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

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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(kln⁡k), improving the ratio O(k2ln⁡k) of [1,2]. For general graphs we obtain the first non-trivial approximation ratio O(k2ln⁡n).

Original languageEnglish
Pages (from-to)30-33
Number of pages4
JournalInformation Processing Letters
StatePublished - Dec 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.


  • Approximation algorithm
  • k-Connected graph
  • m-Dominating set


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