On the Approximability of the Vertex Cover and Related Problems

  • Qiaoming Han
  • Abraham P. Punnen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)


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 \(2-\frac{1}{1+\sigma}\), 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.


Approximation Algorithm Polynomial Time Vertex Cover Optimal Objective Function Active Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Qiaoming Han
    • 1
  • Abraham P. Punnen
    • 2
  1. 1.School of Mathematics and StatisticsZhejiang University of Finance & EconomicsHangzhouChina
  2. 2.Department of MathematicsSimon Fraser UniversitySurreyCanada

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