Abstract
This paper provides a technique for solving general constraint satisfaction problems (CSPs) with continuous variables. Constraints are represented by a hierarchical binary decomposition of the space of feasible values. We propose algorithms for path- and higher degrees of consistency based on logical operations defined on this representation and demonstrate that the algorithms terminate in polynomial time. We show that, in analogy to convex temporal problems and discrete row-convex problems, convexity properties of the solution spaces can be exploited to compute minimal and decomposable networks using path consistency algorithms. Based on these properties, we also show that a certain class of non binary CSPs can be solved using strong 5-consistency.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Davis E.: “Constraint propagation with interval labels”, Artificial Intelligence 32 (1987)
Dechter R., Meiri I., Pearl J.: “Temporal constraint networks”, Artificial Intelligence 49(1–3) (1990)
Dechter R.: “From local to global consistency”, Proceedings of the 8th Canadian Conference on AI (1990)
Deville Y., Van Hetenryck P.: “An efficient arc consistency algorithm for a class of CSP problems”, Proceedings of the 12th International Joint Conference on AI (1991)
Faltings B.: “Arc consistency for continuous variables”, Artificial Intelligence 65 (2) (1994)
Freuder E.C.: “Synthesizing constraint expressions”, Comm. ACM 21 (1978)
Freuder E.C.: “A sufficient condition for backtrack-free search”, J ACM 29 (1982)
Freuder E.C.: “A sufficient condition for backtrack-bounded search”, J. ACM 32 (1985)
Hyvönen E.: “Constraint reasoning based on interval arithmetic: the tolerance propagation approach”, Artificial Intelligence 58(1–3) (1992)
Lhomme O.: “Consistency techniques for numeric CSPs”, Proceedings of the 13th International Joint Conference on AI (1993)
Mackworth A.: “Consistency in networks of relations”, Artificial Intelligence 8 (1977)
Montanari U.: “Networks of constraints: fundamental properties and applications to picture processing”, Inform. Scie. 7 (1974)
Tanimoto T.: “A constraint decomposition method for spatio-temporal configurations problems”, Proceedings of the the 11th National Conference on AI (1993)
Van Beek P.: “Approximation algorithms for temporal reasoning”, Proceedings of the 11th International Joint Conference on AI (1989)
Van Beek P.: “On the minimality and decomposability of constraint networks”, Proceedings of the 10th National Conference on AI (1992)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Haroud, D., Faltings, B. (1994). Global consistency for continuous constraints. In: Borning, A. (eds) Principles and Practice of Constraint Programming. PPCP 1994. Lecture Notes in Computer Science, vol 874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58601-6_88
Download citation
DOI: https://doi.org/10.1007/3-540-58601-6_88
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58601-2
Online ISBN: 978-3-540-49032-6
eBook Packages: Springer Book Archive