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Distributed Approximation Algorithms for the Minimum Dominating Set in K_h-Minor-Free Graphs

Authors Andrzej Czygrinow, Michal Hanckowiak, Wojciech Wawrzyniak, Marcin Witkowski



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Author Details

Andrzej Czygrinow
  • School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804, USA
Michal Hanckowiak
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Wojciech Wawrzyniak
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Marcin Witkowski
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland

Cite AsGet BibTex

Andrzej Czygrinow, Michal Hanckowiak, Wojciech Wawrzyniak, and Marcin Witkowski. Distributed Approximation Algorithms for the Minimum Dominating Set in K_h-Minor-Free Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 22:1-22:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ISAAC.2018.22

Abstract

In this paper we will give two distributed approximation algorithms (in the Local model) for the minimum dominating set problem. First we will give a distributed algorithm which finds a dominating set D of size O(gamma(G)) in a graph G which has no topological copy of K_h. The algorithm runs L_h rounds where L_h is a constant which depends on h only. This procedure can be used to obtain a distributed algorithm which given epsilon>0 finds in a graph G with no K_h-minor a dominating set D of size at most (1+epsilon)gamma(G). The second algorithm runs in O(log^*{|V(G)|}) rounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
Keywords
  • Distributed algorithms
  • minor-closed family of graphs
  • MDS

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References

  1. E. Szymańska A. Czygrinow, M. Hańćkowiak. Fast Distributed Algorithm for the Maximum Matching Problem in Bounded Arboricity Graphs. Proc. of 20th International Symposium, ISAAC, LNCS 5878, pages 668-678, 2009. Google Scholar
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