Abstract
Several branching heuristics for compiling in a top-down fashion finite-domain constraint networks into multi-valued decision diagrams (MDD) or decomposable multi-valued decision graphs (MDDG) are empirically evaluated, using the cn2mddg compiler. This MDDG compiler has been enriched with various additional branching rules. These rules can be gathered into two families, the one consisting of heuristics for the satisfaction problem (which are suited to compiling networks into MDD representations) and the family of heuristics favoring decompositions (which are relevant when the MDDG language is targeted). Our empirical investigation on a large dataset shows the value of decomposability (targeting MDDG allows for compiling many more instances and leads to much smaller compiled representations). The well-known (Dom/Wdeg) heuristics appears as the best choice for compiling networks into MDD. When MDDG is the target, a new rule, based on a dynamic, yet parsimonious use of hypergraph partitioning for the decomposition purpose turns out to be the best option. As expected, the best heuristics for the satisfaction problem perform better than the best heuristics favoring decompositions when MDD is targeted, and the converse is the case when MDDG is targeted.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Amilhastre, J., Fargier, H., Marquis, P.: Consistency restoration and explanations in dynamic CSPs application to configuration. Artif. Intell. 135(1–2), 199–234 (2002)
Amilhastre, J., Fargier, H., Niveau, A., Pralet, C.: Compiling CSPs: a complexity map of (non-deterministic) multivalued decision diagrams. Int. J. Artif. Intell. Tools 23(4) (2014)
Bart, A., Koriche, F., Lagniez, J.M., Marquis, P.: An improved CNF encoding scheme for probabilistic inference. In: Proceedings of ECAI 2016, pp. 613–621 (2016)
Bavelas, A.: Communication patterns in task-oriented groups. J. Acoust. Soc. Am. 22(6), 725–730 (1950)
Brandes, U.: A faster algorithm for betweenness centrality. J. Math. Soc. 25(2), 163–177 (2001)
Brandes, U.: On variants of shortest-path betweenness centrality and their generic computation. Soc. Netw. 30(2), 136–145 (2008)
Catalyürek, U., Aykanat, C.: PaToH (Partitioning Tool for Hypergraphs), pp. 1479–1487. Encyclopedia of Parallel Computing (2011)
Darwiche, A.: Decomposable negation normal form. J. ACM 48(4), 608–647 (2001)
Darwiche, A.: New advances in compiling CNF into decomposable negation normal form. In: Proceedings of ECAI 2004, pp. 328–332 (2004)
Darwiche, A., Hopkins, M.: Using recursive decomposition to construct elimination orders, jointrees, and dtrees. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 180–191. Springer, Heidelberg (2001). doi:10.1007/3-540-44652-4_17
Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM 19(2), 248–264 (1972). http://doi.acm.org/10.1145/321694.321699
Fargier, H., Marquis, P.: On the use of partially ordered decision graphs in knowledge compilation and quantified Boolean formulae. In: Proceedings of AAAI 2006, pp. 42–47 (2006)
Gergov, J., Meinel, C.: Efficient analysis and manipulation of OBDDs can be extended to FBDDs. IEEE Trans. Comput. 43(10), 1197–1209 (1994)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)
Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: Proceedings of ECAI 2004, pp. 146–150 (2004)
Huang, J., Darwiche, A.: The language of search. J. Artif. Intell. Res. 29, 191–219 (2007)
Koriche, F., Lagniez, J.M., Marquis, P., Thomas, S.: Compiling constraint networks into multivalued decomposable decision graphs. In: Proceedings of IJCAI 2015, pp. 332–338 (2015)
Lecoutre, C., Sais, L., Tabary, S., Vidal, V.: Reasoning from last conflict(s) in constraint programming. Artif. Intell. 173(18), 1592–1614 (2009)
Marinescu, R., Dechter, R.: Dynamic orderings for AND/OR branch-and-bound search in graphical models. In: Proceedings of ECAI 2006, pp. 138–142 (2006)
Michel, L., Hentenryck, P.: Activity-based search for black-box constraint programming solvers. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 228–243. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29828-8_15
Narodytska, N., Walsh, T.: Constraint and variable ordering heuristics for compiling configuration problems. In: Proceedings of IJCAI 2007, pp. 149–154 (2007)
Oztok, U., Darwiche, A.: On compiling CNF into decision-DNNF. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 42–57. Springer, Cham (2014). doi:10.1007/978-3-319-10428-7_7
Refalo, P.: Impact-based search strategies for constraint programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30201-8_41
Sang, T., Beame, P., Kautz, H.A.: Performing Bayesian inference by weighted model counting. In: Proceedings of AAAI 2005, pp. 475–482 (2005)
Stoer, M., Wagner, F.: A simple min-cut algorithm. J. ACM 44(4), 585–591 (1997)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Lagniez, JM., Marquis, P., Paparrizou, A. (2017). Defining and Evaluating Heuristics for the Compilation of Constraint Networks. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-66158-2_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66157-5
Online ISBN: 978-3-319-66158-2
eBook Packages: Computer ScienceComputer Science (R0)