A Polynomially Searchable Exponential Neighbourhood for Graph Colouring

Download

Postscript Download (217Kb)

Description/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.