TY - JOUR

T1 - Distributed approximation algorithms for k-dominating set in graphs of bounded genus and linklessly embeddable graphs Regular Submission

AU - Czygrinow, Andrzej

AU - Hańckowiak, Michał

AU - Wawrzyniak, Wojciech

AU - Witkowski, Marcin

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85031940846

VL - 1949

SP - 75

EP - 86

JO - CEUR Workshop Proceedings

JF - CEUR Workshop Proceedings

SN - 1613-0073

ER -