouchard:2023:AOD, author = "S{\'e}bastien Bouchard and Yoann Dieudonn{\'e} and Arnaud Labourel and Andrzej Pelc", title = "Almost-Optimal Deterministic Treasure Hunt in Unweighted Graphs", journal = j-TALG, volume = "19", number = "3", pages = "22:1--22:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3588437", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3588437", abstract = "A mobile agent navigating along edges of a simple connected unweighted graph, either finite or countably infinite, has to find an inert target (treasure) hidden in one of the nodes. This task is known as treasure hunt. The agent has no a priori knowledge \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Golovach:2023:HTM, author = "Petr A. Golovach and Giannos Stamoulis and Dimitrios M. Thilikos", title = "Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable", journal = j-TALG, volume = "19", number = "3", pages = "23:1--23:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3583688", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3583688", abstract = "For a finite collection of graphs F, the F-TM-Deletion problem has as input an n -vertex graph G and an integer k and asks whether there exists a set S \subseteq V(G) with |S| {$<$}= k such that G \ S does not contain any of the graphs in F as a topological minor. We \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Walzer:2023:LTC, author = "Stefan Walzer", title = "Load Thresholds for Cuckoo Hashing with Overlapping Blocks", journal = j-TALG, volume = "19", number = "3", pages = "24:1--24:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3589558", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/hash.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3589558", abstract = "We consider a natural variation of cuckoo hashing proposed by Lehman and Panigrahy (2009). Each of cn objects is assigned k = 2 intervals of size l in a linear hash table of size n and both starting points are chosen independently and uniformly at random. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bose:2023:COS, author = "Prosenjit Bose and Jean Cardinal and John Iacono and Grigorios Koumoutsos and Stefan Langerman", title = "Competitive Online Search Trees on Trees", journal = j-TALG, volume = "19", number = "3", pages = "25:1--25:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3595180", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3595180", abstract = "We consider the design of adaptive data structures for searching elements of a tree-structured space. We use a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of vertices of a \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bressan:2023:ENO, author = "Marco Bressan", title = "Efficient and Near-optimal Algorithms for Sampling Small Connected Subgraphs", journal = j-TALG, volume = "19", number = "3", pages = "26:1--26:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3596495", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3596495", abstract = "We study the following problem: Given an integer k {$>$}= 3 and a simple graph G, sample a connected induced $k$-vertex subgraph of G uniformly at random. This is a fundamental graph mining primitive with applications in social network analysis, bioinformatics, \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Jayaram:2023:TOM, author = "Rajesh Jayaram and David P. Woodruff", title = "Towards Optimal Moment Estimation in Streaming and Distributed Models", journal = j-TALG, volume = "19", number = "3", pages = "27:1--27:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3596494", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3596494", abstract = "One of the oldest problems in the data stream model is to approximate the p th moment \(\Vert \mathbf {X}\Vert _p^p = \sum _{i=1}^n \mathbf {X}_i^p\) of an underlying non-negative vector \(\mathbf {X}\in \mathbb {R}^n\), which is presented as a \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Peserico:2023:MLA, author = "Enoch Peserico and Michele Scquizzato", title = "Matching on the Line Admits no $ o(\sqrt {\log n})$-Competitive Algorithm", journal = j-TALG, volume = "19", number = "3", pages = "28:1--28:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3594873", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3594873", abstract = "We present a simple proof that no randomized online matching algorithm for the line can be \((\sqrt {\log _2(n+1)}/15)\)-competitive against an oblivious adversary for any n = 2$^i$ --- 1 : i \in N. This is the first super-constant lower bound for the problem, \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Buchin:2023:FDU, author = "Kevin Buchin and Chenglin Fan and Maarten L{\"o}ffler and Aleksandr Popov and Benjamin Raichel and Marcel Roeloffzen", title = "{Fr{\'e}chet} Distance for Uncertain Curves", journal = j-TALG, volume = "19", number = "3", pages = "29:1--29:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3597640", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3597640", abstract = "In this article, we study a wide range of variants for computing the (discrete and continuous) Fr{\'e}chet distance between uncertain curves. An uncertain curve is a sequence of uncertainty regions, where each region is a disk, a line segment, or a set of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Aamand:2023:TSP, author = "Anders Aamand and Mikkel Abrahamsen and Peter M. R. Rasmussen and Thomas D. Ahle", title = "Tiling with Squares and Packing Dominos in Polynomial Time", journal = j-TALG, volume = "19", number = "3", pages = "30:1--30:??", month = jul, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3597932", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:54 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3597932", abstract = "A polyomino is a polygonal region with axis-parallel edges and corners of integral coordinates, which may have holes. In this paper, we consider planar tiling and packing problems with polyomino pieces and a polyomino container P. We give polynomial-time \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Deligkas:2023:PTA, author = "Argyrios Deligkas and Michail Fasoulakis and Evangelos Markakis", title = "A Polynomial-Time Algorithm for $ 1 / 3$-Approximate {Nash} Equilibria in Bimatrix Games", journal = j-TALG, volume = "19", number = "4", pages = "31:1--31:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3606697", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3606697", abstract = "Since the celebrated PPAD-completeness result for Nash equilibria in bimatrix games, a long line of research has focused on polynomial-time algorithms that compute \epsilon -approximate Nash equilibria. Finding the best possible approximation guarantee that we \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bille:2023:SIC, author = "Philip Bille and Inge Li G{\o}rtz and Teresa Anna Steiner", title = "String Indexing with Compressed Patterns", journal = j-TALG, volume = "19", number = "4", pages = "32:1--32:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3607141", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/string-matching.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3607141", abstract = "Given a string S of length n, the classic string indexing problem is to preprocess S into a compact data structure that supports efficient subsequent pattern queries. In this article, we consider the basic variant where the pattern is given in compressed \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chang:2023:NOT, author = "Yi-Jun Chang and Ran Duan and Shunhua Jiang", title = "Near-Optimal Time-Energy Tradeoffs for Deterministic Leader Election", journal = j-TALG, volume = "19", number = "4", pages = "33:1--33:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3614429", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3614429", abstract = "We consider the energy complexity of the leader election problem in the single-hop radio network model, where each device v has a unique identifier ID( v ) \in \{ 1, 2, \ldots{}, N \}. Energy is a scarce resource for small battery-powered devices. For such devices, \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Blasius:2023:SPA, author = "Thomas Bl{\"a}sius and Simon D. Fink and Ignaz Rutter", title = "Synchronized Planarity with Applications to Constrained Planarity Problems", journal = j-TALG, volume = "19", number = "4", pages = "34:1--34:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3607474", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3607474", abstract = "We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Lafond:2023:RLP, author = "Manuel Lafond", title = "Recognizing $k$-Leaf Powers in Polynomial Time, for Constant $k$", journal = j-TALG, volume = "19", number = "4", pages = "35:1--35:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3614094", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3614094", abstract = "A graph G is a $k$-leaf power if there exists a tree T whose leaf set is V ( G ), and such that uv \in E ( G ) if and only if the distance