Filtering Algorithms for the Same and UsedBy Constraints
Nicolas Beldiceanu, Irit Katriel, Sven Thiel · 2004
We define the \Same\ and \UsedBy\ constraints. \UsedBy\ takes two sets of variables $X$ and $Z$ such that $|X|\ge |Z|$ 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.