A Better Approximation Ratio for the Vertex Cover Problem

  • George Karakostas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)


We reduce the approximation factor for Vertex Cover to \(2 - \theta(\frac{1}{\sqrt{{\rm log} n}})\) (instead of the previous \(2- \theta(\frac{{\rm log log} n}{{\rm log}\ n})\), obtained by Bar-Yehuda and Even [3], and by Monien and Speckenmeyer[11]). The improvement of the vanishing factor comes as an application of the recent results of Arora, Rao, and Vazirani [2] that improved the approximation factor of the sparsest cut and balanced cut problems. In particular, we use the existence of two big and well-separated sets of nodes in the solution of the semidefinite relaxation for balanced cut, proven in [2]. We observe that a solution of the semidefinite relaxation for vertex cover, when strengthened with the triangle inequalities, can be transformed into a solution of a balanced cut problem, and therefore the existence of big well-separated sets in the sense of [2] translates into the existence of a big independent set.


Vertex Cover Approximation Factor Triangular Inequality Antipodal Point Vertex Cover Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • George Karakostas
    • 1
  1. 1.Department of Computing and SoftwareMcMaster University 

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