Enforcing Arc Consistency on Global Constraints by Solving Subproblems on the Fly

Abstract

Constraint networks are used more and more to solve combinatorial problems in real-life applications. As pointed out in [1], this success requires dealing with non-binary constraints, which are widely needed in real world constraint solvers. Since arc consistency is a fundamental piece of reasoning that seems to be of great help during search for solutions, it is important to have efficient arc consistency algorithms for non-binary constraints. In this paper, we propose a new instantiation of GAC-Schema [1] that achieves arc consistency on global constraints (sets of original constraints taken globally). This algorithm, which searches for supports on these global constraints by solving the corresponding subproblem on the fly, outperforms the previous available techniques, such as GAC-Schema and its instantiation to predicates. It can simultaneously take into account the multidirectionality of the global constraint, and take advantage of the knowledge of the constraints of the subproblem. Furthermore, we show on several experiments the interest of our approach for problem modelling.

This work has been partially financed by ILOG S.A. under research contract ILOG/LIRMM no. 980330.