Abstract
Constraints can be exploited in paradigms outside of constraint programming. In particular, powerful global constraints can often be decomposed into small primitives and these decompositions can simulate complex propagation algorithms that perform sophisticated inference about a problem. We illustrate this approach with examples of exploiting constraints in propositional satisfiability (SAT), pseudo-Boolean (PB) solving, integer linear programming (ILP) and answer set programming (ASP).
Keywords
- Integer Linear Programming
- Global Constraint
- Conjunctive Normal Form
- Joint Conf
- Boolean Circuit
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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Rossi, F., van Beek, P., Walsh, T. (eds.): Handbook of Constraint Programming. Foundations of Artificial Intelligence. Elsevier (2006)
Walsh, T.: Constraint Patterns. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 53–64. Springer, Heidelberg (2003)
Lauriere, J.: Alice: A language and a program for solving combinatorial problems. Artificial Intelligence 10, 29–127 (1978)
Régin, J.C.: A filtering algorithm for constraints of difference in CSPs. In: Proc. of the 12th National Conf. on AI, AAAI, pp. 362–367 (1994)
Bessière, C., Katsirelos, G., Narodytska, N., Quimper, C.G., Walsh, T.: Decompositions of all different, global cardinality and related constraints. In: Proc. of the 21st Int. Joint Conf. on Artificial Intelligence (2009)
Leconte, M.: A bounds-based reduction scheme for constraints of difference. In: Proc. of Second Int. Workshop on Constraint-based Reasoning (Constraint 1996) (1996)
Puget, J.: A fast algorithm for the bound consistency of alldiff constraints. In: 15th National Conf. on Artificial Intelligence, AAAI, pp. 359–366 (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)
Lopez-Ortiz, A., Quimper, C., Tromp, J., van Beek, P.: A fast and simple algorithm for bounds consistency of the alldifferent constraint. In: Proc. of the 18th Int. Joint Conf. on AI, IJCAI (2003)
Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)
Gent, I., Prosser, P., Smith, B.: A 0/1 encoding of the GACLex constraint for pairs of vectors. In: Proc. of ECAI 2002 Workshop on Modelling and Solving Problems with Constraints (2002)
Bessiere, C., Katsirelos, G., Narodytska, N., Quimper, C.-G., Walsh, T.: Decomposition of the NValue Constraint. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 114–128. Springer, Heidelberg (2010)
Drescher, C., Walsh, T.: A translational approach to constraint answer set solving. Theory and Practice of Logic Programming 10(4-6), 465–480 (2010)
Drescher, C., Walsh, T.: Modelling GRAMMAR constraints with answer set programming. In: Proc. of the 27th Int. Conf. on Logic Programming, ICLP 2011 (2011)
Drescher, C., Walsh, T.: Translation-based constraint answer set solving. In: Proc. of the 22nd Int. Joint Conf. on Artificial Intelligence, IJCAI (2011)
Pesant, G.: A Regular Language Membership Constraint for Finite Sequences of Variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004)
Bessiere, C., Katsirelos, G., Narodytska, N., Quimper, C.G., Walsh, T.: Propagating conjunctions of alldifferent constraints. In: Proc. of the Twenty-Fourth AAAI Conf. on Artificial Intelligence (AAAI 2010). AAAI (2010)
Bessière, C., Katsirelos, G., Narodytska, N., Walsh, T.: Circuit complexity and decompositions of global constraints. In: Proc. of the 21st Int. Joint Conf. on Artificial Intelligence, IJCAI (2009)
Brand, S., Narodytska, N., Quimper, C.-G., Stuckey, P.J., Walsh, T.: Encodings of the Sequence Constraint. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 210–224. Springer, Heidelberg (2007)
Maher, M., Narodytska, N., Quimper, C.-G., Walsh, T.: Flow-Based Propagators for the SEQUENCE and Related Global Constraints. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 159–174. Springer, Heidelberg (2008)
Law, Y.C., Lee, J.H.M.: Global Constraints for Integer and Set Value Precedence. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 362–376. Springer, Heidelberg (2004)
Walsh, T.: General Symmetry Breaking Constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 650–664. Springer, Heidelberg (2006)
Walsh, T.: Breaking Value Symmetry. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 880–887. Springer, Heidelberg (2007)
Walsh, T.: Breaking value symmetry. In: Proc. of the 23rd National Conf. on AI, AAAI, pp. 1585–1588 (2008)
Walsh, T.: Symmetry breaking using value precedence. In: Proc. of the 17th European Conf. on Artificial Intelligence (ECAI 2006). IOS Press (2006)
Bessière, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: The range and roots constraints: Specifying counting and occurrence problems. In: Proc. of the 19th Int. Joint Conf. on Artificial Intelligence, IJCAI, pp. 60–65 (2005)
Bessière, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: The Range Constraint: Algorithms and Implementation. In: Beck, J.C., Smith, B.M. (eds.) CPAIOR 2006. LNCS, vol. 3990, pp. 59–73. Springer, Heidelberg (2006)
Bessiere, C., Hebrard, E., Hnich, B., Walsh, T.: The complexity of global constraints. In: Proc. of the 19th National Conf. on AI, AAAI (2004)
Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: The ROOTS Constraint. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 75–90. Springer, Heidelberg (2006)
Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Quimper, C.-G., Walsh, T.: Reformulating Global Constraints: The Slide and Regular Constraints. In: Miguel, I., Ruml, W. (eds.) SARA 2007. LNCS (LNAI), vol. 4612, pp. 80–92. Springer, Heidelberg (2007)
Bessiere, C., Hebrard, E., Hnich, B., Kiziltan, Z., Walsh, T.: SLIDE: a useful special case of the CardPath constraint. In: Proc. of the 18th European Conf. on Artificial Intelligence (ECAI 2008). IOS Press (2008)
Bessière, C., Hebrard, E., Hnich, B., Walsh, T.: The complexity of global constraints. Constraints 12(2), 239–259 (2007)
Bacchus, F.: GAC Via Unit Propagation. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 133–147. Springer, Heidelberg (2007)
Carlsson, M., Beldiceanu, N.: Arc-consistency for a chain of lexicographic ordering constraints. Tech. rep. T2002-18, Swedish Institute of Computer Science (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Walsh, T. (2012). Exploiting Constraints. In: Muggleton, S.H., Tamaddoni-Nezhad, A., Lisi, F.A. (eds) Inductive Logic Programming. ILP 2011. Lecture Notes in Computer Science(), vol 7207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31951-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-31951-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31950-1
Online ISBN: 978-3-642-31951-8
eBook Packages: Computer ScienceComputer Science (R0)
