Filtering Algorithms For The Same Constraint

We define the Same and UsedBy constraints. UsedBy takes two sets of variables X and Z such that \X\ greater than or equal to \Z\ and assigns values to them such that the multiset of values assigned to the variables in Z is contained in the multiset of values assigned to the variables in X. Same is the special case of UsedBy in which \X\ = \Z\. In this paper we show algorithms that achieve arc consistency and bound consistency for the Same constraint and in its extended version we generalize them for the UsedBy constraint.