A Polynomially Searchable Exponential Neighbourhood for Graph Colouring
A Polynomially Searchable Exponential Neighbourhood for Graph Colouring
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. Key words: Graph colouring, Optimisation, Heuristics, Local search, Exponential neighbourhood.
324-330
Glass, Celia A.
4ae457e5-b653-49d7-8adb-1766901371cb
Prügel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e
March 2005
Glass, Celia A.
4ae457e5-b653-49d7-8adb-1766901371cb
Prügel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e
Glass, Celia A. and Prügel-Bennett, Adam
(2005)
A Polynomially Searchable Exponential Neighbourhood for Graph Colouring.
Journal of the Operational Research Society, 56 (3), .
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. Key words: Graph colouring, Optimisation, Heuristics, Local search, Exponential neighbourhood.
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Published date: March 2005
Organisations:
Southampton Wireless Group
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Local EPrints ID: 256036
URI: http://eprints.soton.ac.uk/id/eprint/256036
ISSN: 0160-5682
PURE UUID: 8c0f25d2-3555-4a45-85a1-f1659c1d653b
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Date deposited: 26 Sep 2001
Last modified: 14 Mar 2024 05:38
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Contributors
Author:
Celia A. Glass
Author:
Adam Prügel-Bennett
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