Improved Algorithms for the Global Cardinality Constraint

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We study the global cardinality constraint (gcc) and propose an O(n1.5d) 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(n2d + n2.66) steps, detect if gcc is universal in constant time and prove that it is NP-Hard to maintain domain consistency on extended-GCC.

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