A primal-dual approximation algorithm for the vertex cover P3 problem

Authors:
Jianhua Tu;Wenli Zhou
Affiliations:
School of Science, Beijing University of Chemical Technology, Beijing 100029, China;IBM Research - China, Beijing 100193, China
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

We introduce the vertex coverP"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 first show that the VCP"n problem is NP-hard for any integer n=2. Then we restrict our attention to the VCP"3 problem and give a 2-approximation algorithm using the primal-dual method.