A polynomially searchable exponential neighbourhood for graph colouring

A polynomially searchable exponential neighbourhood for graph colouring

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Article ID: iaor20062252
Country: United Kingdom
Volume: 56
Issue: 3
Start Page Number: 324
End Page Number: 330
Publication Date: Mar 2005
Journal: Journal of the Operational Research Society
Authors: ,
Keywords: graph colouring
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.

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