Near-Optimal Dominating Sets via Random Sampling

A minimum dominating set (MDS) of a simple undirected graph G is a dominating set with the smallest possible cardinality among all dominating sets of G and the MDS problem represents the problem of finding the MDS in a given input graph. Motivated by the transportation, social and biological network...

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Published inAlgorithmic Aspects in Information and Management Vol. 9778; pp. 162 - 172
Main Author Nehéz, Martin
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2016
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Approximation Ratio
Discrete mathematics
Domination Number
Exact Algorithm
Minimum Cardinality
Time Complexity
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Abstract A minimum dominating set (MDS) of a simple undirected graph G is a dominating set with the smallest possible cardinality among all dominating sets of G and the MDS problem represents the problem of finding the MDS in a given input graph. Motivated by the transportation, social and biological networks from a control theory perspective, the main result of this paper is the assertion that a random sampling is usable to find a near-optimal dominating set in an arbitrary connected graph. Our result might be of significance in particular contexts where exact algorithms cannot be run, e.g. in distributed computation environments. Moreover, the analysis of the relationship between the time complexity and the approximation ratio of the corresponding sequential algorithm exposes the counterintuitive behavior.
AbstractList A minimum dominating set (MDS) of a simple undirected graph G is a dominating set with the smallest possible cardinality among all dominating sets of G and the MDS problem represents the problem of finding the MDS in a given input graph. Motivated by the transportation, social and biological networks from a control theory perspective, the main result of this paper is the assertion that a random sampling is usable to find a near-optimal dominating set in an arbitrary connected graph. Our result might be of significance in particular contexts where exact algorithms cannot be run, e.g. in distributed computation environments. Moreover, the analysis of the relationship between the time complexity and the approximation ratio of the corresponding sequential algorithm exposes the counterintuitive behavior.
Author Nehéz, Martin
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  organization: Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Bratislava, Slovak Republic
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Mauri, Giancarlo
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Snippet A minimum dominating set (MDS) of a simple undirected graph G is a dominating set with the smallest possible cardinality among all dominating sets of G and the...
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StartPage 162
SubjectTerms Approximation Ratio
Discrete mathematics
Domination Number
Exact Algorithm
Minimum Cardinality
Time Complexity
Title Near-Optimal Dominating Sets via Random Sampling
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