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') 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(n3/2n') and space O(n · n'). Our algorithm can also narrow the bounds for the number of occurrences of each value, which has not been done before. © Springer-Verlag 2003.