Distributed Approximation Algorithms for the Minimum Dominating Set in K_h-Minor-Free Graphs
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.
Distributed algorithms
minor-closed family of graphs
MDS
Theory of computation~Distributed computing models
22:1-22:12
Regular Paper
Andrzej
Czygrinow
Andrzej Czygrinow
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804, USA
Research supported in part by Simons Foundation Grant # 521777.
Michal
Hanckowiak
Michal Hanckowiak
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Wojciech
Wawrzyniak
Wojciech Wawrzyniak
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
Marcin
Witkowski
Marcin Witkowski
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
10.4230/LIPIcs.ISAAC.2018.22
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Andrzej Czygrinow, Michał Hanćkowiak, Wojciech Wawrzyniak, and Marcin Witkowski
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