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
N1 - Funding Information:
★ Research supported in part by Simons Foundation Grant # 521777.
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.
UR - http://www.scopus.com/inward/record.url?scp=85031940846&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85031940846&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85031940846
SN - 1613-0073
VL - 1949
SP - 75
EP - 86
JO - CEUR Workshop Proceedings
JF - CEUR Workshop Proceedings
T2 - Joint 18th Italian Conference on Theoretical Computer Science and the 32nd Italian Conference on Computational Logic, ICTCS 2017 and CILC 2017
Y2 - 26 September 2017 through 28 September 2017
ER -