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Safe Lower Bounds for Graph Coloring

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Integer Programming and Combinatoral Optimization (IPCO 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6655))

Abstract

The best known method for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique first employed by Mehrotra and Trick in 1996. We present an implementation of the method that provides numerically safe results, independent of the floating-point accuracy of linear-programming software. Our work includes an improved branch-and-bound algorithm for maximum-weight stable sets and a parallel branch-and-price framework for graph coloring. Computational results are presented on a collection of standard test instances, including the unsolved challenge problems created by David S. Johnson in 1989.

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Author information

Authors and Affiliations

  1. University of Bonn, Germany

    Stephan Held

  2. Georgia Institute of Technology, USA

    William Cook

  3. Southern Illinois University Edwardsville, United States

    Edward C. Sewell

Authors
  1. Stephan Held
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  2. William Cook
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  3. Edward C. Sewell
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Editor information

Editors and Affiliations

  1. Mathematical Sciences Department, IBM T. J. Watson Research Center, 10598, Yorktown Heights, NY, USA

    Oktay Günlük

  2. Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600, Eindhoven, MB, The Netherlands

    Gerhard J. Woeginger

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© 2011 Springer-Verlag Berlin Heidelberg

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Held, S., Cook, W., Sewell, E.C. (2011). Safe Lower Bounds for Graph Coloring. In: Günlük, O., Woeginger, G.J. (eds) Integer Programming and Combinatoral Optimization. IPCO 2011. Lecture Notes in Computer Science, vol 6655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20807-2_21

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  • DOI: https://doi.org/10.1007/978-3-642-20807-2_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20806-5

  • Online ISBN: 978-3-642-20807-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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