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.
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Quimper, CG., López-Ortiz, A., van Beek, P., Golynski, A. (2004). Improved Algorithms for the Global Cardinality Constraint. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_40
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DOI: https://doi.org/10.1007/978-3-540-30201-8_40
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