Near-optimal distributed dominating set in bounded arboricity graphs

Michal Dory, Mohsen Ghaffari, Saeed Ilchi

Research output: Contribution to journalArticlepeer-review

Abstract

We describe a simple deterministic O(ε- 1log Δ) round distributed algorithm for (2 α+ 1) (1 + ε) approximation of minimum weighted dominating set on graphs with arboricity at most α . Here Δ denotes 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 et al. in JACM 63:116, 2016). Our algorithm improves on all the previous results (that work only for unweighted graphs) including a randomized O(α2) approximation in O(log n) rounds (Lenzen et al. in International symposium on distributed computing, Springer, 2010), a deterministic O(αlog Δ) approximation in O(log Δ) rounds (Lenzen et al. in international symposium on distributed computing, Springer, 2010), a deterministic O(α) approximation in O(log 2Δ) rounds (implicit in Bansal et al. in Inform Process Lett 122:21–24, 2017; Proceeding 17th symposium on discrete algorithms (SODA), 2006), and a randomized O(α) approximation in O(αlog n) rounds (Morgan et al. in 35th International symposiumon distributed computing, 2021). We also provide a randomized O(αlog Δ) 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 - ε approximation (Bansal et al. in Inform Process Lett 122:21-24, 2017).

Original languageEnglish
JournalDistributed Computing
DOIs
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).

Keywords

  • Approximation algorithms
  • Arboricity
  • Distributed computing
  • Dominating set

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Computational Theory and Mathematics

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