Near-Optimal Dominating Sets via Random Sampling

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9778)

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.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Information Engineering, Automation and Mathematics, Faculty of Chemical and Food TechnologySlovak University of Technology in BratislavaBratislavaSlovak Republic

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