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A Tight Local Algorithm for the Minimum Dominating Set Problem in Outerplanar Graphs

Authors Marthe Bonamy , Linda Cook, Carla Groenland , Alexandra Wesolek

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Author Details

Marthe Bonamy
  • CNRS, LaBRI, Université de Bordeaux, France
Linda Cook
  • Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, Republic of Korea
Carla Groenland
  • Utrecht University, The Netherlands
Alexandra Wesolek
  • Department of Mathematics, Simon Fraser University, Burnaby, Canada

Funding

  • Bonamy, Marthe: Supported by the ANR project GrR (ANR-18-CE40-0032).
  • Cook, Linda: This work was supported by AFOSR grant A9550-19-1-0187, NSF grant DMS-1800053 and the Institute for Basic Science (IBS-R029-C1).
  • Groenland, Carla: Supported by the European Research Council Horizon 2020 project CRACKNP (grant agreement no. 853234).
  • Wesolek, Alexandra: Supported by the Vanier Canada Graduate Scholarships program.

Acknowledgements

We thank the referees for helpful comments which improved the presentation of the paper.

Cite AsGet BibTex

Marthe Bonamy, Linda Cook, Carla Groenland, and Alexandra Wesolek. A Tight Local Algorithm for the Minimum Dominating Set Problem in Outerplanar Graphs. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.DISC.2021.13

Abstract

We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a (5-ε)-approximation, for any ε > 0. Our algorithm only requires knowledge of the degree of a vertex and of its neighbors, so that large messages and unique identifiers are not needed.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Approximation algorithms
Keywords
  • Outerplanar graphs
  • dominating set
  • LOCAL model
  • constant-factor approximation algorithm

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References

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