Abstract
In [2, 1], Bessière and Cordier said that the AC-6 arc-consistency algorithm is optimal in time on constraint networks where nothing is known about the constraint semantics. However, in constraint networks, it is always assumed that constraints are bidirectional. None of the previous algorithms achieving arc-consistency (AC-3 [8, 9], AC-4 [10], AC-6) use constraint bidirectionality. We propose here an improved version of AC-6 which uses this property. Then, we claim that our new algorithm is optimal in the number of constraint checks performed (i.e. given a variable, value, and arc ordering, it performs the minimum possible number of constraint checks according to these orders).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
C. Bessière and M.O. Cordier. Arc-consistency and arc-consistency again. In AAAI-93, Proceedings Eleventh National Conference on Artificial Intelligence, pages 108–113, Washington, DC, 1993.
C. Bessière. Arc-consistency and arc-consistency again. Artificial Intelligence, 65(1):179–190, 1994.
C. Bessière. A fast algorithm to establish arc-consistency in constraint networks. Technical Report TR 94-003, LIRMM University of Montpellier II, France, January 1994.
C. Bessière and J.C. Régin. An arc-consistency algorithm optimal in the number of constraint checks. In ECAI'94, Proceedings of the Workshop on Constraint Processing, pages 9–16, Amsterdam, The Netherlands, 1994.
R. Dechter. Enhancement schemes for constraint processing: Backjumping, learning, and cutset decomposition. Artificial Intelligence, 41:273–312, 1990.
E.C. Freuder. Using metalevel constraint knowledge to reduce constraint checking. In ECAI'94, Proceedings of the Workshop on Constraint Processing, pages 27–33, Amsterdam, The Netherlands, 1994.
R.M. Haralick and G.L. Elliot. Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14:263–313, 1980.
A.K. Mackworth. Consistency in networks of relations. Artificial Intelligence, 8:99–118, 1977.
A.K. Mackworth and E.C. Freuder. The complexity of some polynomial network consistency algorithms for constraint satisfaction problems. Artificial Intelligence, 25:65–74, 1985.
R. Mohr and T.C. Henderson. Arc and path consistency revisited. Artificial Intelligence, 28:225–233, 1986.
M. Perlin. Arc consistency for factorable relations. Artificial Intelligence, 53:329–342, 1992.
P. Van Hentenryck, Y. Deville, and C.M. Teng. A generic arcconsistency algorithm and its specializations. Artificial Intelligence, 57:291–321, 1992.
R. J. Wallace. Why AC-3 is almost always better than AC-4 for establishing arc consistency in CSPs. In IJCAI'93, Proceedings Thirteenth International Joint Conference on Artificial Intelligence, pages 239–245, Chambéry, France, 1993.
R.J. Wallace and E.C. Freuder. Ordering heuristics for arc consistency algorithms. In Proceedings Ninth Canadian Conference on Artificial Intelligence, pages 163–169, Vancouver, Canada, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bessière, C., Régin, JC. (1995). Using bidirectionality to speed up arc-consistency processing. In: Meyer, M. (eds) Constraint Processing. CP CP 1994 1993. Lecture Notes in Computer Science, vol 923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59479-5_24
Download citation
DOI: https://doi.org/10.1007/3-540-59479-5_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59479-6
Online ISBN: 978-3-540-49281-8
eBook Packages: Springer Book Archive