Abstract
In Constraint Programming (CP), Generalized Arc Consistency (GAC) is the central property used for making inferences when solving Constraint Satisfaction Problems (CSPs). Developing simple and practical filtering algorithms based on consistencies stronger than GAC is a challenge for the CP community. In this paper, we propose to combine k-Wise Consistency (kWC) with GAC, where kWC states that every tuple in a constraint can be extended to every set of k − 1 additional constraints. Our contribution is as follows. First, we derive a domain-filtering consistency, called Domain k-Wise Consistency (DkWC), from the combination of kWC and GAC. Roughly speaking, this property corresponds to the pruning of values of GAC, when enforced on a CSP previously made kWC. Second, we propose a procedure to enforce DkWC, relying on an encoding of kWC to generate a modified CSP called k-interleaved CSP. Formally, we prove that enforcing GAC on the k-interleaved CSP corresponds to enforcing DkWC on the initial CSP. Consequently, we show that the strong DkWC can be enforced very easily in constraint solvers since the k-interleaved CSP is rather immediate to generate and only existing GAC propagators are required: in a nutshell, DkWC is made as simple and practical as GAC. Our experimental results show the benefits of our approach on a variety of benchmarks.
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References
Bessiere, C.: Constraint propagation. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming. Elsevier, New York (2006)
Bessière, C., Régin, J.-C.: Enforcing arc consistency on global constraints by solving subproblems on the fly. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 103–117. Springer, Heidelberg (1999)
Bessiere, C., Stergiou, K., Walsh, T.: Domain filtering consistencies for non-binary constraints. Artificial Intelligence 72(6-7), 800–822 (2008)
Debruyne, R., Bessière, C.: Domain filtering consistencies. Journal of Artificial Intelligence Research 14, 205–230 (2001)
Fleming, P., Wallace, J.: How not to lie with statistics: the correct way to summarize benchmark results. Communications of the ACM 29(3), 218–221 (1986)
Janssen, P., Jégou, P., Nouguier, B., Vilarem, M.-C.: A filtering process for general constraint-satisfaction problems: achieving pairwise-consistency using an associated binary representation. In: Proceedings of IEEE Workshop on Tools for Artificial Intelligence, pp. 420–427 (1989)
Jégou, P.: Contribution à l’étude des Problèmes de Satisfaction de Contraintes: Algorithmes de propagation et de résolution. Propagation de contraintes dans les réseaux dynamique. PhD thesis, Université de Montpellier II (1991)
Karakashian, S., Woodward, R., Reeson, C., Choueiry, B., Bessiere, C.: A first practical algorithm for high levels of relational consistency. In: Proceedings of AAAI 2010, pp. 101–107 (2010)
Lecoutre, C.: Instances of the Constraint Solver Competition, http://www.cril.fr/~lecoutre/
Lecoutre, C.: Constraint Networks: Techniques and Algorithms. ISTE/Wiley (2009)
Lecoutre, C., Paparrizou, A., Stergiou, K.: Extending STR to a higher-order consistency. In: Proceedings of AAAI 2013, pp. 576–582 (2013)
Lhomme, O.: Practical reformulations with table constraints. In: Proceedings of ECAI 2012, pp. 911–912 (2012)
Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8(1), 99–118 (1977)
Mairy, J.-B., Van Hentenryck, P., Deville, Y.: An optimal filtering algorithm for table constraints. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 496–511. Springer, Heidelberg (2012)
Paparrizou, A., Stergiou, K.: An efficient higher-order consistency algorithm for table constraints. In: Proceedings of AAAI 2012, pp. 335–541 (2012)
Stergiou, K.: Strong inverse consistencies for non-binary CSPs. In: Proceedings of ICTAI 2007, pp. 215–222 (2007)
Stergiou, K.: Strong domain filtering consistencies for non-binary constraint satisfaction problems. International Journal on Artificial Intelligence Tools 17(5), 781–802 (2008)
van Dongen, M., Lecoutre, C., Roussel, O.: CSP solver competition (2008), http://www.cril.univ-artois.fr/CPAI08/
Vion, J., Petit, T., Jussien, N.: Integrating strong local consistencies into constraint solvers. In: Larrosa, J., O’Sullivan, B. (eds.) CSCLP 2009. LNCS (LNAI), vol. 6384, pp. 90–104. Springer, Heidelberg (2011)
Woodward, R., Karakashian, S., Choueiry, B., Bessiere, C.: Solving difficult CSPs with relational neighborhood inverse consistency. In: Proceedings of AAAI 2011, pp. 112–119 (2011)
Xu, K., Boussemart, F., Hemery, F., Lecoutre, C.: Random constraint satisfaction: easy generation of hard (satisfiable) instances. Artificial Intelligence 171(8-9), 514–534 (2007)
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Mairy, JB., Deville, Y., Lecoutre, C. (2014). Domain k-Wise Consistency Made as Simple as Generalized Arc Consistency. In: Simonis, H. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2014. Lecture Notes in Computer Science, vol 8451. Springer, Cham. https://doi.org/10.1007/978-3-319-07046-9_17
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DOI: https://doi.org/10.1007/978-3-319-07046-9_17
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