Abstract
This paper presents a novel domain-consistency algorithm which does not maintain supports dynamically during propagation, but rather maintain forbidden values. It introduces the optimal NAC4 (negative AC4) algorithm based on this idea. It further shows that maintaining forbidden values dynamically allows the generic algorithm AC5 to achieve domain consistency in time O(ed) for classes of constraints in which the number of supports is O(d 2) but the number of forbidden values is O(d). The paper also shows how forbidden values and supports can be used jointly to achieve domain consistency on logical combinations of constraints and to compute validity as well as entailment of constraints. Experimental results show the benefits of the joint exploitation of supports and forbidden values.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bessiere, C.: Constraint propagation. In: Rossi, F., Beek, P.v., Walsh, T. (eds.) Handbook of Constraint Programming. Elsevier Science Inc., New York (2006)
Van Hentenryck, P., Deville, Y., Teng, C.M.: A generic arc-consistency algorithm and its specializations. Artif. Intell. 57(2-3), 291–321 (1992)
Bessière, C., Régin, J.C.: Arc consistency for general constraint networks: Preliminary results. In: IJCAI, pp. 398–404 (1997)
Lecoutre, C.: Constraint Networks: Techniques and Algorithms. ISTE/Wiley (2009)
Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Support inference for generic filtering. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 721–725. Springer, Heidelberg (2004)
Mehta, D., van Dongen, M.R.C.: Reducing checks and revisions in coarse-grained MAC algorithms. In: IJCAI, pp. 236–241 (2005)
Bessière, C., Régin, J.C.: Local consistency on conjunctions of constraints. In: Proceedings Workshop on Non Binary Constraints on ECAI 1998, pp. 53–60 (1998)
Lhomme, O.: Arc-consistency filtering algorithms for logical combinations of constraints. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 209–224. Springer, Heidelberg (2004)
Van Hentenryck, P., Deville, Y.: The cardinality operator: A new logical connective for constraint logic programming. In: ICLP, pp. 745–759 (1991)
Van Hentenryck, P., Saraswat, V.A., Deville, Y.: Design, Implementation, and Evaluation of the Constraint Language cc(FD). In: Constraint Programming: Basics and Trends, pp. 293–316. Springer, Heidelberg (1994)
Bacchus, F., Walsh, T.: Propagating logical combinations of constraints. In: IJCAI, pp. 35–40 (2005)
Gent, I.P., Jefferson, C., Miguel, I., Nightingale, P.: Data structures for generalised arc consistency for extensional constraints. In: AAAI 2007, pp. 191–197 (2007)
Katsirelos, G., Walsh, T.: A compression algorithm for large arity extensional constraints. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 379–393. Springer, Heidelberg (2007)
Cheng, K.C.K., Yap, R.H.C.: Maintaining generalized arc consistency on ad hoc r-ary constraints. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 509–523. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deville, Y., Van Hentenryck, P. (2010). Domain Consistency with Forbidden Values. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-15396-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15395-2
Online ISBN: 978-3-642-15396-9
eBook Packages: Computer ScienceComputer Science (R0)