Extending Generalized Arc Consistency

Abstract

Generalized arc consistency (GAC) is the most widely used local consistency in constraint programming. Several GAC algorithms for specific constraints, as well as generic algorithms that can be used on any constraint, have been proposed in the literature. Stronger local consistencies than GAC have also been studied but algorithms for such consistencies are generally considered too expensive. In this paper we propose an extension to the standard GAC algorithm GAC2001/3.1 that achieves a stronger local consistency than GAC by considering intersections of constraints. Importantly, the worst-case time complexity of the proposed algorithm, called GAC+, is higher than that of GAC2001/3.1 only by a factor e, where e is the number of constraints in the problem. Experimental results demonstrate that in many cases GAC+ can reduce the size of the search tree compared to GAC, resulting in improved cpu times. Also, in cases where there is no gain in search tree size, there is only a negligible overhead in cpu time.