Abstract
In many real-life problems, constraints are explicitly defined as a set of solutions. This ad hoc (table) representation uses exponential memory and makes support checking (for enforcing GAC) difficult. In this paper, we address both problems simultaneously by representing an ad hoc constraint with a multi-valued decision diagram (MDD), a memory efficient data structure that supports fast support search. We explain how to convert a table constraint into an MDD constraint and how to maintain GAC on the MDD constraint. Thanks to a sparse set data structure, our MDD-based GAC algorithm, mddc, achieves full incrementality in constant time. Our experiments on structured problems, car sequencing and still-life, show that mddc is a fast GAC algorithm for ad hoc constraints. It can replace a Boolean sequence constraint [1], and scales up well for structural MDD constraints with 208 variables and 340984 nodes. We also show why it is possible for mddc to be faster than the state-of-the-art generic GAC algorithms in [2,3,4]. Its efficiency on non-structural ad hoc constraints is justified empirically.
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
Beldiceanu, N., Contejean, E.: Introducing global constraints in CHIP. Journal of Mathematical and Computer Modelling 20(12), 97–123 (1994)
Gent, I.P., Jefferson, C., Miguel, I., Nightingale, P.: Data structures for generalized arc consistency for extensional constraints. In: National Conference on Artificial Intelligence (2007)
Lecoutre, C., Szymanek, R.: Generalized arc consistency for positive table constraints. In: International Conference on Principles and Practice of Constraint Programming, pp. 284–298 (2006)
Lhomme, O., Régin, J.C.: A fast arc consistency algorithm for n-ary constraints. In: National Conference on Artificial Intelligence, pp. 405–410 (2005)
Bessière, C., Régin, J.C.: Arc consistency for general constraint networks: preliminary results. In: International Joint Conference on Artificial Intelligence, pp. 398–404 (1997)
Srinivasan, A., Kam, T., Malik, S., Brayton, R.: Algorithms for discrete function manipulation. In: Computer Aided Design, pp. 92–95 (1990)
Carlsson, M.: Filtering for the case constraint. Talk given at Advanced School on Global Constraints (2006)
Cheng, K.C.K., Yap, R.H.C.: Maintaining generalized arc consistency on ad-hoc n-ary boolean constraints. In: European Conference on Artificial Intelligence, pp. 78–82 (2006)
Briggs, P., Torczon, L.: An efficient representation for sparse sets. ACM Letters on Programming Languages and Systems 2(1–4), 59–69 (1993)
Mackworth, A.K.: On reading sketch maps. In: International Joint Conference on Artificial Intelligence, pp. 598–606 (1977)
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. on Comp. 35(8), 667–691 (1986)
Lhomme, O.: Arc-consistency filtering algorithm for logical combinations of constraints. In: International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, pp. 209–224 (2004)
Pesant, G.: A regular language membership constraint for finite sequences of variables. In: International Conference on Principles and Practice of Constraint Programming, pp. 482–495 (2004)
Cheng, K.C.K., Yap, R.H.C.: Applying ad-hoc global constraints with the case constraint to Still-life. Constraints 11(2–3), 91–114 (2006)
van Hoeve, W.J., Pesant, G., Rousseau, L.M., Sabharwal, A.: Revisiting the sequence constraint. In: International Conference on Principles and Practice of Constraint Programming, pp. 620–634 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cheng, K.C.K., Yap, R.H.C. (2008). Maintaining Generalized Arc Consistency on Ad Hoc r-Ary Constraints. In: Stuckey, P.J. (eds) Principles and Practice of Constraint Programming. CP 2008. Lecture Notes in Computer Science, vol 5202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85958-1_34
Download citation
DOI: https://doi.org/10.1007/978-3-540-85958-1_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85957-4
Online ISBN: 978-3-540-85958-1
eBook Packages: Computer ScienceComputer Science (R0)