Abstract
A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency and of bounds propagators. We clarify the differences among the three commonly used notions of bounds consistency in the literature. This serves as a reference for implementations of bounds propagators by defining (for the first time) the a priori behavior of bounds propagators on arbitrary constraints.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Apt, K.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)
Benhamou, F., McAllester, D., Van Hentenryck, P.: CLP (Intervals) revisited. In: ILPS 1994, pp. 124–138 (1994)
Benhamou, F., Older, W.J.: Applying interval arithmetic to real, integer, and boolean constraints. JLP 32(1), 1–24 (1997)
Cheadle, A., Harvey, W., Sadler, A., Schimpf, J., Shen, K., Wallace, M.: ECLiPSe: An introduction. Technical Report IC-Parc-03-1, IC-Parc, Imperial College London (2003)
Choi, C.W., Harvey, W., Lee, J.H.M., Stuckey, P.J.: A note on the definition of constraint monotonicity (2004), available from http://www.cse.cuhk.edu.hk/~cwchoi/monotonicity.pdf
Dechter, R.: Constraint Processing. Morgan Kaufmann, San Francisco (2003)
Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Global constraints for lexicographic orderings. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 93–108. Springer, Heidelberg (2002)
Gervet, C.: Interval propagation to reason about sets: Definition and implementation of a practical language. Constraints 1(3), 191–244 (1997)
Harvey, W., Schimpf, J.: Bounds consistency techniques for long linear constraints. In: Proceedings of TRICS: Techniques for Implementing Constraint programming Systems, pp. 39–46 (2002)
ILOG. ILOG Solver 5.2: User’s Manual (2001)
Katriel, I., Thiel, S.: Fast bound consistency for the global cardinality constraint. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 437–451. Springer, Heidelberg (2003)
Lallouet, A., Legtchenko, A., Dao, T., Ed-Dbali, A.: Intermediate (learned) consistencies. Research Report RR-LIFO-2003-04, Laboratoire d’Informatique Fondamentale d’Orléans (2003)
Lhomme, O.: Consistency techniques for numeric CSPs. In: IJCAI 1993, pp. 232–238 (1993)
López-Ortiz, A., Quimper, C.-G., Tromp, J., van Beek, P.: A fast and simple algorithm for bounds consistency of the alldifferent constraint. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI 2003), pp. 245–250 (2003)
Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8(1), 99–118 (1977)
Maher, M.: Propagation completeness of reactive constraints. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 148–162. Springer, Heidelberg (2002)
Marriott, K., Stuckey, P.J.: Programming with Constraints: an Introduction. MIT Press, Cambridge (1998)
Mehlhorn, K., Thiel, S.: Faster algorithms for bound-consistency of the sortedness and the alldifferent constraint. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 306–319. Springer, Heidelberg (2000)
Puget, J.-F.: A fast algorithm for the bound consistency of alldiff constraints. In: Proceedings of the 15th National Conference on Artificial Intelligence (AAAI 1998), pp. 359–366 (1998)
Quimper, C.-G., van Beek, P., López-Ortiz, A., Golynski, A., Sadjad, S.B.: An efficient bounds consistency algorithm for the global cardinality constraint. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 600–614. Springer, Heidelberg (2003)
Régin, J.-C., Rueher, M.: A global constraint combining a sum constraint and difference constraints. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 384–395. Springer, Heidelberg (2000)
Schulte, C., Stuckey, P.J.: When do bounds and domain propagation lead to the same search space. In: Proceedings of the 3rd International Conference on Principles and Practice of Declarative Programming (PPDP 2001), pp. 115–126 (2001)
SICStus Prolog. SICStus Prolog User’s Manual, Release 3.10.1 (2003)
Van Hentenryck, P., Saraswat, V., Deville, Y.: Design, implementation and evaluation of the constraint language cc (FD). Journal of Logic Programming 37(1-3), 139–164 (1998)
Walsh, T.: Relational consistencies. Research Report APES-28-2001, APES Research Group (2001)
Walsh, T.: Consistency and propagation with multiset constraints: A formal viewpoint. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 724–738. Springer, Heidelberg (2003)
Zhang, Y., Yap, R.H.C.: Arc consistency on n-ary monotonic and linear constraints. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 470–483. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Choi, C.W., Harvey, W., Lee, J.H.M., Stuckey, P.J. (2006). Finite Domain Bounds Consistency Revisited. In: Sattar, A., Kang, Bh. (eds) AI 2006: Advances in Artificial Intelligence. AI 2006. Lecture Notes in Computer Science(), vol 4304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11941439_9
Download citation
DOI: https://doi.org/10.1007/11941439_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49787-5
Online ISBN: 978-3-540-49788-2
eBook Packages: Computer ScienceComputer Science (R0)