Fast Bound Consistency for the Global Cardinality Constraint

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 Regin's arc consistency algorithm [6] which runs in time O(n(3/2) n') 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.