between u and v in T is at most k (and u /= v ). The graph classes of $k$-leaf powers have several applications in computational \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Garg:2023:ANS, author = "Jugal Garg and Pooja Kulkarni and Rucha Kulkarni", title = "Approximating {Nash} Social Welfare under Submodular Valuations through (Un){Matchings}", journal = j-TALG, volume = "19", number = "4", pages = "36:1--36:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3613452", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3613452", abstract = "We study the problem of approximating maximum Nash social welfare (NSW) when allocating m indivisible items among n asymmetric agents with submodular valuations. The NSW is a well-established notion of fairness and efficiency, defined as the weighted \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Birmpilis:2023:CAC, author = "Stavros Birmpilis and George Labahn and Arne Storjohann", title = "A Cubic Algorithm for Computing the {Hermite} Normal Form of a Nonsingular Integer Matrix", journal = j-TALG, volume = "19", number = "4", pages = "37:1--37:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3617996", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3617996", abstract = "A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix A of dimension n. The algorithm uses quadratic integer multiplication and cubic matrix multiplication and has running time bounded by $ O(n^3 (\log n + \ldots {})) $ \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Baswana:2023:MCD, author = "Surender Baswana and Koustav Bhanja and Abhyuday Pandey", title = "Minimum+1 $ (s, t)$-cuts and Dual-edge Sensitivity Oracle", journal = j-TALG, volume = "19", number = "4", pages = "38:1--38:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3623271", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3623271", abstract = "Let G be a directed multi-graph on n vertices and m edges with a designated source vertex s and a designated sink vertex t. We study the ( s,t )-cuts of capacity minimum+1 and as an important application of them, we give a solution to the dual-edge \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Filtser:2023:SSD, author = "Arnold Filtser and Omrit Filtser", title = "Static and Streaming Data Structures for {Fr{\'e}chet} Distance Queries", journal = j-TALG, volume = "19", number = "4", pages = "39:1--39:??", month = oct, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1145/3610227", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Nov 3 14:37:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3610227", abstract = "Given a curve P with points in R$^d$ in a streaming fashion, and parameters $\epsilon > 0$ and $k$, we construct a distance oracle that uses $O(\frac{1}{\varepsilon })^{kd}\log \varepsilon ^{-1}$ space, and given a query curve $Q$ with $k$ points in $R^d$ returns in \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Pelleg:2024:ASC, author = "Eden Pelleg and Stanislav Zivn{\'y}", title = "Additive Sparsification of {CSPs}", journal = j-TALG, volume = "20", number = "1", pages = "1:1--1:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3625824", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3625824", abstract = "Multiplicative cut sparsifiers, introduced by Bencz{\'u}r and Karger [STOC'96], have proved extremely influential and found various applications. Precise characterisations were established for sparsifiability of graphs with other 2-variable predicates on \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fomin:2024:SCM, author = "Fedor V. Fomin and Petr A. Golovach and Tuukka Korhonen and Daniel Lokshtanov and Giannos Stamoulis", title = "Shortest Cycles with Monotone Submodular Costs", journal = j-TALG, volume = "20", number = "1", pages = "2:1--2:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3626824", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3626824", abstract = "We introduce the following submodular generalization of the Shortest Cycle problem. For a nonnegative monotone submodular cost function f defined on the edges (or the vertices) of an undirected graph G, we seek for a cycle C in G of minimum cost OPT = \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Li:2024:CEP, author = "Shaohua Li and Marcin Pilipczuk and Manuel Sorge", title = "Cluster Editing Parameterized above Modification-disjoint {$ P_3 $}-packings", journal = j-TALG, volume = "20", number = "1", pages = "3:1--3:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3626526", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3626526", abstract = "Given a graph G =( V,E ) and an integer k, the Cluster Editing problem asks whether we can transform G into a union of vertex-disjoint cliques by at most k modifications (edge deletions or insertions). In this paper, we study the following variant of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cairo:2024:GAP, author = "Massimo Cairo and Romeo Rizzi and Alexandru I. Tomescu and Elia C. Zirondelli", title = "Genome Assembly, from Practice to Theory: Safe, Complete and Linear-Time", journal = j-TALG, volume = "20", number = "1", pages = "4:1--4:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3632176", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3632176", abstract = "Genome assembly asks to reconstruct an unknown string from many shorter substrings of it. Even though it is one of the key problems in Bioinformatics, it is generally lacking major theoretical advances. Its hardness stems both from practical issues \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Blanca:2024:FPS, author = "Antonio Blanca and Sarah Cannon and Will Perkins", title = "Fast and Perfect Sampling of Subgraphs and Polymer Systems", journal = j-TALG, volume = "20", number = "1", pages = "5:1--5:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3632294", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3632294", abstract = "We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets ) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and works under a \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chalermsook:2024:ASC, author = "Parinya Chalermsook and Matthias Kaul and Matthias Mnich and Joachim Spoerhase and Sumedha Uniyal and Daniel Vaz", title = "Approximating Sparsest Cut in Low-treewidth Graphs via Combinatorial Diameter", journal = j-TALG, volume = "20", number = "1", pages = "6:1--6:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3632623", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3632623", abstract = "The fundamental Sparsest Cut problem takes as input a graph G together with edge capacities and demands and seeks a cut that minimizes the ratio between the capacities and demands across the cuts. For n -vertex graphs G of treewidth k, Chlamt{\'a}c, \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bezakova:2024:FSS, author = "Ivona Bez{\'a}kov{\'a} and Andreas Galanis and Leslie Ann Goldberg and Daniel Stefankovic", title = "Fast Sampling via Spectral Independence Beyond Bounded-degree Graphs", journal = j-TALG, volume = "20", number = "1", pages = "7:1--7:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3631354", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3631354", abstract = "Spectral independence is a recently developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal O(n log n) sampling algorithms on bounded-degree graphs for a large class \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kavitha:2024:PMO, author = "Telikepalli Kavitha", title = "Popular Matchings with One-Sided Bias", journal = j-TALG, volume = "20", number = "1", pages = "8:1--8:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3638764", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3638764", abstract = "Let G = (A \cup B, E) be a bipartite graph where the set A consists of agents or main players and the set B consists of jobs or secondary players. Every vertex in A \cup B has a strict ranking of its neighbors. A matching M is popular if for any matching N, the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Gottesburen:2024:SHQ, author = "Lars Gottesb{\"u}ren and Tobias Heuer and Nikolai Maas and Peter Sanders and Sebastian Schlag", title = "Scalable High-Quality Hypergraph Partitioning", journal = j-TALG, volume = "20", number = "1", pages = "9:1--9:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3626527", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3626527", abstract = "Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across k different blocks of bounded size, such that hyperedges span as \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Blasius:2024:EVA, author = "Thomas Bl{\"a}sius and Philipp Fischbeck", title = "On the External Validity of Average-case Analyses of Graph Algorithms", journal = j-TALG, volume = "20", number = "1", pages = "10:1--10:??", month = jan, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3633778", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Feb 3 11:06:37 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3633778", abstract = "The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Focke:2024:CLH, author = "Jacob Focke and D{\'a}niel Marx and Pawe{\l} Rzazewski", title = "Counting List Homomorphisms from Graphs of Bounded Treewidth: Tight Complexity Bounds", journal = j-TALG, volume = "20", number = "2", pages = "11:1--11:??", month = apr, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3640814", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Apr 27 08:30:45 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3640814", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kim:2024:FAI, author = "Eun Jung Kim and Stefan Kratsch and Marcin Pilipczuk and Magnus Wahlstr{\"o}m", title = "Flow-augmentation {II}: Undirected Graphs", journal = j-TALG, volume = "20", number = "2", pages = "12:1--12:??", month = apr, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3641105", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Apr 27 08:30:45 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3641105", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Caceres:2024:WHH, author = "Manuel C{\'a}ceres and Massimo Cairo and Andreas Grigorjew and Shahbaz Khan and Brendan Mumey and Romeo Rizzi and Alexandru I. Tomescu and Lucia Williams", title = "Width Helps and Hinders Splitting Flows", journal = j-TALG, volume = "20", number = "2", pages = "13:1--13:??", month = apr, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3641820", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Apr 27 08:30:45 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3641820", abstract = "Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation X on a directed graph G into weighted source-to-sink paths whose weighted sum equals X. We show that, for acyclic graphs, considering \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Gudmundsson:2024:MMQ, author = "Joachim Gudmundsson and Martin P. Seybold and Sampson Wong", title = "Map Matching Queries on Realistic Input Graphs Under the {Fr{\'e}chet} Distance", journal = j-TALG, volume = "20", number = "2", pages = "14:1--14:??", month = apr, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3643683", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Apr 27 08:30:45 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3643683", abstract = "Map matching is a common preprocessing step for analysing vehicle trajectories. In the theory community, the most popular approach for map matching is to compute a path on the road network that is the most spatially similar to the trajectory, where \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Panolan:2024:CDU, author = "Fahad Panolan and Saket Saurabh and Meirav Zehavi", title = "Contraction Decomposition in Unit Disk Graphs and Algorithmic Applications in Parameterized Complexity", journal = j-TALG, volume = "20", number = "2", pages = "15:1--15:??", month = apr, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3648594", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Apr 27 08:30:45 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3648594", abstract = "We give a new decomposition theorem in unit disk graphs (UDGs) and demonstrate its applicability in the fields of Structural Graph Theory and Parameterized Complexity. First, our new decomposition theorem shows that the class of UDGs admits an ``almost'' \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Merino:2024:TDK, author = "Arturo Merino and Andreas Wiese", title = "On the Two-Dimensional Knapsack Problem for Convex Polygons", journal = j-TALG, volume = "20", number = "2", pages = "16:1--16:??", month = apr, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3644390", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Apr 27 08:30:45 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3644390", abstract = "We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly into the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Boehmer:2024:CFF, author = "Niclas Boehmer and Tomohiro Koana", title = "The Complexity of Finding Fair Many-to-One Matchings", journal = j-TALG, volume = "20", number = "2", pages = "17:1--17:??", month = apr, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3649220", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Apr 27 08:30:45 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3649220", abstract = "We analyze the (parameterized) computational complexity of ``fair'' variants of bipartite many-to-one matching, where each vertex from the ``left'' side is matched to exactly one vertex and each vertex from the ``right'' side may be matched to multiple \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Olbrich:2024:GNR, author = "Jannik Olbrich and Enno Ohlebusch and Thomas B{\"u}chler", title = "Generic Non-recursive Suffix Array Construction", journal = j-TALG, volume = "20", number = "2", pages = "18:1--18:??", month = apr, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3641854", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Apr 27 08:30:45 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3641854", abstract = "The suffix array is arguably one of the most important data structures in sequence analysis and consequently there is a multitude of suffix sorting algorithms. However, to this date the GSACA algorithm introduced in 2015 is the only known non-recursive \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Ganian:2024:FGC, author = "Robert Ganian and Thekla Hamm and Viktoriia Korchemna and Karolina Okrasa and Kirill Simonov", title = "The Fine-Grained Complexity of Graph Homomorphism Parameterized by Clique-Width", journal = j-TALG, volume = "20", number = "3", pages = "19:1--19:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3652514", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3652514", abstract = "The generic homomorphism problem, which asks whether an input graph $G$ admits a homomorphism into a fixed target graph $H$, has been widely studied in the literature. In this article, we provide a fine-grained complexity classification of the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bandyapadhyay:2024:TCD, author = "Sayan Bandyapadhyay and William Lochet and Daniel Lokshtanov and Saket Saurabh and Jie Xue", title = "True Contraction Decomposition and Almost {ETH}-Tight Bipartization for Unit-Disk Graphs", journal = j-TALG, volume = "20", number = "3", pages = "20:1--20:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3656042", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3656042", abstract = "We prove a structural theorem for unit-disk graphs, which (roughly) states that given a set $ \mathcal {D} $ of $n$ unit disks inducing a unit-disk graph $ G_{\mathcal {D}}$ and a number $ p \in [n]$, one can partition $ \mathcal {D}$ into $p$ \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Dadush:2024:IAS, author = "Daniel Dadush and Martin Milanic and Tami Tamir", title = "Introduction: {ACM-SIAM Symposium on Discrete Algorithms (SODA) 2022} Special Issue", journal = j-TALG, volume = "20", number = "3", pages = "21:1--21:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3655622", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3655622", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Klein:2024:CTC, author = "Kim-Manuel Klein and Janina Reuter", title = "Collapsing the Tower-On the Complexity of Multistage Stochastic {IPs}", journal = j-TALG, volume = "20", number = "3", pages = "22:1--22:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3604554", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3604554", abstract = "In this article, we study the computational complexity of solving a class of block structured integer programs (IPs), the so-called multistage stochastic IPs. A multistage stochastic IP is an IP of the form min { c$^T$ x | Ax = b, x $>$ = 0, x integral} where the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Le:2024:GSE, author = "Hung Le and Cuong Than", title = "Greedy Spanners in {Euclidean} Spaces Admit Sublinear Separators", journal = j-TALG, volume = "20", number = "3", pages = "23:1--23:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3590771", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3590771", abstract = "The greedy spanner in a low-dimensional Euclidean space is a fundamental geometric construction that has been extensively studied over three decades, as it possesses the two most basic properties of a good spanner: constant maximum degree and constant \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chan:2024:HPL, author = "Timothy M. Chan and Da Wei Zheng", title = "{Hopcroft}'s Problem, Log* Shaving, Two-dimensional Fractional Cascading, and Decision Trees", journal = j-TALG, volume = "20", number = "3", pages = "24:1--24:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3591357", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3591357", abstract = "We revisit Hopcroft's problem and related fundamental problems about geometric range searching. Given n points and n lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line pairs in O ( n$^{4 / 3}$ ) time, \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Neuen:2024:ITG, author = "Daniel Neuen", title = "Isomorphism Testing for Graphs Excluding Small Topological Subgraphs", journal = j-TALG, volume = "20", number = "3", pages = "25:1--25:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3651986", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3651986", abstract = "We give an isomorphism test that runs in time n$^{polylog(h)}$ on all n -vertex graphs excluding some h -vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time n$^{polylog(h)}$ (Babai, STOC 2016) and \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fried:2024:IAD, author = "Dvir Fried and Shay Golan and Tomasz Kociumaka and Tsvi Kopelowitz and Ely Porat and Tatiana Starikovskaya", title = "An Improved Algorithm for the $k$-{Dyck} Edit Distance Problem", journal = j-TALG, volume = "20", number = "3", pages = "26:1--26:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3627539", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3627539", abstract = "A Dyck sequence is a sequence of opening and closing parentheses (of various types) that is balanced. The Dyck edit distance of a given sequence of parentheses S is the smallest number of edit operations (insertions, deletions, and substitutions) needed \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Beretta:2024:BSE, author = "Lorenzo Beretta and Jakub Tetek", title = "Better Sum Estimation via Weighted Sampling", journal = j-TALG, volume = "20", number = "3", pages = "27:1--27:??", month = jul, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3650030", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Jul 4 12:18:49 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3650030", abstract = "Given a large set U where each item $ a \in U $ has weight $ w(a) $, we want to estimate the total weight \ldots{} to within factor of $ 1 \pm \epsilong $ with some constant probability $ > 1 / 2 $. Since $ n = | U | $ is large, we want to do this without looking at the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Czumaj:2024:SAG, author = "Artur Czumaj and Shaofeng H.-C. Jiang and Robert Krauthgamer and Pavel Vesel{\'y}", title = "Streaming Algorithms for Geometric {Steiner} Forest", journal = j-TALG, volume = "20", number = "4", pages = "28:1--28:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3663666", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3663666", abstract = "We consider a generalization of the Steiner tree problem, the Steiner forest problem, in the Euclidean plane: the input is a multiset $ X \subseteq {\mathbb {R}}^2 $, partitioned into $k$ color classes $ C_1, \ldots, C_k \subseteq X$. The goal is \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Conradi:2024:CSF, author = "Jacobus Conradi and Anne Driemel", title = "On Computing the $k$-Shortcut {Fr{\'e}chet} Distance", journal = j-TALG, volume = "20", number = "4", pages = "29:1--29:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3663762", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3663762", abstract = "The Fr{\'e}chet distance is a popular measure of dissimilarity for polygonal curves. It is defined as a min-max formulation that considers all orientation-preserving bijective mappings between the two curves. Because of its susceptibility to noise, Driemel \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Filtser:2024:SSP, author = "Arnold Filtser", title = "Scattering and Sparse Partitions, and Their Applications", journal = j-TALG, volume = "20", number = "4", pages = "30:1--30:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3672562", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3672562", abstract = "A partition $ \mathcal {P} $ of a weighted graph $G$ is $ (\sigma, \tau, \Delta)$-sparse if every cluster has diameter at most $ \Delta $, and every ball of radius $ \Delta / \sigma $ intersects at most $ \tau $ clusters. Similarly, \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Juge:2024:ASS, author = "Vincent Jug{\'e}", title = "Adaptive Shivers Sort: an Alternative Sorting Algorithm", journal = j-TALG, volume = "20", number = "4", pages = "31:1--31:55", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3664195", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3664195", abstract = "We present a new sorting algorithm, called adaptive ShiversSort, that exploits the existence of monotonic runs for sorting efficiently partially sorted data. This algorithm is a variant of the well-known algorithm TimSort, which is the sorting algorithm used in standard libraries of programming languages, such as Python or Java (for non-primitive types). More precisely, adaptive ShiversSort is a so-called $k$-aware merge-sort algorithm, a class that captures TimSort-like algorithms and that was introduced by Buss and Knop.\par In this article, we prove that, although adaptive ShiversSort is simple to implement and differs only slightly from TimSort, its computational cost, in number of comparisons performed, is optimal within the class of natural merge-sort algorithms, up to a small additive linear term. This makes adaptive ShiversSort the first $k$-aware algorithm to benefit from this property, which is also a 33\% improvement over TimSort's worst-case. This suggests that adaptive ShiversSort could be a strong contender for being used instead of TimSort.\par Then, we investigate the optimality of $k$-aware algorithms. We give lower and upper bounds on the best approximation factors of such algorithms, compared to optimal stable natural merge-sort algorithms. In particular, we design generalisations of adaptive ShiversSort whose computational costs are optimal up to arbitrarily small multiplicative factors.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Jin:2024:QSU, author = "Ce Jin and Jakob Nogler", title = "Quantum Speed-Ups for String Synchronizing Sets, Longest Common Substring, and $k$-mismatch Matching", journal = j-TALG, volume = "20", number = "4", pages = "32:1--32:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3672395", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/string-matching.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3672395", abstract = "Longest common substring (LCS) is an important text processing problem, which has recently been investigated in the quantum query model. The decision version of this problem, LCS with threshold $d$, asks whether two length-$n$ input strings have a \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Nakajima:2024:CSV, author = "Tamio-Vesa Nakajima and Stanislav Zivn{\'y}", title = "On the Complexity of Symmetric vs. Functional {PCSPs}", journal = j-TALG, volume = "20", number = "4", pages = "33:1--33:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3673655", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3673655", abstract = "The complexity of the promise constraint satisfaction problem $ \operatorname {(PCSP)}(\mathbf {A}, \mathbf {B}) $ is largely unknown, even for symmetric $ \mathbf {A} $ and $ \mathbf {B} $, except for the case when $ \mathbf {A} $ and $ \mathbf {B} $ \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{S:2024:DRP, author = "Karthik C. S. and Merav Parter", title = "Deterministic Replacement Path Covering", journal = j-TALG, volume = "20", number = "4", pages = "34:1--34:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3673760", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3673760", abstract = "In this article, we provide a unified and simplified approach to derandomize central results in the area of fault-tolerant graph algorithms. Given a graph $G$, a vertex pair $ (s, t) \in V(G) \times V(G)$, and a set of edge faults $ F \subseteq E(G)$ \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Los:2024:IDT, author = "Dimitrios Los and Thomas Sauerwald", title = "An Improved Drift Theorem for Balanced Allocations", journal = j-TALG, volume = "20", number = "4", pages = "35:1--35:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3673900", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3673900", abstract = "In the balanced allocations framework, there are $m$ jobs (balls) to be allocated to $n$ servers (bins). The goal is to minimize the gap, the difference between the maximum and the average load. In 2015, Peres, Talwar and Wieder used the \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fomin:2024:FPT, author = "Fedor V. Fomin and Petr A. Golovach and Tuukka Korhonen and Kirill Simonov and Giannos Stamoulis", title = "Fixed-Parameter Tractability of Maximum Colored Path and Beyond", journal = j-TALG, volume = "20", number = "4", pages = "36:1--36:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3674835", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3674835", abstract = "We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as follows. We give a \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Mathieu:2024:CDS, author = "Claire Mathieu and Rajmohan Rajaraman and Neal E. Young and Arman Yousefi", title = "Competitive Data-Structure Dynamization", journal = j-TALG, volume = "20", number = "4", pages = "37:1--37:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3672614", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3672614", abstract = "Data-structure dynamization is a general approach for making static data structures dynamic. It is used extensively in geometric settings and in the guise of so-called merge (or compaction) policies in big-data databases such as LevelDB and Google \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Antoniadis:2024:BBC, author = "Antonios Antoniadis and Matthias Englert and Nicolaos Matsakis and Pavel Vesel{\'y}", title = "Breaking the Barrier of 2 for the Competitiveness of Longest Queue Drop", journal = j-TALG, volume = "20", number = "4", pages = "38:1--38:??", month = oct, year = "2024", CODEN = "????", DOI = "https://doi.org/10.1145/3676887", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Sat Oct 12 11:56:24 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", URL = "https://dl.acm.org/doi/10.1145/3676887", abstract = "We consider the problem of managing the buffer of a shared-memory switch that transmits packets of unit value. A shared-memory switch consists of an input port, a number of output ports, and a buffer with a specific capacity. In each time step, an \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Sala:2025:ECP, author = "Evan Sala and Joe Sawada and Abbas Alhakim", title = "Efficient Constructions of the Prefer-Same and Prefer-Opposite {de Bruijn} Sequences", journal = j-TALG, volume = "21", number = "1", pages = "1:1--1:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3679015", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The greedy Prefer-same de Bruijn sequence construction was first presented by Eldert, Gray, Gurk, and Rubinoff in 1958. As a greedy algorithm, it has one major downside: it requires an exponential amount of space to store the length $ 2^n $ de Bruijn \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Li:2025:PIG, author = "Shi Li and Bundit Laekhanukit", title = "Polynomial Integrality Gap of Flow {LP} for Directed {Steiner} Tree", journal = j-TALG, volume = "21", number = "1", pages = "2:1--2:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3681791", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the Directed Steiner Tree (DST) problem, we are given a directed graph $ G = (V, E) $ on $n$ vertices with edge-costs $ c \in {\mathbb {R}}_{\geq 0}^E $, a root vertex $ r \in V $, and a set $ K \subseteq V \setminus \{ r \} $ of $k$ terminals. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Harris:2025:PEG, author = "David G. Harris and Vladimir Kolmogorov", title = "Parameter Estimation for {Gibbs} Distributions", journal = j-TALG, volume = "21", number = "1", pages = "3:1--3:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3685676", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We consider sampling problems coming from Gibbs distributions, which are families of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Filtser:2025:FCP, author = "Arnold Filtser", title = "A Face Cover Perspective to $ l_1 $ Embeddings of Planar Graphs", journal = j-TALG, volume = "21", number = "1", pages = "4:1--4:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3686800", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "It was conjectured by Gupta et al. that every planar graph can be embedded into $ \ell_1 $ with constant distortion. However, given an $n$-vertex weighted planar graph, the best upper bound on the distortion is only $ O(\sqrt {\log n}) $, by Rao. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bhore:2025:OES, author = "Sujoy Bhore and Csaba D. T{\'o}th", title = "Online {Euclidean} Spanners", journal = j-TALG, volume = "21", number = "1", pages = "5:1--5:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3681790", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we study the online Euclidean spanners problem for points in $ \mathbb {R}^d $. Given a set $S$ of $n$ points in $ \mathbb {R}^d $, a $t$-spanner on $S$ is a subgraph of the underlying complete graph \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kawarabayashi:2025:AIM, author = "Ken-ichi Kawarabayashi and Bojan Mohar and Roman Nedela and Peter Zeman", title = "Automorphisms and Isomorphisms of Maps in Linear Time", journal = j-TALG, volume = "21", number = "1", pages = "6:1--6:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3686798", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "A map is a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. An automorphism of a map can be thought of as a permutation of the vertices, which preserves the vertex-. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Blanca:2025:CHD, author = "Antonio Blanca and Zongchen Chen and Daniel STefankovic and Eric Vigoda", title = "Complexity of High-Dimensional Identity Testing with Coordinate Conditional Sampling", journal = j-TALG, volume = "21", number = "1", pages = "7:1--7:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3686799", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the identity testing problem for high-dimensional distributions. Given as input an explicit distribution $ \mu $, an $ \varepsilon \gt 0 $, and access to sampling oracle(s) for a hidden distribution $ \pi $, the goal in identity testing is \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Focke:2025:ACA, author = "Jacob Focke and Leslie Ann Goldberg and Marc Roth and Stanislav Zivn{\'y}", title = "Approximately Counting Answers to Conjunctive Queries with Disequalities and Negations", journal = j-TALG, volume = "21", number = "1", pages = "8:1--8:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3689634", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the complexity of approximating the number of answers to a small query $ \varphi $ in a large database $ \mathcal {D} $. We establish an exhaustive classification into tractable and intractable cases if $ \varphi $ is a conjunctive query \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Gabow:2025:MCM, author = "Harold N. Gabow", title = "Maximum Cardinality $f$-Matching in Time {$ O(n^{2 / 3} m)$}", journal = j-TALG, volume = "21", number = "1", pages = "9:1--9:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3696668", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present an algorithm that finds a maximum cardinality $f$-matching of a simple graph in time $ O(n^{2 / 3}m) $. Here, $ f : V \to \mathbb {N} $ is a given function and an $f$-matching is a subgraph wherein each vertex $ v \in V $ has degree \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Narayanaswamy:2025:PRS, author = "N. S. Narayanaswamy and S. M. Dhannya", title = "Perfect Resolution of Strong Conflict-Free Colouring of Interval Hypergraphs", journal = j-TALG, volume = "21", number = "1", pages = "10:1--10:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3698880", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Dutting:2025:FDS, author = "Paul D{\"u}tting and Federico Fusco and Silvio Lattanzi and Ashkan Norouzi-Fard and Morteza Zadimoghaddam", title = "Fully Dynamic Submodular Maximization over Matroids", journal = j-TALG, volume = "21", number = "1", pages = "11:1--11:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3698397", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this significant problem in the fully dynamic setting, where elements can be both \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Navarro:2025:CMR, author = "Gonzalo Navarro", title = "Computing {MEMs} and Relatives on Repetitive Text Collections", journal = j-TALG, volume = "21", number = "1", pages = "12:1--12:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3701561", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cardinal:2025:CGP, author = "Jean Cardinal and Arturo Merino and Torsten M{\"u}tze", title = "Combinatorial Generation via Permutation Languages. {IV}. {Elimination} Trees", journal = j-TALG, volume = "21", number = "1", pages = "13:1--13:??", month = jan, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3689633", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:46 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An elimination tree for a connected graph $G$ is a rooted tree on the vertices of $G$ obtained by choosing a root $x$ and recursing on the connected components of $ G - x $ to produce the subtrees of $x$. Elimination trees appear in many \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "13", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Terao:2025:FMP, author = "Tatsuya Terao", title = "Faster Matroid Partition Algorithms", journal = j-TALG, volume = "21", number = "2", pages = "14:1--14:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3707208", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the matroid partitioning problem, we are given $k$ matroids $ \mathcal {M}_1 = (V, \mathcal {I}_1), \dots, \mathcal {M}_k = (V, \mathcal {I}_k) $ defined over a common ground set $V$ of $n$ elements, and we need to find a partitionable set \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "14", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Brodal:2025:SFH, author = "Gerth St{\o}lting Brodal and George Lagogiannis and Robert E. Tarjan", title = "Strict {Fibonacci} Heaps", journal = j-TALG, volume = "21", number = "2", pages = "15:1--15:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3707692", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present the strict Fibonacci heap, the first pointer-based heap implementation with time bounds matching those of Fibonacci heaps in the worst case. Strict Fibonacci heaps support make-heap, insert, find-min, meld and decrease-key in worst-case \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "15", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Agrawal:2025:OCT, author = "Akanksha Agrawal and Paloma T. Lima and Daniel Lokshtanov and Pawe{\l} Rz{\k{a}}{\.z}ewski and Saket Saurabh and Roohani Sharma", title = "Odd Cycle Transversal on {$ P_5 $}-free Graphs in Polynomial Time", journal = j-TALG, volume = "21", number = "2", pages = "16:1--16:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3708544", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "An independent set in a graph $G$ is a set of pairwise non-adjacent vertices. A graph $G$ is bipartite if its vertex set can be partitioned into two independent sets. In the Odd Cycle Transversal problem, the input is a graph $G$ along with a \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "16", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chrobak:2025:CTW, author = "Marek Chrobak and Neal E. Young", title = "Classification via Two-Way Comparisons", journal = j-TALG, volume = "21", number = "2", pages = "17:1--17:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3709361", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Given a weighted, ordered query set $Q$ and a partition of $Q$ into classes, we study the problem of computing a minimum-cost decision tree that, given any query $ q \in Q $, uses equality tests and less-than tests to determine $q$'s class. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "17", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Boczkowski:2025:QCS, author = "Lucas Boczkowski and Uriel Feige and Amos Korman and Yoav Rodeh", title = "The Query Complexity of Searching Trees with Permanently Noisy Advice", journal = j-TALG, volume = "21", number = "2", pages = "18:1--18:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3707207", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We consider a search problem on trees aiming to find a treasure that an adversary places at one of the nodes. The algorithm can query nodes and extract directional information from them. That is, each node holds a pointer, termed advice, to one of its \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "18", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Agarwal:2025:THP, author = "Pankaj K. Agarwal and Boris Aronov and Tzvika Geft and Dan Halperin", title = "On Two-Handed Planar Assembly Partitioning with Connectivity Constraints", journal = j-TALG, volume = "21", number = "2", pages = "19:1--19:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3711823", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Assembly planning is a fundamental problem in robotics and automation, which involves designing a sequence of motions to bring the separate constituent parts of a product into their final placement in the product. Assembly planning is naturally cast as a \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "19", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Ito:2025:RPC, author = "Takehiro Ito and Yuni Iwamasa and Naonori Kakimura and Yusuke Kobayashi and Shun-Ichi Maezawa and Yuta Nozaki and Yoshio Okamoto and Kenta Ozeki", title = "Rerouting Planar Curves and Disjoint Paths", journal = j-TALG, volume = "21", number = "2", pages = "20:1--20:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3715694", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider a transformation of k disjoint paths in a graph. For a graph and a pair of k disjoint paths $ \mathcal {P} $ and $ \mathcal {Q} $ connecting the same set of terminal pairs, we aim to determine whether $ \mathcal {P} $ can \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "20", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chakraborty:2025:NEB, author = "Diptarka Chakraborty and Keerti Choudhary", title = "New Extremal Bounds for Reachability and Strong-Connectivity Preservers under Failures", journal = j-TALG, volume = "21", number = "2", pages = "21:1--21:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3720545", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we consider the question of computing sparse subgraphs for any input directed graph $ G = (V, E) $ on n vertices and m edges that preserves reachability and/or strong-connectivity structures. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "21", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kavitha:2025:PAT, author = "Telikepalli Kavitha and Kazuhisa Makino and Ildik{\'o} Schlotter and Yu Yokoi", title = "Popular Arborescences and Their Matroid Generalization", journal = j-TALG, volume = "21", number = "2", pages = "22:1--22:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3715329", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Consider a directed, rooted graph $ G = (V \cup \{ r \}, E) $ where each vertex in V has a partial order preference over its incoming edges. The preferences of a vertex naturally extend to preferences over arborescences rooted at r. We present a polynomial-. \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "22", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Dallant:2025:CLB, author = "Justin Dallant and John Iacono", title = "Conditional Lower Bounds for Dynamic Geometric Measure Problems", journal = j-TALG, volume = "21", number = "2", pages = "23:1--23:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3727878", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We give new polynomial lower bounds for a number of dynamic measure problems in computational geometry. These lower bounds hold in the Word RAM model, conditioned on the hardness of 3SUM, APSP, or the Online Matrix-Vector Multiplication problem \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "23", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Ayyadevara:2025:NOA, author = "Nikhil Ayyadevara and Rajni Dabas and Arindam Khan and K. V. N. Sreenivas", title = "Near-optimal Algorithms for Stochastic Online Bin Packing", journal = j-TALG, volume = "21", number = "2", pages = "24:1--24:??", month = apr, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3728642", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri May 16 06:36:47 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We study the online bin packing problem under two stochastic settings. In the bin packing problem, we are given n items with sizes in $ (0, 1] $ and the goal is to pack them into the minimum number of unit-sized bins. First, we study bin packing under \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "24", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Agarwal:2025:IQF, author = "Pankaj K. Agarwal and Boris Aronov and Esther Ezra and Matthew J. Katz and Micha Sharir", title = "Intersection Queries for Flat Semi-Algebraic Objects in Three Dimensions and Related Problems", journal = j-TALG, volume = "21", number = "3", pages = "25:1--25:59", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3721290", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Let $ \mathscr {T} $ be a set of n flat (planar) semi-algebraic regions in $ \mathbb {R}^3 $ of constant complexity (e.g., triangles, disks), which we call plates. We wish to preprocess \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "25", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Campos:2025:NML, author = "Victor Campos and Jonas Costa and Raul Lopes and Ignasi Sau", title = "New {Menger}-Like Dualities in Digraphs and Applications to Half-Integral Linkages", journal = j-TALG, volume = "21", number = "3", pages = "26:1--26:28", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3724120", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present new min-max relations in digraphs between the number of paths satisfying certain conditions and the order of the corresponding cuts. We define these objects in order \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "26", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Focke:2025:TCB, author = "Jacob Focke and D{\'a}niel Marx and Fionn {Mc Inerney} and Daniel Neuen and Govind S. Sankar and Philipp Schepper and Philip Wellnitz", title = "Tight Complexity Bounds for Counting Generalized Dominating Sets in Bounded-Treewidth Graphs --- {Part I}: Algorithmic Results", journal = j-TALG, volume = "21", number = "3", pages = "27:1--27:45", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3731452", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets $ \sigma, \rho $ of non-negative