TY - JOUR

T1 - Improved approximation algorithms for k-connected m-dominating set problems

AU - Nutov, Zeev

N1 - Publisher Copyright:
© 2018 Elsevier B.V.

PY - 2018/12

Y1 - 2018/12

N2 - A graph is k-connected if it has k pairwise internally node disjoint paths between every pair of its nodes. A subset S of nodes in a graph G is a k-connected set if the subgraph G[S] induced by S is k-connected; S is an m-dominating set if every v∈V∖S has at least m neighbors in S. If S is both k-connected and m-dominating then S is a k-connected m-dominating set, or (k,m)-cds for short. In the k-CONNECTED m-DOMINATING SET ((k,m)-CDS) problem the goal is to find a minimum weight (k,m)-cds in a node-weighted graph. We consider the case m≥k and obtain the following approximation ratios. For unit disc graphs we obtain ratio O(klnk), improving the ratio O(k2lnk) of [1,2]. For general graphs we obtain the first non-trivial approximation ratio O(k2lnn).

AB - A graph is k-connected if it has k pairwise internally node disjoint paths between every pair of its nodes. A subset S of nodes in a graph G is a k-connected set if the subgraph G[S] induced by S is k-connected; S is an m-dominating set if every v∈V∖S has at least m neighbors in S. If S is both k-connected and m-dominating then S is a k-connected m-dominating set, or (k,m)-cds for short. In the k-CONNECTED m-DOMINATING SET ((k,m)-CDS) problem the goal is to find a minimum weight (k,m)-cds in a node-weighted graph. We consider the case m≥k and obtain the following approximation ratios. For unit disc graphs we obtain ratio O(klnk), improving the ratio O(k2lnk) of [1,2]. For general graphs we obtain the first non-trivial approximation ratio O(k2lnn).

KW - Approximation algorithm

KW - k-Connected graph

KW - m-Dominating set

UR - http://www.scopus.com/inward/record.url?scp=85051963708&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2018.08.003

DO - 10.1016/j.ipl.2018.08.003

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85051963708

SN - 0020-0190

VL - 140

SP - 30

EP - 33

JO - Information Processing Letters

JF - Information Processing Letters

ER -