Abstract
We propose two algorithms achieving generalized arc consistency for the soft global cardinality constraint with variable-based violation and with value-based violation. They are based on graph theory and their complexity is \(O(\sqrt{n}m)\) where n is the number of variables and m is the sum of the cardinalities of the domains. They improve previous algorithms that ran respectively in O(n(m+nlog n)) and O((n+k)(m+nlog n)) where k is the cardinality of the union of the domains.
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Zanarini, A., Milano, M., Pesant, G. (2006). Improved Algorithm for the Soft Global Cardinality Constraint. In: Beck, J.C., Smith, B.M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2006. Lecture Notes in Computer Science, vol 3990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11757375_23
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DOI: https://doi.org/10.1007/11757375_23
Publisher Name: Springer, Berlin, Heidelberg
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