Improved algorithms for the global cardinality constraint

Abstract. We study the global cardinality constraint (gcc) and propose an O(n 1.5 d) algorithm for domain consistency and an O(cn + dn) algorithm for range consistency, where n is the number of variables, d the number of values in the domain, and c an output dependent variable smaller than or equal to n. We show how to prune the cardinality variables in O(n 2 d + n 2.66) steps, detect if gcc is universal in constant time and prove that it is NP-Hard to maintain domain consistency on extended-GCC.