A k-dominating set in a graph G = (V,E) is a set U ¢ V such that ever 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 local model for the minimum k-dominating set problem for k ≥ 2 in graphs with no K3,h-minor 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 + €)-Approximation for an arbitrary fixed € > 0 which runs in O(log∗ n) rounds where n is the order of a graph.
|Original language||English (US)|
|Number of pages||12|
|Journal||CEUR Workshop Proceedings|
|State||Published - 2017|
ASJC Scopus subject areas
- Computer Science(all)