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(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.