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

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

doi:10.4230/LIPIcs.DISC.2021.13

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Document Identifiers

DOI: 10.4230/LIPIcs.DISC.2021.13
URN: urn:nbn:de:0030-drops-148159

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

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

Saeed Akhoondian Amiri, Patrice Ossona de Mendez, Roman Rabinovich, and Sebastian Siebertz. Distributed domination on graph classes of bounded expansion. In Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures, SPAA quotesingle18, pages 143-151, 2018.
Saeed Akhoondian Amiri, Stefan Schmid, and Sebastian Siebertz. A local constant factor mds approximation for bounded genus graphs. In Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC quotesingle16, page 227–233, 2016.
Sharareh Alipour, Ehsan Futuhi, and Shayan Karimi. On distributed algorithms for minimum dominating set problem, from theory to application, 2021. URL: http://arxiv.org/abs/2012.04883.
Sharareh Alipour and Amir Jafari. A local constant approximation factor algorithm for minimum dominating set of certain planar graphs. In Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA quotesingle20, pages 501-502, 2020.
Saeed Akhoondian Amiri, Stefan Schmid, and Sebastian Siebertz. Distributed dominating set approximations beyond planar graphs. ACM Transactions on Algorithms (TALG), 15(3):1-18, 2019.
Marthe Bonamy, Linda Cook, Carla Groenland, and Alexandra Wesolek. A tight local algorithm for the minimum dominating set problem in outerplanar graphs, 2021. URL: http://arxiv.org/abs/2108.02697.
Andrzej Czygrinow, Michal Hańćkowiak, and Wojciech Wawrzyniak. Fast distributed approximations in planar graphs. In International Symposium on Distributed Computing, DISC quotesingle08, pages 78-92. Springer, 2008.
Laurent Feuilloley. Bibliography of distributed approximation beyond bounded degree, 2020. URL: http://arxiv.org/abs/2001.08510.
Michael R. Garey and David S. Johnson. Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., San Francisco, 1979.
Daniel Gonçalves. Edge partition of planar graphs into two outerplanar graphs. In Proceedings of the thirty-seventh annual ACM Symposium on Theory of Computing, STOC quotesingle05, pages 504-512, 2005.
Miikka Hilke, Christoph Lenzen, and Jukka Suomela. Brief announcement: local approximability of minimum dominating set on planar graphs. In Proceedings of the 2014 ACM symposium on Principles of Distributed Computing, PODC quotesingle14, pages 344-346, 2014.
Simeon Kublenz, Sebastian Siebertz, and Alexandre Vigny. Constant round distributed domination on graph classes with bounded expansion, 2021. URL: http://arxiv.org/abs/2012.02701.
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. Local computation: Lower and upper bounds. Journal of the ACM (JACM), 63(2):1-44, 2016.
Christoph Lenzen, Yvonne Anne Oswald, and Roger Wattenhofer. What can be approximated locally? case study: Dominating sets in planar graphs. In Proceedings of the twentieth annual Symposium on Parallelism in Algorithms and Architectures, SPAA quotesingle08, pages 46-54, 2008.
Crispin St. John Alvah. Nash-Williams. Decomposition of finite graphs into forests. Journal of the London Mathematical Society (JLMS), s1-39(1):12-12, 1964.
Ran Raz and Shmuel Safra. A sub-constant error-probability low-degree test, and a sub-constant error-probability pcp characterization of np. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, STOC quotesingle97, page 475–484, 1997.
Jukka Suomela. Survey of local algorithms. ACM Computing Surveys (CSUR), 45(2):1-40, 2013.
Wojciech Wawrzyniak. Brief announcement: a local approximation algorithm for mds problem in anonymous planar networks. In Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, PODC quotesingle13, pages 406-408, 2013.
Wojciech Wawrzyniak. A strengthened analysis of a local algorithm for the minimum dominating set problem in planar graphs. Information Processing Letters (IPL), 114(3):94-98, 2014.