New lower bounds of constraint violations for over-constrained problems

Abstract. In recent years, many works have been carried out to solve over-constrained problems, and more speci cally the Maximal Constraint Satisfaction Problem (Max-CSP), where the goal is to minimize the number of constraint violations. Some lower bounds on this number of violations have been proposed in the literature. In this paper, we characterize the constraints that are ignored by the existing results, we propose new lower bounds which takes into account some of these ignored constraints and we show how these new bounds can be integrated into existing ones in order to improve the previous results. Our work also generalize the previous studies by dealing with any kind of constraints, as non binary constraints, or constraints with speci c ltering algorithms. Furthermore, in order to integrate these algorithms into any constraint solver, we suggest to represent a Max-CSP as a single global constraint. This constraint can be itself included into any set of constraint. In this way, anover-constrained part of a problem can be isolated from constraints that must be necessarily satis ed.