Fast Bound Consistency for the Global Cardinality Constraint

Abstract

We show an algorithm for bound consistency of global cardinality constraints, which runs in time $O(n+n')\phantom{}$ plus the time required to sort the assignment variables by range endpoints, where n is the number of assignment variables and n′ is the number of values in the union of their ranges. We thus offer a fast alternative to Régin’s arc consistency algorithm [6] which runs in time $O(n^{3/2}n')\phantom{}$ and space $O(n \cdot{} n')\phantom{}$. Our algorithm can also narrow the bounds for the number of occurrences of each value, which has not been done before.