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Approximating maximum independent sets by excluding subgraphs

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SWAT 90 (SWAT 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 447))

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Abstract

An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known to \({\cal O}\)(n/(log n)2). We also obtain the same performance guarantee for graph coloring. The results can be combined into a surprisingly strong simultaneous performance guarantee for the clique and coloring problems.

The framework of subgraph excluding algorithms is presented. We survey the known approximation algorithms for the independent set (clique), coloring, and vertex cover problems and show how almost all fit into that framework. It is shown that among subgraph excluding algorithms, the ones presented achieve the optimal asymptotic performance guarantees.

Supported in part by National Science Foundation Grant number CCR-8902522

Supported in part by Center for Discrete Mathematics and Theoretical Computer Science fellowship

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Author information

Authors and Affiliations

  1. Department of Computer Science, New York University, 10012, New York, NY

    Ravi Boppana

  2. Department of Computer Science, Rutgers University, 08903, New Brunswick, NJ

    Ravi Boppana & Magnús M. Halldórsson

Authors
  1. Ravi Boppana
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  2. Magnús M. Halldórsson
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John R. Gilbert Rolf Karlsson

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© 1990 Springer-Verlag Berlin Heidelberg

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Boppana, R., Halldórsson, M.M. (1990). Approximating maximum independent sets by excluding subgraphs. In: Gilbert, J.R., Karlsson, R. (eds) SWAT 90. SWAT 1990. Lecture Notes in Computer Science, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52846-6_74

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  • DOI: https://doi.org/10.1007/3-540-52846-6_74

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52846-3

  • Online ISBN: 978-3-540-47164-6

  • eBook Packages: Springer Book Archive

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