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Vertex Cover Approximations on Random Graphs

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Experimental Algorithms (WEA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4525))

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Abstract

The vertex cover problem is a classical NP-complete problem for which the best worst-case approximation ratio is 2 − o(1). In this paper, we use a collection of simple graph transformations, each of which guarantees an approximation ratio of \(\frac{3}{2}\), to find approximate vertex covers for a large collection of randomly generated graphs. These reductions are extremely fast and even though they, by themselves are not guaranteed to find a vertex cover, we manage to find a \(\frac{3}{2}\)-approximate vertex cover for almost every single random graph we generate.

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Authors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Eyjolfur Asgeirsson

  2. Department of IEOR, Columbia University, New York, NY,  

    Cliff Stein

Authors
  1. Eyjolfur Asgeirsson
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  2. Cliff Stein
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Camil Demetrescu

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Asgeirsson, E., Stein, C. (2007). Vertex Cover Approximations on Random Graphs. In: Demetrescu, C. (eds) Experimental Algorithms. WEA 2007. Lecture Notes in Computer Science, vol 4525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72845-0_22

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  • DOI: https://doi.org/10.1007/978-3-540-72845-0_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72844-3

  • Online ISBN: 978-3-540-72845-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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