A Parallel Algorithm for GAC Filtering of the Alldifferent Constraint

Wijnand Suijlen, Félix de Framond, Arnaud Lallouet, Antoine Petitet

Abstract: In constraint programming the Alldifferent constraint is one of the oldest and most used global constraints. The algorithm by Régin enforces generalized arc-consistency, which is the strongest level of consistency for a single constraint. It is also the most time consuming despite several optimizations that were developed by others. This paper parallelizes the Alldifferent generalized arc-consistent filtering algorithm, which is one of the first attempts for any global constraint. It does so by using a parallel graph search algorithm for two major parts of Régin’s algorithm: finding a maximum matching and finding the strongly connected components. Most effective known optimizations are also ported. Experiments solving a large N-queens problem or a resource constrained scheduling problem show that generalized arc-consistent filtering can be significantly sped-up on a 64-core shared-memory system and on a 200-core distributed-memory system. We discuss also several scenarios where this algorithm should be applied or not.