Reducing the Number of Useless Revisions Performed by Constraint Solvers Based on AC-3

Abstract

Maintaining arc-consistency during the search is one of the most widely used techniques in solving constraint satisfaction problems. Many algorithms have been developed in order to implement effectively arc-consistency, such as AC-3, AC-4, AC-6 or AC-7. While not as elaborate as others, AC-3 is simple to implement and proves to be efficient for many types of problems. In order to improve the overall performance of an AC-3 based solver it is essential to exploit any specific feature of the problem being solved. In this paper we describe a generic method to reduce the number of useless revisions performed by AC-3 based on the semantics of the constraints, as long as they provide custom information needed by our algorithm. Arithmetic constraints of the form ax + by ? c where x, y are variables of the constraint network, a,b,c are integer values and the operator ? ? {} fit naturally into this framework and AC3-OP becomes a particular case of our algorithm.