On the approximability of the vertex cover and related problems

Authors:
Qiaoming Han;Abraham P. Punnen
Affiliations:
School of Mathematics and Statistics, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang, China;Department of Mathematics, Simon Fraser University, Surrey, BC, Canada
Venue:
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Year:
2010

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Abstract

In this paper we show that the problem of identifying an edge (i, j) in a graph G such that there exists an optimal vertex cover S of G containing exactly one of the nodes i and j is NP-hard. Such an edge is called a weak edge. We then develop a polynomial time approximation algorithm for the vertex cover problem with performance guarantee 2 - 1/1+σ, where σ is an upper bound on a measure related to a weak edge of a graph. Further, we discuss a new relaxation of the vertex cover problem which is used in our approximation algorithm to obtain smaller values of σ.