Approximation algorithms for connected dominating sets

S. Guha*, Samir Khuller

*Corresponding author for this work

Research output: Contribution to journalArticle

826 Scopus citations

Abstract

The dominating set problem in graphs asks for a minimum size subset of vertices with the following property: each vertex is required to be either in the dominating set, or adjacent to some vertex in the dominating set. We focus on the related question of finding a connected dominating set of minimum size, where the graph induced by vertices in the dominating set is required to be connected as well. This problem arises in network testing, as well as in wireless communication. Two polynomial time algorithms that achieve approximation factors of 2H(Δ) + 2 and H(Δ) + 2 are presented, where Δ is the maximum degree and H is the harmonic function. This question also arises in relation to the traveling tourist problem, where one is looking for the shortest tour such that each vertex is either visited or has at least one of its neighbors visited. We also consider a generalization of the problem to the weighted case, and give an algorithm with an approximation factor of (cn + 1) ln n where cn ln k is the approximation factor for the node weighted Steiner tree problem (currently cn = 1.6103). We also consider the more general problem of finding a connected dominating set of a specified subset of vertices and provide a polynomial time algorithm with a (c + 1)H(Δ) + c - 1 approximation factor, where c is the Steiner approximation ratio for graphs (currently c = 1.644).

Original languageEnglish (US)
Pages (from-to)374-387
Number of pages14
JournalAlgorithmica (New York)
Volume20
Issue number4
DOIs
StatePublished - Jan 1 1998

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Keywords

  • Approximation algorithms
  • Dominating sets
  • Graph algorithms
  • Steiner trees

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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