Abstract
We address the problem of verifying a constraint by a set of solutions S. This problem is present in almost all systems aiming at learning or acquiring constraints or constraint parameters. We propose an original approach based on MDDs. Indeed, the set of solutions can be represented by the MDD denoted by \(MDD_S\). Checking whether S satisfies a given constraint C can be done using MDD(C), the MDD that contains the set of solutions of C, and by searching if the intersection between MDD(S) and MDD(C) is equal to MDD(S). This step is equivalent to searching whether MDD(S) is included in MDD(C). Thus, we give an inclusion algorithm to speed up these calculations. Then, we generalize this approach for the computation of global constraint parameters satisfying C. Next, we introduce the notion of properties on the MDD nodes and define a new algorithm allowing to compute in only one step the set of parameters we are looking for. Finally, we present experimental results showing the interest of our approach.
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Notes
- 1.
Unlike Perez and Régin [9], the complementary of an MDD M is computed by making the difference between the universal MDD and M. This avoids the need of a dedicated algorithm.
- 2.
We could also perform the intersection between MDD(S) and the negation of MDD(C) and check whether it is empty or not. However the computation of the negation is required so it does not improve the classical intersection.
References
Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. J. Math. Comput. Modell. 20(12), 97–123 (1994)
Beldiceanu, N., Simonis, H.: A constraint seeker: finding and ranking global constraints from examples. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 12–26. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23786-7_4
Bergman, D., Ciré, A.A., van Hoeve, W., Hooker, J.N.: Decision Diagrams for Optimization. Artificial Intelligence: Foundations, Theory, and Algorithms. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-319-42849-9
Bessière, C., Coletta, R., Petit, T.: Learning implied global constraints. In: IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, 6–12 January 2007, pp. 44–49 (2007)
Bryant, R.E.: Graph-based algorithms for boolean function manipulation 35(8), 677–691 (1986)
Hoda, S., van Hoeve, W.-J., Hooker, J.N.: A systematic approach to MDD-based constraint programming. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 266–280. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15396-9_23
Kam, T., Brayton, R.K.: Multi-valued decision diagrams. Technical report UCB/ERL M90/125, EECS Department, University of California, Berkeley, December 1990. http://www2.eecs.berkeley.edu/Pubs/TechRpts/1990/1671.html
Leo, K., Mears, C., Tack, G., Garcia de la Banda, M.: Globalizing constraint models. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 432–447. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40627-0_34
Perez, G., Régin, J.C.: Efficient operations on MDDs for building constraint programming models. In: International Joint Conference on Artificial Intelligence, IJCAI-15, Argentina, pp. 374–380 (2015)
Perez, G.: Decision diagrams: constraints and algorithms. Ph.D. thesis, Université Nice Sophia Antipolis (2017)
Picard-Cantin, É., Bouchard, M., Quimper, C.-G., Sweeney, J.: Learning parameters for the sequence constraint from solutions. In: Rueher, M. (ed.) CP 2016. LNCS, vol. 9892, pp. 405–420. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44953-1_26
Picard-Cantin, É., Bouchard, M., Quimper, C.-G., Sweeney, J.: Learning the parameters of global constraints using branch-and-bound. In: Beck, J.C. (ed.) CP 2017. LNCS, vol. 10416, pp. 512–528. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66158-2_33
Srinivasan, A., Ham, T., Malik, S., Brayton, R.K.: Algorithms for discrete function manipulation. In: 1990 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers, pp. 92–95 (1990). https://doi.org/10.1109/ICCAD.1990.129849
Acknowledgments
This work has been supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002.
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Jung, V., Régin, JC. (2021). Checking Constraint Satisfaction. In: Stuckey, P.J. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2021. Lecture Notes in Computer Science(), vol 12735. Springer, Cham. https://doi.org/10.1007/978-3-030-78230-6_21
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