SYMÉTRIES ET DOMINANCES DANS LES RÉSEAUX DE CONTRAINTES DE DIFFÉRENCE.

Abstract

Many practical problems (coloring maps, design of schedules, allocation of network re- sources ...) can be modeled by graphical problems of graphs that can express themselves by CSPs with constraints of difference (NECSPs). Although we currently have several methods to effec- tively solve problems of reasonable size, it remains only in theory, this problem is NP-complete, that is to say that all these techniques have an exponential complexity in the worst cases. There are still several ways to reduce this complexity, one of which is the elimination of symmetry. The detection of the symmetries of the problem during the search for solutions thus makes it possible not to consider certain redundant (symmetrical) cases where the search for solutions is doomed to failure. In this report, our work consists in making improvements for an exact algorithm in order to solve the graph coloring problem formalized in the form of NECSPs proposed in 2006 that is based on the detection and elimination of symmetries and dominance. The proposed heuristics improve the choice of the next variable to be affected. The results of the experiments are very encouraging.