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A Better Approximation Ratio for the Vertex Cover Problem

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

Abstract

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.

Keywords

Vertex Cover Approximation Factor Triangular Inequality Antipodal Point Vertex Cover Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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