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On the Approximability of the Vertex Cover and Related Problems

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Algorithmic Aspects in Information and Management (AAIM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6124))

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

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Zhejiang University of Finance & Economics, Hangzhou, Zhejiang, 310018, China

    Qiaoming Han

  2. Department of Mathematics, Simon Fraser University, 14th Floor Central City Tower, 13450 102nd Ave., Surrey, BC, V3T5X3, Canada

    Abraham P. Punnen

Authors
  1. Qiaoming Han
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  2. Abraham P. Punnen
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Editor information

Editors and Affiliations

  1. Warwick Business School/ DIMAP - Centre for Discrete Mathematics and its Applications Coventry, University of Warwick, CV4 7AL, UK

    Bo Chen

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Han, Q., Punnen, A.P. (2010). On the Approximability of the Vertex Cover and Related Problems. In: Chen, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2010. Lecture Notes in Computer Science, vol 6124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14355-7_17

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  • DOI: https://doi.org/10.1007/978-3-642-14355-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14354-0

  • Online ISBN: 978-3-642-14355-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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