integers, a", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "27", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Khan:2025:TAA, author = "Arindam Khan and Aditya Lonkar and Arnab Maiti and Amatya Sharma and Andreas Wiese", title = "Tight Approximation Algorithms for {2D} Guillotine Strip Packing", journal = j-TALG, volume = "21", number = "3", pages = "28:1--28:30", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3736723", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the Strip Packing (SP) problem, we are given a vertical half-strip $ [0, W] \times [0, \infty) $ and a set of $n$ axis-aligned rectangles of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "28", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Ene:2025:IAS, author = "Alina Ene and Troy Lee and Piotr Micek and Sushant Sachdeva", title = "Introduction: {ACM--SIAM Symposium on Discrete Algorithms (SODA) 2021} Special Issue", journal = j-TALG, volume = "21", number = "3", pages = "29:1--29:2", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3744924", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "29", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chen:2025:PTT, author = "Xi Chen and Anindya De and Chin Ho Lee and Rocco Servedio and Sandip Sinha", title = "Polynomial-time Trace Reconstruction in the Smoothed Complexity Model", journal = j-TALG, volume = "21", number = "3", pages = "30:1--30:28", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3560819", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In the trace reconstruction problem, an unknown source string $x \in \{0, 1\}^n$ is sent through a probabilistic deletion channel that independently deletes each bit with probability $\delta$ and \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "30", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Jambulapati:2025:UUF, author = "Arun Jambulapati and Aaron Sidford", title = "Ultrasparse Ultrasparsifiers and Faster {Laplacian} System Solvers", journal = j-TALG, volume = "21", number = "3", pages = "31:1--31:49", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3593809", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we provide an $O (m \log\log^{O(1)} n \log (1/ \epsilon ))$-expected time algorithm for solving Laplacian systems on $n$-node $m$-edge graphs, improving upon the previous best \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "31", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Austrin:2025:OIU, author = "Per Austrin and Jonah Brown-Cohen and Johan H{\aa}stad", title = "Optimal Inapproximability with Universal Factor Graphs", journal = j-TALG, volume = "21", number = "3", pages = "32:1--32:39", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3631119", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The factor graph of an instance of a constraint satisfaction problem (CSP) is the bipartite graph indicating which variables appear in each constraint. An instance of the CSP is \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "32", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Walzer:2025:PCO, author = "Stefan Walzer", title = "Peeling Close to the Orientability Threshold Spatial Coupling in Hashing-Based Data Structures", journal = j-TALG, volume = "21", number = "3", pages = "33:1--33:23", month = jul, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3711822", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/hash.bib; https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In multiple-choice data structures each element $x$ in a set $S$ of $m$ keys is associated with a random set $ e(x) \subseteq [n] $ of buckets with capacity $ \ell \geq 1 $ by hash \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "33", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bansal:2025:IAS, author = "Nikhil Bansal and Eun Jung Kim and Viswanath Nagarajan and Aaron Potechin and Lars Rohwedder", title = "Introduction: {ACM--SIAM Symposium on Discrete Algorithms (SODA) 2023} Special Issue", journal = j-TALG, volume = "21", number = "4", pages = "34:1--34:2", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3742858", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "34", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Leverrier:2025:EDC, author = "Anthony Leverrier and Gilles Z{\'e}mor", title = "Efficient Decoding up to a Constant Fraction of the Code Length for Asymptotically Good Quantum Codes", journal = j-TALG, volume = "21", number = "4", pages = "35:1--35:34", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3663763", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We introduce and analyse an efficient decoder for quantum Tanner codes that can correct adversarial errors of linear weight. Previous decoders for quantum low-density \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "35", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Assadi:2025:TBM, author = "Sepehr Assadi and Mart{\'\i}n Farach-Colton and William Kuszmaul", title = "Tight Bounds for Monotone Minimal Perfect Hashing", journal = j-TALG, volume = "21", number = "4", pages = "36:1--36:23", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3677608", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The monotone minimal perfect hash function (MMPHF) problem is the following indexing problem. Given a set $ S = \{ s_1, \ldots, s_n \} $ of $n$ distinct keys from a universe $U$ of size", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "36", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Sinnamon:2025:ESA, author = "Corwin Sinnamon and Robert E. Tarjan", title = "Efficiency of Self-Adjusting Heaps", journal = j-TALG, volume = "21", number = "4", pages = "37:1--37:39", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3708989", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Since the invention of the pairing heap by Fredman, Sedgewick, Sleator, and Tarjan [ 8 ], it has been an open question whether this or any other simple ``self-adjusting'' heap \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "37", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bender:2025:TP, author = "Michael Bender and Alex Conway and Mart{\'\i}n Farach-Colton and William Kuszmaul and Guido Tagliavini", title = "Tiny Pointers", journal = j-TALG, volume = "21", number = "4", pages = "38:1--38:43", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3700594", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "This article introduces a new data-structural object that we call the tiny pointer. In many applications, traditional $ \log n $-bit pointers can be replaced with $ o(\log n) $-bit \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "38", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Woodruff:2025:OLW, author = "David P. Woodruff and Taisuke Yasuda", title = "Online {Lewis} Weight Sampling", journal = j-TALG, volume = "21", number = "4", pages = "39:1--39:50", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3715127", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The seminal work of Cohen and Peng (STOC 2015) introduced Lewis weight sampling to the theoretical computer science community, which yields fast row sampling algorithms for \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "39", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Belova:2025:PFB, author = "Tatiana Belova and Alexander Golovnev and Alexander S. Kulikov and Ivan Mihajlin and Denil Sharipov", title = "Polynomial Formulations as a Barrier for Reduction-Based Hardness Proofs", journal = j-TALG, volume = "21", number = "4", pages = "40:1--40:44", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3721134", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The Strong Exponential Time Hypothesis (SETH) asserts that for every $ \varepsilon > 0 $ there exists $k$ such that $k$-SAT requires time $ (2 - \varepsilon)^n $. The field of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "40", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Chapuy:2025:SSW, author = "Guillaume Chapuy and Guillem Perarnau", title = "Short Synchronizing Words for Random Automata", journal = j-TALG, volume = "21", number = "4", pages = "41:1--41:55", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3736722", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We prove that a uniformly random automaton with $n$ states on a 2-letter alphabet has a synchronizing word of length $ O(n^{1 / 2} \log n) $ with high probability (w.h.p.). That \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "41", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Faour:2025:LDR, author = "Salwa Faour and Mohsen Ghaffari and Christoph Grunau and Fabian Kuhn and V{\'a}clav Rozho{\v{n}}", title = "Local Distributed Rounding: Generalized to {MIS}, Matching, Set Cover, and Beyond", journal = j-TALG, volume = "21", number = "4", pages = "42:1--42:48", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3742476", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We develop a general deterministic distributed method for locally rounding fractional solutions