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Solution sampling with random table constraints

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A Correction to this article was published on 07 September 2023

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Abstract

Constraint programming provides generic techniques to efficiently solve combinatorial problems. In this paper, we tackle the natural question of using constraint solvers to sample combinatorial problems in a generic way. We propose an algorithm, inspired from Meel’s ApproxMC algorithm on SAT, to add hashing constraints to a CP model in order to split the search space into small cells. By uniformly sampling the solutions in one cell, we can generate random solutions without revamping the model of the problem. We ensure the randomness by introducing a new family of hashing constraints: randomly generated tables, which keeps the cost of the hashing process tractable. We implemented this solving method using the constraint solver Choco-solver. The quality of the randomness and the running time of our approach are experimentally compared to a random branching strategy. We show that our approach improves the randomness while being in the same order of magnitude in terms of running time. We also use our algorithm with an other, more powerful, set of hashing constraints: linear modular equalities. We experimentally show that the resulting sampling is uniform, at the cost of a longer running time.

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Notes

  1. https://github.com/MathieuVavrille/tableSampling

  2. https://github.com/PesantGilles/MiniCPBP

  3. https://github.com/MiniZinc/minizinc-benchmarks/tree/master/on-call-rostering

  4. We use the library “Apache Commons Mathematics Library” (https://commons.apache.org/proper/commons-math/) for the probability computations

  5. https://www.minizinc.org/challenge.html

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Acknowledgements

This article is an extended version of a conference paper: Solution sampling with random table constraints, Mathieu Vavrille, Charlotte Truchet, Charles Prud’homme, Proceedings of CP 2021, 56:1-56:17. This work was presented at the conference on October 2021: https://cp2021.lirmm.fr/submissions/74. Compared to the conference article, this version has been extended with the implementation of another series of hashing constraints, proposed in [8], inside the framework, more extensive experiments on a wider benchmark, and a more thorough analysis of the results and algorithm behaviour.

Funding

Partial financial support was received from the French National Research Agency as part of the DeCrypt project (ANR-18-CE39-0007) for two of the authors (Prud’homme and Truchet).

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Author notes

  1. Charlotte Truchet and Charles Prud’homme contributed equally to this work.

Authors and Affiliations

  1. Laboratoire des Sciences du Numérique de Nantes, 2 Chemin de la Houssinière, Nantes, 44322, France

    Mathieu Vavrille & Charlotte Truchet

  2. TASC, IMT-Atlantique, LS2N-CNRS, 4 rue Alfred Kastler, Nantes, 44307, France

    Charles Prud’homme

Authors
  1. Mathieu Vavrille
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  2. Charlotte Truchet
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  3. Charles Prud’homme
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Corresponding author

Correspondence to Mathieu Vavrille.

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Competing interest

Apart from the project mentioned above, the authors have no other competing interests to declare that are relevant to the content of this article.

Additional information

The original online version of this article was revised: The main results of the article remains unchanged, but we misinterpreted a figure. The mistake is on the analysis of Figure 6a, the figure itself is correct, but we did not analyze it correctly.

Raw results of the MiniZinc benchmark

Raw results of the MiniZinc benchmark

This appendix presents in Table 1 the computation results.

Table 1 First table of raw results
Full size table

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Vavrille, M., Truchet, C. & Prud’homme, C. Solution sampling with random table constraints. Constraints 27, 381–413 (2022). https://doi.org/10.1007/s10601-022-09329-w

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