Filtering Algorithms for the Same and UsedBy Constraints

We define the Same and UsedBy constraints. UsedBy takes two sets of variables X and Z such that X 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. We show algorithms that achieve arc-consistency and bound- consistency for these constraints.