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
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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
SN - 0304-3975
VL - 809
SP - 327
EP - 338
JO - Theoretical Computer Science
JF - Theoretical Computer Science
ER -