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


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
Number of pages9
ISBN (Electronic)9781450392624
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


Conference41st ACM Symposium on Principles of Distributed Computing, PODC 2022

Bibliographical note

Publisher Copyright:
© 2022 ACM.


  • approximation algorithms
  • arboricity
  • distributed computing
  • dominating set

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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