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Brief Announcement: Distributed Algorithms for Minimum Dominating Set Problem and Beyond, a New Approach

Authors Sharareh Alipour , Mohammadhadi Salari



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Author Details

Sharareh Alipour
  • Tehran Institute for Advanced Studies, Iran
Mohammadhadi Salari
  • Simon Fraser University, Burnaby, Canada

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Sharareh Alipour and Mohammadhadi Salari. Brief Announcement: Distributed Algorithms for Minimum Dominating Set Problem and Beyond, a New Approach. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 40:1-40:3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.DISC.2022.40

Abstract

In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set (MTDS) problem. We propose a new idea to compute approximate MDS and MTDS. This new approach can be implemented in a distributed model or parallel model. We also show how to use this new approach in other related problems such as set cover problem and k-distance dominating set problem.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Distributed algorithms
Keywords
  • Minimum dominating set problem
  • set cover problem
  • k-distance dominating set problem
  • distributed algorithms

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References

  1. Krishnendu Chakrabarty, S. Sitharama Iyengar, Hairong Qi, and Eungchun Cho. Grid coverage for surveillance and target location in distributed sensor networks. IEEE Trans. Computers, 51(12):1448-1453, 2002. URL: https://doi.org/10.1109/TC.2002.1146711.
  2. Mohsen Ghaffari and Fabian Kuhn. Derandomizing distributed algorithms with small messages: Spanners and dominating set. In 32nd International Symposium on Distributed Computing, DISC 2018, New Orleans, LA, USA, October 15-19, 2018, pages 29:1-29:17, 2018. URL: https://doi.org/10.4230/LIPIcs.DISC.2018.29.
  3. Fabrizio Grandoni, Jochen Könemann, and Alessandro Panconesi. Distributed weighted vertex cover via maximal matchings. ACM Trans. Algorithms, 5(1):6:1-6:12, 2008. URL: https://doi.org/10.1145/1435375.1435381.
  4. Michal Hanckowiak, Michal Karonski, and Alessandro Panconesi. On the distributed complexity of computing maximal matchings. SIAM J. Discret. Math., 15(1):41-57, 2001. URL: https://doi.org/10.1137/S0895480100373121.
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