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Conjunctions of Among Constraints

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Principles and Practice of Constraint Programming (CP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10416))

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Abstract

Many existing global constraints can be encoded as a conjunction of among constraints. An among constraint holds if the number of the variables in its scope whose value belongs to a prespecified set, which we call its range, is within some given bounds. It is known that domain filtering algorithms can benefit from reasoning about the interaction of among constraints so that values can be filtered out taking into consideration several among constraints simultaneously. The present paper embarks into a systematic investigation on the circumstances under which it is possible to obtain efficient and complete domain filtering algorithms for conjunctions of among constraints. We start by observing that restrictions on both the scope and the range of the among constraints are necessary to obtain meaningful results. Then, we derive a domain flow-based filtering algorithm and present several applications. In particular, it is shown that the algorithm unifies and generalizes several previous existing results.

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Notes

  1. 1.

    We want to stress here that a global constraint is not a single constraint but, in fact, a family of them.

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Acknowledgments

The author would like to thank the anonymous referees for many useful comments. This work was supported by the MEIC under grant TIN2016-76573-C2-1-P and the MECD under grant PRX16/00266.

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  1. Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain

    Víctor Dalmau

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  1. Víctor Dalmau
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Correspondence to Víctor Dalmau .

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  1. University of Toronto, Toronto, Ontario, Canada

    J. Christopher Beck

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Dalmau, V. (2017). Conjunctions of Among Constraints. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-66158-2_6

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