Maximum-weight stable sets and safe lower bounds for graph coloring

  • The best method known for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique, where variables correspond to stable sets, 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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Metadaten
Author:Stephan Held, William Cook, Edward C. Sewell
DOI:https://doi.org/10.1007/s12532-012-0042-3
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2012
Tag:Software; Theoretical Computer Science
Volume:4
Issue:4
Page Number:19
First Page:363
Last Page:381
Mathematical Programming Computation :MPC 2012 - Issue 4
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