The Ordered Distribute Constraint

In this paper we introduce a new cardinality constraint: Ordered Distribute. Given a set of variables, this constraint limits for each value v the number of times v or any value greater than v is taken. It extends the global cardinality constraint, that constrains only the number of times a value v is taken by a set of variables and does not consider at the same time the occurrences of all the values greater than v. We design an algorithm for achieving generalized arc-consistency on Ordered Distribute, with a time complexity linear in the sum of the number of variables and the number of values in the union of their domains. In addition, we give some experiments showing the advantage of this new constraint for problems where values represent levels whose overrunning has to be under control. Finally, we present three extensions of our constraint that can be particularly useful in practice.