Approximation algorithms for connected dominating sets

Sudipto Guha, Samir Khuller

Research output: Chapter in Book/Report/Conference proceedingConference contribution

100 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 either be in the dominating set, or adjacent to at least one node in the dominating set. We focus on the 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. This problem arises in network testing, as well as in wireless communication. Two polynomial time algorithms that achieve approximation factors of O(H(A)) are presented, where A 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 one of its neighbors visited. We study a generalization of the problem when the vertices have weights, and give an algorithm which achieves a performance ratio of 3 Inn. We also consider the more general problem of finding a connected dominating set of a specified set of vertices and provide a 3 Inn approximation factor. To prove the bound we also develop an optimal approximation algorithm for the unit node weighted Steiner tree problem.

Original languageEnglish (US)
Title of host publicationAlgorithms - ESA 1996 - 4th Annual European Symposium, Proceedings
EditorsJosep Diaz, Maria Serna
PublisherSpringer Verlag
Pages179-193
Number of pages15
ISBN (Print)3540616802, 9783540616801
DOIs
StatePublished - 1996
Event4th European Symposium on Algorithms, ESA 1996 - Barcelona, Spain
Duration: Sep 25 1996Sep 27 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1136
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th European Symposium on Algorithms, ESA 1996
CountrySpain
CityBarcelona
Period9/25/969/27/96

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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