Abstract
In this chapter, our objective is to heuristically discover a simplified form of functional dependencies between variables called weak dependencies. Once discovered, these relations are used to rank the variables. Our method shows that these relations can be detected with some acceptable overhead during constraint propagation. More precisely, each time a variable y gets instantiated as a result of the instantiation of x, a weak dependency (x,y) is recorded. As a consequence, the weight of x is raised, and the variable becomes more likely to be selected by the variable ordering heuristic. Experiments on a large set of problems show that on the average search trees are reduced by a factor 3 while runtime is decreased by 31 % when compared against dom-wdeg, one of the best dynamic variable ordering heuristics.
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In the following, we will use this as a synonym for constraints.
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Available from http://www.gecode.org/gecode-doc-latest/group__ExProblem.html.
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References
D. Achlioptas, C.P. Gomes, H.A. Kautz, B. Selman, Generating satisfiable problem instances, in Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence, Austin, Texas, USA (AAAI Press/MIT Press, Menlo Park/Cambridge, 2000), pp. 256–261
A. Arbelaez, Y. Hamadi, Exploiting weak dependencies in tree-based search, in ACM Symposium on Applied Computing (SAC), Honolulu, Hawaii, USA (ACM, New York, 2009), pp. 1385–1391
F. Boussemart, F. Hemery, C. Lecoutre, L. Sais, Boosting systematic search by weighting constraints, in Proceedings of the 16th European Conference on Artificial Intelligence, Valencia, Spain, ed. by R.L. de Mántaras, L. Saitta (IOS Press, Amsterdam, 2004), pp. 146–150
D. Brelaz, New methods to color the vertices of a graph. Commun. ACM 22, 251–256 (1979)
B.N. Dilkina, C.P. Gomes, A. Sabharwal, Tradeoffs in the complexity of backdoor detection, in CP’07, ed. by C. Bessiere. LNCS, vol. 4741 (Springer, Berlin, 2007), pp. 256–270
Gecode Team, Gecode: GenE. Constraint development environment (2006). Available from http://www.gecode.org
M.Z. Lagerkvist, C. Schulte, Advisors for incremental propagation, in 13th International Conference on Principles and Practice of Constraint Programming, Providence, RI, USA, ed. by C. Bessiere. LNCS (Springer, Berlin, 2007), pp. 409–422
R. Ostrowski, E. Grégoire, B. Mazure, L. Sais, Recovering and exploiting structural knowledge from CNF formulas, in CP, ed. by P. Van Hentenryck. Lecture Notes in Computer Science, vol. 2470 (Springer, Berlin, 2002), pp. 185–199
P. Refalo, Impact-based search strategies for constraint programming, in 10th International Conference on Principles and Practice of Constraint Programming, Toronto, Canada, ed. by M. Wallace. LNCS, vol. 2004 (Springer, Berlin, 2004), pp. 557–571
C. Schulte, M. Carlsson, Finite domain constraint programming systems, in Handbook of Constraint Programming, ed. by F. Rossi, P. van Beek, T. Walsh. Foundations of Artificial Intelligence (Elsevier, Amsterdam, 2006), pp. 495–526. Chapter 14
D. Sabin, E.C. Freuder, Contradicting conventional wisdom in constraint satisfaction, in ECAI (1994), pp. 125–129
R. Williams, C.P. Gomes, B. Selman, Backdoors to typical case complexity, in IJCAI (2003), pp. 1173–1178
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Hamadi, Y. (2013). Learning Variable Dependencies. In: Combinatorial Search: From Algorithms to Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41482-4_5
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