Abstract
Non-binary constraints are present in many real-world constraint satisfaction problems. Certain classes of these constraints, like the all-different constraint, are “decomposable”. That is, they can be represented by binary constraints on the same set of variables. For example, a non-binary all-different constraint can be decomposed into a clique of binary not-equals constraints. In this paper we make a theoretical analysis of local consistency and search algorithms for decomposable constraints. First, we prove a new lower bound for the worst-case time complexity of arc consistency on binary not-equals constraints. We show that the complexity is O(e), where e is the number of constraints, instead of O(ed), with d being the domain size, as previously known. Then, we compare theoretically local consistency and search algorithms that operate on the non-binary representation of decomposable constraints to their counterparts for the binary decomposition. We also extend previous results on arc consistency algorithms to the case of singleton arc consistency.
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References
C. Bessière, P. Meseguer, E. Freuder, and J. Larrosa. On forward checking for non-binary constraint satisfaction. In Proceedings CP-99, pages 88–102.
R. Debruyne and C. Bessière. Some practicable filtering techniques for the constraint satisfaction problem. In Proceedings of IJCAI-97, pages 412–417.
I. Gent, K. Stergiou, and T. Walsh. Decomposable Constraints. Artifcial Intelligence, 123:133–156, 2000.
C. P. Gomes and B. Selman. Problem structure in the presence of perturbations. In Proceedings of AAAI-97, pages 221–226.
C. P. Gomes, B. Selman, and N. Crato. Heavy-tailed probability distributions in combinatorial search. In Proceedings of CP-97, pages 121–135.
U. Montanari. Networks of Constraints: Fundamental Properties and Applications to Picture Processing. Information Science, 7:95–132, 1974.
P. Prosser, K. Stergiou, and T. Walsh. Singleton consistencies. In Proceedings of CP-2000.
J. C. Régin. A filtering algorithm for constraints of difference in csps. In Proceedings of AAAI-94, pages 362–367.
K. Stergiou, and T. Walsh. The difference all-di.erence makes. In Proceedings of IJCAI-99.
P. Van Hentenryck, Y. Deville, and C. Teng. A Generic Arc Consistency Algorithm and its Specializations. Artificial Intelligence, 57:291–321, 1992.
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© 2002 Springer-Verlag Berlin Heidelberg
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Stergiou, K. (2002). On Algorithms for Decomposable Constraints. In: Vlahavas, I.P., Spyropoulos, C.D. (eds) Methods and Applications of Artificial Intelligence. SETN 2002. Lecture Notes in Computer Science(), vol 2308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46014-4_7
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DOI: https://doi.org/10.1007/3-540-46014-4_7
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