Approximation algorithm for minimum connected 3-path vertex cover

Abstract A vertex subset S of a given graph G = ( V , E ) is called a connected k -path vertex cover (CVCP k ) if every k -path of G contains at least one vertex from S , and the subgraph of G induced by S is connected. This concept has its background in the field of security and supervisory and the computation of a minimum CVCP k is NP-hard. In this paper, we give a ( 2 α + 1 ∕ 2 )-approximation algorithm for MinCVCP 3 , where α is the performance ratio of an algorithm for MinVCP 3 .

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