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Solution counting algorithms for constraint-centered search heuristics

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Abstract

Constraints have played a central role in cp because they capture key substructures of a problem and efficiently exploit them to boost inference. This paper intends to do the same thing for search, proposing constraint-centered heuristics which guide the exploration of the search space toward areas that are likely to contain a high number of solutions. We first propose new search heuristics based on solution counting information at the level of individual constraints. We then describe efficient algorithms to evaluate the number of solutions of two important families of constraints: occurrence counting constraints, such as alldifferent, and sequencing constraints, such as regular. In both cases we take advantage of existing filtering algorithms to speed up the evaluation. Experimental results on benchmark problems show the effectiveness of our approach.

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Authors and Affiliations

  1. Department of Computer and Software Engineering, École Polytechnique de Montréal, C.P. 6079, succ. Centre-ville, Montreal, Canada

    Alessandro Zanarini & Gilles Pesant

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  1. Alessandro Zanarini
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  2. Gilles Pesant
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Correspondence to Alessandro Zanarini.

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An earlier version of this paper appeared as [24].

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Zanarini, A., Pesant, G. Solution counting algorithms for constraint-centered search heuristics. Constraints 14, 392–413 (2009). https://doi.org/10.1007/s10601-008-9065-9

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