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Communication Dans Un Congrès Année : 2019

Estimating the Number of Solutions of Cardinality Constraints through range and roots Decompositions

Résumé

This paper introduces a systematic approach for estimating the number of solutions of cardinality constraints. A main difficulty of solutions counting on a specific constraint lies in the fact that it is, in general, at least as hard as developing the constraint and its propaga-tors, as it has been shown on alldifferent and gcc constraints. This paper introduces a probabilistic model to systematically estimate the number of solutions on a large family of cardinality constraints including alldifferent, nvalue, atmost, etc. Our approach is based on their decomposition into range and roots, and exhibits a general pattern to derive such estimates based on the edge density of the associated variable-value graph. Our theoretical result is finally implemented within the maxSD search heuristic, that aims at exploring first the area where there are likely more solutions.
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Dates et versions

hal-02276566 , version 1 (06-12-2019)

Identifiants

Citer

Giovanni Lo Bianco, Xavier Lorca, Charlotte Truchet. Estimating the Number of Solutions of Cardinality Constraints through range and roots Decompositions. CP 2019-25th International Conference on Principles and Practice of Constraint Programming, Sep 2019, Stamford, United States. p. 317-332, ⟨10.1007/978-3-030-30048-7_19⟩. ⟨hal-02276566⟩
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