Near-Optimal Distributed Dominating Set in Bounded Arboricity Graphs

Michal Dory, Mohsen Ghaffari, Saeed Ilchi

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

Abstract

We describe a simple deterministic O(-1 log ") round distributed algorithm for (2α+ 1) (1 + ) approximation of minimum weighted dominating set on graphs with arboricity at most α. Here Δdenotes the maximum degree. We also show a lower bound proving that this round complexity is nearly optimal even for the unweighted case, via a reduction from the celebrated KMW lower bound on distributed vertex cover approximation [Kuhn, Moscibroda, and Wattenhofer JACM'16]. Our algorithm improves on all the previous results (that work only for unweighted graphs) including a randomized O(α2) approximation inO(logn) rounds [Lenzen andWattenhofer DISC'10], a deterministic O(α log ") approximation in O(log ") rounds [Lenzen and Wattenhofer DISC'10], a deterministic O(α) approximation in O(log2 ") rounds [implicit in Bansal and Umboh IPL'17 and Kuhn, Moscibroda, and Wattenhofer SODA'06], and a randomized O(α) approximation in O(α logn) rounds [Morgan, Solomon and Wein DISC'21]. We also provide a randomized O(α log ") round distributed algorithm that sharpens the approximation factor to α (1 + o (1)). If each node is restricted to do polynomial-time computations, our approximation factor is tight in the first order as it is NP-hard to achieve α - 1 - approximation [Bansal and Umboh IPL'17].

Original languageEnglish
Title of host publicationPODC 2022 - Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages292-300
Number of pages9
ISBN (Electronic)9781450392624
DOIs
StatePublished - 20 Jul 2022
Externally publishedYes
Event41st ACM Symposium on Principles of Distributed Computing, PODC 2022 - Salerno, Italy
Duration: 25 Jul 202229 Jul 2022

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference41st ACM Symposium on Principles of Distributed Computing, PODC 2022
Country/TerritoryItaly
CitySalerno
Period25/07/2229/07/22

Bibliographical note

Publisher Copyright:
© 2022 ACM.

Keywords

  • approximation algorithms
  • arboricity
  • distributed computing
  • dominating set

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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