Distributed set cover approximation: Primal-dual with optimal locality

Guy Even, Mohsen Ghaffari, Moti Medina

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

This paper presents a deterministic distributed algorithm for computing an f(1+ε) approximation of the well-studied minimum set cover problem, for any constant ε > 0, in O(log(f∆)/log log(f∆)) rounds. Here, f denotes the maximum element frequency and ∆ denotes the cardinality of the largest set. This f(1 + ε) approximation almost matches the f-approximation guarantee of standard centralized primal-dual algorithms, which is known to be essentially the best possible approximation for polynomial-time computations. The round complexity almost matches the Ω(log(∆)/log log(∆)) lower bound of Kuhn, Moscibroda, Wattenhofer [JACM’16], which holds for even f = 2 and for any poly(log ∆) approximation. Our algorithm also gives an alternative way to reproduce the time-optimal 2(1+ε)-approximation of vertex cover, with round complexity O(log ∆/log log ∆), as presented by Bar-Yehuda, Censor-Hillel, and Schwartzman [PODC’17] for weighted vertex cover. Our method is quite different and it can be viewed as a locality-optimal way of performing primal-dual for the more general case of set cover. We note that the vertex cover algorithm of Bar-Yehuda et al. does not extend to set cover (when f ≥ 3).

Original languageEnglish
Title of host publication32nd International Symposium on Distributed Computing, DISC 2018
EditorsUlrich Schmid, Josef Widder
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770927
DOIs
StatePublished - 1 Oct 2018
Event32nd International Symposium on Distributed Computing, DISC 2018 - New Orleans, United States
Duration: 15 Oct 201819 Oct 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume121
ISSN (Print)1868-8969

Conference

Conference32nd International Symposium on Distributed Computing, DISC 2018
Country/TerritoryUnited States
CityNew Orleans
Period15/10/1819/10/18

Keywords

  • And phrases Distributed Algorithms
  • Approximation Algorithms
  • Set Cover
  • Vertex Cover

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