ISSN : 1796-217X
Volume : 1    Issue : 2    Date : August 2006

Increasing the Efficiency of Graph Colouring Algorithms with a Representation Based on Vector
István Juhos and Jano I. van Hemert
Page(s): 24-33
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We introduce a novel representation for the graph colouring problem, called the Integer Merge
Model, which aims to reduce the time complexity of graph colouring algorithms. Moreover, this
model provides useful information to aid in the creation of heuristics that can make the colouring
process even faster. It also serves as a compact definition for the description of graph colouring
algorithms. To verify the potential of the model, we use it in the complete algorithm DSATUR, and in
two version of an incomplete approximation algorithm; an evolutionary algorithm and the same
evolutionary algorithm extended with guiding heuristics. Both theoretical and empirical results are
provided investigation is performed to show an increase in the efficiency of solving graph colouring
problems. Two problem suites were used for the empirical evidence: a set of practical problem
instances and a set of hard problem instances from the phase transition.

Index Terms
graph colouring, representation, node merging, colouring strategies, evolutionary algorithm,