Abstract
We introduce GAC-4R, MDD-4, and MDD-4R three new algorithms for maintaining arc consistency for table and MDD constraints. GAC-4R improves the well-known GAC-4 algorithm by managing the internal data structures in a different way. Instead of maintaining the internal data structures only by studying the consequences of deletions, we propose to reset the data structures by recomputing them from scratch whenever it saves time. This idea avoids the major drawback of the GAC-4 algorithm, i.e., its cost at a shallow search-tree depth. We also show that this idea can be exploited in MDD constraints. Experiments show that GAC-4R is competitive with the best arc-consistency algorithms for table constraints, and that MDD-4R clearly outperforms all classical algorithms for table or MDD constraints.
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References
Andersen, H.R., Hadzic, T., Hooker, J.N., Tiedemann, P.: A Constraint Store Based on Multivalued Decision Diagrams. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 118–132. Springer, Heidelberg (2007)
Bergman, D., van Hoeve, W.-J., Hooker, J.N.: Manipulating MDD Relaxations for Combinatorial Optimization. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 20–35. Springer, Heidelberg (2011)
Bessière, C., Régin, J.-C.: Arc consistency for general constraint networks: preliminary results. In: Proceedings of IJCAI 1997, Nagoya, pp. 398–404 (1997)
Bessière, C., Régin, J.-C.: Refining the basic constraint propagation algorithm. In: Proceedings of IJCAI 2001, Seattle, WA, USA, pp. 309–315 (2001)
Briggs, P., Torczon, L.: An efficient representation for sparse sets. ACM Letters on Programming Languages and Systems 2, 59–69 (1993)
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers C35(8), 677–691 (1986)
Cheng, K., Yap, R.: An mdd-based generalized arc consistency algorithm for positive and negative table constraints and some global constraints. Constraints 15 (2010)
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)
Gent, I., Jefferson, C., Miguel, I., Nightingale, P.: Data structures for generalised arc consistency for extensional constraints. In: Proc. AAAI 2007, Vancouver, Canada, pp. 191–197 (2007)
Hadzic, T., Hooker, J.N., O’Sullivan, B., Tiedemann, P.: Approximate Compilation of Constraints into Multivalued Decision Diagrams. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 448–462. Springer, Heidelberg (2008)
Hoda, S., van Hoeve, W.-J., Hooker, J.N.: A systematic approach to MDD-based constraint programming. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 266–280. Springer, Heidelberg (2010)
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)
Lecoutre, C.: Csp/maxcsp/wcsp solver competitions (2009), http://www.cril.univ-artois.fr/~lecoutre/benchmarks.html
Lecoutre, C.: Str2: optimized simple tabular reduction for table constraints. Constraints 16(4), 341–371 (2011)
Lecoutre, C., Likitvivatanavong, C., Yap, R.H.C.: A path-optimal gac algorithm for table constraints. In: ECAI, pp. 510–515 (2012)
Lhomme, O., Régin, J.-C.: A fast arc consistency algorithm for n-ary constraints. In: Proc. AAAI 2005, Pittsburgh, USA, pp. 405–410 (2005)
Lhomme, O.: Practical reformulations with table constraints. In: ECAI, pp. 911–912 (2012)
Mairy, J.-B., Van Hentenryck, P., Deville, Y.: Optimal and efficient filtering algorithms for table constraints. Constraints 19(1), 77–120 (2014)
Mohr, R., Masini, G.: Good old discrete relaxation. In: Proceedings of ECAI 1988, pp. 651–656 (1988)
Régin, J.-C.: AC-*: A configurable, generic and adaptive arc consistency algorithm. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 505–519. Springer, Heidelberg (2005)
Régin, J.-C.: Improving the expressiveness of table constraints. In: CP 2011, Proceedings Workshop ModRef 2011 (2011)
Rice, M., Kulhari, S.: A survey of static variable ordering heuristics for efficient bdd/mdd construction. University of California, Tech. Rep. (2008)
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Perez, G., Régin, JC. (2014). Improving GAC-4 for Table and MDD Constraints. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_44
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DOI: https://doi.org/10.1007/978-3-319-10428-7_44
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