A randomized algorithm for determining dominating sets in graphs of maximum degree five

Authors:
Soheir M. Khamis;Sameh S. Daoud;Hanaa A. E. Essa
Affiliations:
Division of Computer Science, Department of Math., Faculty of Science, Ain Shams University, Cairo, Egypt;Division of Computer Science, Department of Math., Faculty of Science, Ain Shams University, Cairo, Egypt;Department of Math., Faculty of Science, Tanta University, Tanta, Egypt
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

The paper is devoted to demonstrating a randomized algorithm for determining a dominating set in a given graph having a maximum degree of five. The algorithm follows the Las Vegas technique. Furthermore, the concept of a 2-separated collection of subsets of vertices in graphs is used. The suggested algorithm is based on a condition of the upper bound of the cardinality of a local dominating set. If the condition is not satisfied, then the algorithm halts with an appropriate message. Otherwise, the algorithm determines the dominating set. The given algorithm is considered a polynomial-time approximation one.