A factor 2 approximation algorithm for the vertex cover P 3 problem

We consider the vertex cover P n ( VCP n ) problem, that is, the problem of finding a minimum weight set F ⊂ V such that the graph G [ V − F ] has no P n , where P n is a path with n vertices. The problem also has its application background. In this paper, we restrict our attention to the VCP 3 prob...

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Bibliographic Details
Published inInformation processing letters Vol. 111; no. 14; pp. 683 - 686
Main Authors Tu, Jianhua, Zhou, Wenli
Format Journal Article
LanguageEnglish
Published Elsevier B.V 31.07.2011
Subjects
Approximation algorithm
Combinatorial optimization
Vertex cover [formula omitted] problem
Vertex cover P n problem
Combinatorial optimization
Approximation algorithm
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ISSN0020-0190
1872-6119
DOI10.1016/j.ipl.2011.04.009

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Summary:We consider the vertex cover P n ( VCP n ) problem, that is, the problem of finding a minimum weight set F ⊂ V such that the graph G [ V − F ] has no P n , where P n is a path with n vertices. The problem also has its application background. In this paper, we restrict our attention to the VCP 3 problem and give a 2-approximation algorithm using the technique of layering. ► In the article we translate the camera layout problem into the vertex cover P n problem in graph theory. ► We first proved two important inequalities on the problem to show the main result. ► We designed an approximation algorithm to solve the vertex cover P 3 problem. ► We proved the performance factor of the algorithm is no more than 2.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2011.04.009