TY - JOUR

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

AU - Czygrinow, Andrzej

AU - Hanćkowiak, Michał

AU - Wawrzyniak, Wojciech

AU - Witkowski, Marcin

N1 - Funding Information:
Research supported in part by Simons Foundation Grant # 521777.
Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/2/24

Y1 - 2020/2/24

N2 - 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.

AB - 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.

KW - Bounded genus graphs

KW - Distributed algorithms

KW - Dominating set

UR - http://www.scopus.com/inward/record.url?scp=85077663109&partnerID=8YFLogxK

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U2 - 10.1016/j.tcs.2019.12.027

DO - 10.1016/j.tcs.2019.12.027

M3 - Article

AN - SCOPUS:85077663109

VL - 809

SP - 327

EP - 338

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -