Disjoint, partition and intersection constraints for set and multiset variables

Abstract

We have started a systematic study of global constraints on set and multiset variables. We consider here disjoint, partition, and intersection constraints in conjunction with cardinality constraints. These global constraints fall into one of three classes. In the first class, we show that we can decompose the constraint without hindering bound consistency. No new algorithms therefore need be developed for such constraints. In the second class, we show that decomposition hinders bound consistency but we can present efficient polynomial algorithms for enforcing bound consistency. Many of these algorithms exploit a dual viewpoint, and call upon existing global constraints for finite-domain variables like the global cardinality constraint. In the third class, we show that enforcing bound consistency is NP-hard. We have little choice therefore but to enforce a lesser level of local consistency when the size of such constraints grows. © Springer-Verlag Berlin Heidelberg 2004.