of graph problems for which the analysis can be broken down into analyzing pairs of \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "42", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bender:2025:PAT, author = "Michael A. Bender and Abhishek Bhattacharjee and Alex Conway and Mart{\'\i}n Farach-Colton and Rob Johnson and Sudarsun Kannan and William Kuszmaul and Nirjhar Mukherjee and Don Porter and Guido Tagliavini and Janet Vorobyeva and Evan West", title = "Paging and the Address-Translation Problem", journal = j-TALG, volume = "21", number = "4", pages = "43:1--43:22", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3737700", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "The classical paging problem, introduced by Sleator and Tarjan in 1985, formalizes the problem of caching pages in RAM in order to minimize IOs. Their online formulation \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "43", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Dabrowski:2025:ACS, author = "Konrad K. Dabrowski and Peter Jonsson and Sebastian Ordyniak and George Osipov and Magnus Wahlstr{\"o}m", title = "Almost Consistent Systems of Linear Equations", journal = j-TALG, volume = "21", number = "4", pages = "44:1--44:55", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3733107", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "44", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Friggstad:2025:ADS, author = "Zachary Friggstad and Ramin Mousavi", title = "A {$ O({\rm log}, k) $}-Approximation for Directed {Steiner} Tree in Planar Graphs", journal = j-TALG, volume = "21", number = "4", pages = "45:1--45:14", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3734525", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "We present a $ O(\log k) $-approximation for both the edge-weighted and node-weighted versions of Directed Steiner Tree in \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "45", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kolmogorov:2025:SPA, author = "Vladimir Kolmogorov", title = "A Simpler and Parallelizable {$ O(\sqrt {\log n}) $}-Approximation Algorithm for Sparsest Cut", journal = j-TALG, volume = "21", number = "4", pages = "46:1--46:22", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3748723", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "46", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Feldmann:2025:PAS, author = "Andreas Emil Feldmann and Michael Lampis", title = "Parameterized Algorithms for {Steiner} Forest in Bounded Width Graphs", journal = j-TALG, volume = "21", number = "4", pages = "47:1--47:26", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3748724", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "In this article, we reassess the parameterized complexity and approximability of the well-studied Steiner Forest problem in \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "47", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Akitaya:2025:MPB, author = "Hugo A. Akitaya and Ahmad Biniaz and Erik D. Demaine and Linda Kleist and Frederick Stock and Csaba D. T{\'o}th", title = "Minimum Plane Bichromatic Spanning Trees", journal = j-TALG, volume = "21", number = "4", pages = "48:1--48:14", month = oct, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1145/3747591", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Thu Oct 2 14:58:40 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", abstract = "For a set of red and blue points in the plane, a Minimum Bichromatic Spanning Tree (MinBST) is a shortest spanning tree of the points such that every edge has a red and a blue \ldots{}", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "48", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Georgiadis:2026:CEC, author = "Loukas Georgiadis and Giuseppe F. Italiano and Evangelos Kosinas", title = "Computing the $4$-Edge-Connected Components of a Graph: an Experimental Study", journal = j-TALG, volume = "22", number = "1", pages = "1:1--1:34", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3757919", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "1", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Kalemaj:2026:NDP, author = "Iden Kalemaj and Sofya Raskhodnikova and Adam Smith and Charalampos Tsourakakis", title = "Node-Differentially Private Estimation of the Number of Connected Components", journal = j-TALG, volume = "22", number = "1", pages = "2:1--2:22", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3762664", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "2", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Jain:2026:PAS, author = "Pallavi Jain and Lawqueen Kanesh and Fahad Panolan and Souvik Saha and Abhishek Sahu and Saket Saurabh and Anannya Upasana", title = "Parameterized Approximation Schemes for Biclique-Free Max $k$-Weight {SAT} and Max Coverage", journal = j-TALG, volume = "22", number = "1", pages = "3:1--3:30", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3763238", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "3", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bullinger:2026:OCF, author = "Martin Bullinger and Ren{\'e} Romen", title = "Online Coalition Formation under Random Arrival or Coalition Dissolution", journal = j-TALG, volume = "22", number = "1", pages = "4:1--4:43", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3758324", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "4", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cabello:2026:LPT, author = "Sergio Cabello and Michael Hoffmann and Katharina Klost and Wolfgang Mulzer and Josef Tkadlec", title = "Long Plane Trees", journal = j-TALG, volume = "22", number = "1", pages = "5:1--5:40", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3765740", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "5", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Petruschka:2026:CFT, author = "Asaf Petruschka and Shay Sapir and Elad Tzalik", title = "Color Fault-Tolerant Spanners", journal = j-TALG, volume = "22", number = "1", pages = "6:1--6:21", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3750728", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "6", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Cobas:2026:FSS, author = "Dustin Cobas and Travis Gagie and Gonzalo Navarro", title = "Fast and Small Subsampled {$R$}-indexes", journal = j-TALG, volume = "22", number = "1", pages = "7:1--7:29", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3750729", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "7", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Bentert:2026:PSC, author = "Matthias Bentert and Fedor V. Fomin and Petr A. Golovach and Tuukka Korhonen and William Lochet and Fahad Panolan and M. S. Ramanujan and Saket Saurabh and Kirill Simonov", title = "Packing Short Cycles", journal = j-TALG, volume = "22", number = "1", pages = "8:1--8:35", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3765285", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "8", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Fomin:2026:TCA, author = "Fedor V. Fomin and Petr A. Golovach and Danil Sagunov and Kirill Simonov", title = "Tree Containment above Minimum Degree Is {FPT}", journal = j-TALG, volume = "22", number = "1", pages = "9:1--9:44", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3768573", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "9", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Grandoni:2026:MEG, author = "Fabrizio Grandoni and Chris Schwiegelshohn and Shay Solomon and Amitai Uzrad", title = "Maintaining an {EDCS} in General Graphs: Simpler, Density-Sensitive and with Worst-Case Time Bounds", journal = j-TALG, volume = "22", number = "1", pages = "10:1--10:16", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3765900", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "10", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Shin:2026:ILA, author = "Yongho Shin and Changyeol Lee and Gukryeol Lee and Hyung-Chan An", title = "Improved Learning-Augmented Algorithms and (Tight) Lower Bounds for Multi-Option Ski Rental Problem", journal = j-TALG, volume = "22", number = "1", pages = "11:1--11:30", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3763239", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "11", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", } @Article{Dallard:2026:CTD, author = "Cl{\'e}ment Dallard and Fedor V. Fomin and Petr A. Golovach and Tuukka Korhonen and Martin Milanic", title = "Computing Tree Decompositions with Small Independence Number", journal = j-TALG, volume = "22", number = "1", pages = "12:1--12:25", month = jan, year = "2026", CODEN = "????", DOI = "https://doi.org/10.1145/3767730", ISSN = "1549-6325 (print), 1549-6333 (electronic)", ISSN-L = "1549-6325", bibdate = "Fri Jan 9 10:14:47 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/talg.bib", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Algorithms", articleno = "12", fjournal = "ACM Transactions on Algorithms (TALG)", journal-URL = "https://dl.acm.org/loi/talg", }