Abstract
Cardinality matrix problems are the underlying structure of several real world problems such as rostering, sports scheduling , and timetabling. These are hard computational problems given their inherent combinatorial structure. Constraint based approaches have been shown to outperform other approaches for solving these problems. In this paper we propose the cardinality matrix constraint, a specialized global constraint for cardinality matrix problems. The cardinality matrix constraint takes advantage of the intrinsic structure of the cardinality matrix problems. It uses a global cardinality constraint per row and per column and one cardinality (0,1)-matrix constraint per symbol. This latter constraint corresponds to solving a special case of a network flow problem, the transportation problem, which effectively captures the interactions between rows, columns, and symbols of cardinality matrix problems. Our results show that the cardinality matrix constraint outperforms standard constraint based formulations of cardinality matrix problems.
Supported by the Intelligent Information Systems Institute, Cornell University (AFOSR grant F49620-01-1-0076) and EOARD grant FA8655-03-1-3022.
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Régin, JC., Gomes, C.P. (2004). The Cardinality Matrix 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_42
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DOI: https://doi.org/10.1007/978-3-540-30201-8_42
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