eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-06
22:1
22:12
10.4230/LIPIcs.ISAAC.2018.22
article
Distributed Approximation Algorithms for the Minimum Dominating Set in K_h-Minor-Free Graphs
Czygrinow, Andrzej
1
Hanckowiak, Michal
2
Wawrzyniak, Wojciech
2
Witkowski, Marcin
2
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287-1804, USA
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol123-isaac2018/LIPIcs.ISAAC.2018.22/LIPIcs.ISAAC.2018.22.pdf
Distributed algorithms
minor-closed family of graphs
MDS