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Solution Sampling with Random Table Constraints

Authors Mathieu Vavrille, Charlotte Truchet, Charles Prud'homme

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Mathieu Vavrille
  • Laboratoire des Sciences du Numérique de Nantes, 44322 Nantes, France
Charlotte Truchet
  • Laboratoire des Sciences du Numérique de Nantes, 44322 Nantes, France
Charles Prud'homme
  • TASC, IMT-Atlantique, LS2N-CNRS, F-44307 Nantes, France

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Mathieu Vavrille, Charlotte Truchet, and Charles Prud'homme. Solution Sampling with Random Table Constraints. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 56:1-56:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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 of solutions. By sampling the solutions in the restricted search space, we can randomly generate solutions without revamping the model of the problem. We ensure the randomness by introducing a new family of hashing constraints: randomly generated tables. 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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Randomized search
  • solutions
  • sampling
  • table constraint


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  1. Jérôme Amilhastre, Hélène Fargier, and Pierre Marquis. Consistency restoration and explanations in dynamic csps—application to configuration. Artificial Intelligence, 135(1-2):199-234, 2002. Google Scholar
  2. Eric Bach. Realistic analysis of some randomized algorithms. In Proceedings of the nineteenth annual ACM symposium on Theory of computing, pages 453-461, 1987. Google Scholar
  3. Frédéric Boussemart, Fred Hemery, Christophe Lecoutre, and Lakhdar Sais. Boosting systematic search by weighting constraints. In ECAI, volume 16, page 146, 2004. Google Scholar
  4. Rina Dechter, Kalev Kask, Eyal Bin, Roy Emek, et al. Generating random solutions for constraint satisfaction problems. In AAAI/IAAI, pages 15-21, 2002. Google Scholar
  5. Jordan Demeulenaere, Renaud Hartert, Christophe Lecoutre, Guillaume Perez, Laurent Perron, Jean-Charles Régin, and Pierre Schaus. Compact-table: efficiently filtering table constraints with reversible sparse bit-sets. In International Conference on Principles and Practice of Constraint Programming, pages 207-223. Springer, 2016. Google Scholar
  6. Stefano Ermon, Carla P Gomes, and Bart Selman. Uniform solution sampling using a constraint solver as an oracle. arXiv preprint, 2012. URL:
  7. Vibhav Gogate and Rina Dechter. A new algorithm for sampling csp solutions uniformly at random. In International Conference on Principles and Practice of Constraint Programming, pages 711-715. Springer, 2006. Google Scholar
  8. Renaud Hartert and Pierre Schaus. A support-based algorithm for the bi-objective pareto constraint. In Carla E. Brodley and Peter Stone, editors, Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, July 27 -31, 2014, Québec City, Québec, Canada, pages 2674-2679. AAAI Press, 2014. URL:
  9. E. Hebrard. Robust Solutions for Constraint Satisfaction and Optimisation under Uncertainty. PhD thesis, University of New South Wales, 2006. Google Scholar
  10. Emmanuel Hebrard, Brahim Hnich, Barry O'Sullivan, and Toby Walsh. Finding diverse and similar solutions in constraint programming. In AAAI, volume 5, pages 372-377, 2005. Google Scholar
  11. Donald E Knuth. Art of computer programming, volume 2: Seminumerical algorithms. Addison-Wesley Professional, 2014. Google Scholar
  12. Christophe Lecoutre, Lakhdar Sais, Sébastien Tabary, and Vincent Vidal. Last conflict based reasoning. In Gerhard Brewka, Silvia Coradeschi, Anna Perini, and Paolo Traverso, editors, ECAI 2006, 17th European Conference on Artificial Intelligence, August 29 - September 1, 2006, Riva del Garda, Italy, Including Prestigious Applications of Intelligent Systems (PAIS 2006), Proceedings, volume 141 of Frontiers in Artificial Intelligence and Applications, pages 133-137. IOS Press, 2006. URL:
  13. Kuldeep S Meel. Constrained counting and sampling: bridging the gap between theory and practice. arXiv preprint, 2018. URL:
  14. Karl Pearson. X. on the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 50(302):157-175, 1900. Google Scholar
  15. Gilles Pesant, Kuldeep S. Meel, and Mahshid Mohammadalitajrishi. On the usefulness of linear modular arithmetic in constraint programming. In Integration of Constraint Programming, Artificial Intelligence, and Operations Research - 18th International Conference, CPAIOR 2021, Vienna, Austria, September 21-24, 2021, Proceedings, Lecture Notes in Computer Science. Springer, 2021. Google Scholar
  16. Charles Prud'homme, Jean-Guillaume Fages, and Xavier Lorca. Choco Solver Documentation. TASC, INRIA Rennes, LINA CNRS UMR 6241, COSLING S.A.S., 2016. URL:
  17. Björn Regnell and Krzysztof Kuchcinski. Exploring software product management decision problems with constraint solving-opportunities for prioritization and release planning. In 2011 Fifth International Workshop on Software Product Management (IWSPM), pages 47-56. IEEE, 2011. Google Scholar
  18. Francesca Rossi, Kristen Brent Venable, and Toby Walsh. Preferences in constraint satisfaction and optimization. AI Mag., 29(4):58-68, 2008. URL:
  19. Günther Ruhe and Moshood Omolade Saliu. The art and science of software release planning. IEEE software, 22(6):47-53, 2005. Google Scholar
  20. Yevgeny Schreiber. Value-ordering heuristics: Search performance vs. solution diversity. In International Conference on Principles and Practice of Constraint Programming, pages 429-444. Springer, 2010. Google Scholar
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