Abstract
The performance of a constraint model can often be improved by converting a subproblem into a single table constraint. In this paper we study heuristics for identifying promising subproblems. We propose a small set of heuristics to identify common cases such as expressions that will propagate weakly. The process of discovering promising subproblems and tabulating them is entirely automated in the tool Savile Row. A cache is implemented to avoid tabulating equivalent subproblems many times. We give a simple algorithm to generate table constraints directly from a constraint expression in Savile Row. We demonstrate good performance on the benchmark problems used in earlier work on tabulation, and also for several new problem classes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Mohr, R., Masini, G.: Good old discrete relaxation. In: Proceedings of ECAI 1988, pp. 651–656. Pitman Publishing (1988)
Gent, I.P., Jefferson, C., Miguel, I., Nightingale, P.: Data structures for generalised arc consistency for extensional constraints. In: Proceedings of AAAI 2007, pp. 191–197. AAAI Press (2007). http://www.aaai.org/Papers/AAAI/2007/AAAI07-029.pdf
Lecoutre, C.: STR2: optimized simple tabular reduction for table constraints. Constraints 16(4), 341–371 (2011). https://doi.org/10.1007/s10601-011-9107-6
Bessiere, C.: Constraint propagation. In: Handbook of Constraint Programming, pp. 29–83. Elsevier (2006)
Gent, I.P., Jefferson, C., Kelsey, T., Lynce, I., Miguel, I., Nightingale, P., Smith, B.M., Tarim, S.A.: Search in the patience game ‘Black Hole’. AI Communications 20(3), 211–226 (2007). https://content.iospress.com/articles/ai-communications/aic405
Gargani, A., Refalo, P.: An efficient model and strategy for the steel mill slab design problem. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 77–89. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74970-7_8
Dekker, J.J., Björdal, G., Carlsson, M., Flener, P., Monette, J.N.: Auto-tabling for subproblem presolving in MiniZinc. Constraints 22(4), 512–529 (2017). https://doi.org/10.1007/s10601-017-9270-5
Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.: MiniZinc: towards a standard cp modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74970-7_38
IBM Knowledge Center: The strong constraint (2017). https://www.ibm.com/support/knowledgecenter/SSSA5P_12.8.0/ilog.odms.ide.help/OPL_Studio/opllang_quickref/topics/tlr_oplsch_strong.html
Le Provost, T., Wallace, M.: Domain independent propagation. In: Proceedings of FGCS: International Conference on Fifth Generation Computer Systems, pp. 1004–1011. IOS Press (1992). http://www.webmail.eclipseclp.org/reports/corefgcs.pdf
Nightingale, P., Akgün, Ö., Gent, I.P., Jefferson, C., Miguel, I.: Automatically improving constraint models in Savile Row through associative-commutative common subexpression elimination. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 590–605. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10428-7_43
Nightingale, P., Spracklen, P., Miguel, I.: Automatically improving SAT encoding of constraint problems through common subexpression elimination in savile row. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 330–340. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_23
Nightingale, P., Akgün, O., Gent, I.P., Jefferson, C., Miguel, I., Spracklen, P.: Automatically improving constraint models in Savile Row. Artif. Intell. 251, 35–61 (2017). https://doi.org/10.1016/j.artint.2017.07.001
Nightingale, P., Rendl, A.: Essence’ description (2016). arXiv:1601.02865 [cs.AI]
Bessière, C., Hebrard, E., Hnich, B., Walsh, T.: The complexity of reasoning with global constraints. Constraints 12(2), 239–259 (2007). https://doi.org/10.1007/s10601-006-9007-3
Régin, J.C.: Generalized arc consistency for global cardinality constraint. In: Proceedings of AAAI 1996, pp. 209–215. AAAI Press (1996). http://www.aaai.org/Papers/AAAI/1996/AAAI96-031.pdf
Gent, I.P., Jefferson, C., Miguel, I.: Minion: A fast scalable constraint solver. In: Proceedings of ECAI 2006, pp. 98–102. IOS Press (2006). http://ebooks.iospress.nl/volumearticle/2658
Lecoutre, C., Sais, L., Tabary, S., Vidal, V.: Last conflict based reasoning. In: Proceedings of ECAI 2006, pp. 133–137. IOS Press (2006). http://ebooks.iospress.nl/volumearticle/2665
Chu, G., Stuckey, P.J., Schutt, A., Ehlers, T., Gange, G., Francis, K.: Chuffed (2018). https://github.com/chuffed/chuffed/
Akgün, Ö., Gent, I.P., Jefferson, C., Miguel, I., Nightingale, P., Salamon, A.Z.: Tabulation experimental software and additional results (2018). https://doi.org/10.5281/zenodo.1290656, https://github.com/stacs-cp/cp2018-tabulation
Van Hentenryck, P., Michel, L., Perron, L., Régin, J.-C.: Constraint programming in OPL. In: Nadathur, G. (ed.) PPDP 1999. LNCS, vol. 1702, pp. 98–116. Springer, Heidelberg (1999). https://doi.org/10.1007/10704567_6
CSPLib: A problem library for constraints (1999). http://www.csplib.org
Erdos, P., Sárközy, A.: On sets of coprime integers in intervals. Hardy-Ramanujan J. 16, 1–20 (1993). https://hal.archives-ouvertes.fr/hal-01108688
Acknowledgements
We thank EPSRC for grants EP/P015638/1 and EP/P026842/1. Dr Jefferson holds a Royal Society University Research Fellowship.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Akgün, Ö., Gent, I.P., Jefferson, C., Miguel, I., Nightingale, P., Salamon, A.Z. (2018). Automatic Discovery and Exploitation of Promising Subproblems for Tabulation. In: Hooker, J. (eds) Principles and Practice of Constraint Programming. CP 2018. Lecture Notes in Computer Science(), vol 11008. Springer, Cham. https://doi.org/10.1007/978-3-319-98334-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-98334-9_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98333-2
Online ISBN: 978-3-319-98334-9
eBook Packages: Computer ScienceComputer Science (R0)