On Importance of a Special Sorting in the Maximum-Weight Clique Algorithm Based on Colour Classes

In this paper a new sorting strategy is proposed to be used in the maximum weight clique finding algorithm, which is known to be the fastest at the moment. It is based on colour classes, i.e. on heuristic colouring that is used to prune efficiently branches by excluding from the calculation formulae vertices of the same colours. That is why the right ordering before colouring is so crucial before executing the heuristic colouring and consequently the main maximum weight clique searching routine. Computational experiments with random graphs were conducted and have shown a sufficient increase of performance considering the type of application dealt with in the article.