Multiset Ordering Constraints

Alan M. Frisch, Ian Miguel, Zeynep Kiziltan, Brahim Hnich, Toby Walsh

Abstract: We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement an efficient linear time algorithm for enforcing generalised arc consistency on such a multiset ordering constraint. Experimental results on several problem domains show considerable promise.