Abstract
The Circuit constraint is useful to model many combinatorial problems in Constraint Programming. cp solvers extended with Belief Propagation, such as MiniCPBP, require that constraints be equipped with weighted counting algorithms in order to propagate probability mass functions over domains. This is not yet the case for Circuit. To this purpose we introduce a probabilistic sampling algorithm to count Hamiltonian circuits in a weighted graph. We show that our resulting estimator is unbiased, measure its empirical accuracy, and evaluate its impact on search performance.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Babaki, B., Omrani, B., Pesant, G.: Combinatorial search in CP-based iterated belief propagation. In: Simonis, H. (ed.) CP 2020. LNCS, vol. 12333, pp. 21–36. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58475-7_2
Benchimol, P., van Hoeve, W.J., Régin, J.C., Rousseau, L.M., Rueher, M.: Improved filtering for weighted circuit constraints. Constraints An Int. J. 17(3), 205–233 (2012). https://doi.org/10.1007/s10601-012-9119-x
Isoart, N., Régin, J.C.: A linear time algorithm for the k-cutset constraint. In: Michel, L.D. (ed.) 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), vol. 210, pp. 29:1–29:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Dagstuhl, Germany (2021). https://drops.dagstuhl.de/opus/volltexte/2021/15320
Pesant, G.: From support propagation to belief propagation in constraint programming. J. Artif. Intell. Res. 66, 123–150 (2019). https://doi.org/10.1613/jair.1.11487
Pesant, G., Gendreau, M., Potvin, J.Y., Rousseau, J.M.: An exact constraint logic programming algorithm for the traveling salesman problem with time windows. Transp. Sci. 32(1), 12–29 (1998). https://doi.org/10.1287/trsc.32.1.12
Rasmussen, L.E.: Approximating the permanent: a simple approach. Random Struct. Algorithms 5(2), 349–362 (1994). https://doi.org/10.1002/rsa.3240050208
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Pezzoli, G., Pesant, G. (2023). A Weighted Counting Algorithm for the Circuit Constraint. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_24
Download citation
DOI: https://doi.org/10.1007/978-3-031-33271-5_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-33270-8
Online ISBN: 978-3-031-33271-5
eBook Packages: Computer ScienceComputer Science (R0)