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A polynomially searchable exponential neighbourhood for graph colouring

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  • C A Glass

    (City University)

  • A Prügel-Bennett

    (University of Southampton)

Abstract

In this paper, we develop a new graph colouring strategy. Our heuristic is an example of a so-called polynomially searchable exponential neighbourhood approach. The neighbourhood is that of permutations of the colours of vertices of a subgraph. Our approach provides a solution method for colouring problems with edge weights. Results for initial tests on unweighted K-colouring benchmark problems are presented. Our colour permutation move was found in practice to be too slow to justify its use on these problems. By contrast, our implementation of iterative descent, which incorporates a permutation kickback move, performed extremely well. Moreover, our approach may yet prove valuable for weighted K-colouring. In addition, our approach offers an improved measure of the distance between colourings of a graph.

Suggested Citation

  • C A Glass & A Prügel-Bennett, 2005. "A polynomially searchable exponential neighbourhood for graph colouring," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 324-330, March.
    • Handle: RePEc:pal:jorsoc:v:56:y:2005:i:3:d:10.1057_palgrave.jors.2601815
    DOI: 10.1057/palgrave.jors.2601815
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    References listed on IDEAS

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    1. David S. Johnson & Cecilia R. Aragon & Lyle A. McGeoch & Catherine Schevon, 1991. "Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning," Operations Research, INFORMS, vol. 39(3), pages 378-406, June.
    2. Richard K. Congram & Chris N. Potts & Steef L. van de Velde, 2002. "An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 52-67, February.
    3. Philippe Galinier & Jin-Kao Hao, 1999. "Hybrid Evolutionary Algorithms for Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 379-397, December.
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    Cited by:

    1. M Plumettaz & D Schindl & N Zufferey, 2010. "Ant Local Search and its efficient adaptation to graph colouring," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 819-826, May.

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