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

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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.

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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

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

Funding

  • Czygrinow, Andrzej: Research supported in part by Simons Foundation Grant # 521777.

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
  2. W. Wawrzyniak A. Czygrinow, M. Hańćkowiak. Fast distributed approximations in planar graphs. International Symposium on Distributed Computing, DISC, Arcachon, France, September 2008, LNCS 5218, pages 78-92, 2008. Google Scholar
  3. R. Wattenhofer C. Lenzen. Minimum Dominating Set Approximation in Graphs of Bounded Arboricity. International Symposium on Distributed Computing, DISC 2010, pages 510-524, 2010. Google Scholar
  4. R. Wattenhofer C. Lenzen, Y. A. Oswald. Distributed minimum dominating set approximations in restricted families of graphs. Distrib. Comput., 26 (2), pages 119-137, 2013. Google Scholar
  5. S. Gutner N. Alon. Kernels for the Dominating Set Problem on Graphs with an Excluded Minor. Electronic Colloquium on Computational Complexity, Report No. 66, 2008. Google Scholar
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