Distributed approximation algorithms for k-dominating set in graphs of bounded genus and linklessly embeddable graphs

Abstract

A k-dominating set in a graph G=(V,E) is a set U⊆V such that every vertex of G is either in U or has at least k neighbors in U. In this paper we give simple distributed approximation algorithms in the standard Local model of computations for the minimum k-dominating set problem for k≥2 in graphs with no K3,h-minor for some h∈Z+ and graphs with no K4,4-minor. In particular, this gives fast distributed approximations for graphs of bounded genus and linklessly embeddable graphs. The algorithms give a constant approximation ratio and run in a constant number of rounds. In addition, we will give a (1+ϵ)-approximation for an arbitrary fixed ϵ>0 which runs in O(log⁎⁡n) rounds where n is the order of a graph.