Abstract
Constraint satisfaction problems can be SAT-encoded in more than one way, and the choice of encoding can be as important as the choice of search algorithm. Theoretical results are few but experimental comparisons have been made between encodings, using both local and backtrack search algorithms. This paper compares local search performance on seven encodings of graph colouring benchmarks. Two of the encodings are new and one of them gives generally better results than known encodings. We also find better results than expected for two variants of the log encoding, and surprisingly poor results for the support encoding.
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Bessiere, C., Hebrard, E., Walsh, T.: Local Consistencies in SAT. In: Sixth International Conference on Theory and Applications of Satisfiability Testing, Santa Margherita Ligure, Italy, pp. 400–407 (2003)
Clark, D., Frank, J., Gent, I., MacIntyre, E., Tomov, N., Walsh, T.: Local Search and the Number of Solutions. In: Second International Conference on Principles and Practices of Constraint Programming, pp. 119–133 (1996)
Davis, M., Logemann, G., Loveland, D.: A Machine Program for Theorem Proving. Communications of the ACM 5, 394–397 (1962)
Ernst, M., Millstein, T., Weld, D.: Automatic SAT-Compilation of Planning Problems. In: Fifteenth International Joint Conference on Artificial Intelligence, Nagoya, Japan, pp. 1169–1176 (1997)
Frisch, A., Peugniez, T.: Solving Non-Boolean Satisfiability Problems with Stochastic Local Search. In: Seventeenth International Joint Conference on Artificial Intelligence, Seattle, Washington, USA (2001)
van Gelder, A.: Another Look at Graph Coloring via Propositional Satisfiability. In: Computational Symposium on Graph Coloring and its Generalizations, Ithaca, NY, pp. 48–54 (2002)
Genisson, R., Jegou, P.: Davis and PutnamWere Already Forward Checking. In: Twelfth European Conference on Artificial Intelligence, Budapest, Hungary, pp. 180–184 (1996)
Gent, I.: Arc Consistency in SAT. In: Fifteenth European Conference on Artificial Intelligence, Lyons, France (2002)
Hanatani, Y., Horiyama, T., Iwama, K.: Density Condensation of Boolean Formulas. In: Sixth International Conference on the Theory and Applications of Satisfiability Testing, Santa Margherita Ligure, Italy, pp. 126–133 (2003)
Hoos, H.H.: SAT-Encodings, Search Space Structure, and Local Search Performance. In: Sixteenth International Joint Conference on Artificial Intelligence, Stockholm, Sweden, pp. 296–302. Morgan Kaufmann, San Francisco (1999)
Hoos, H.H.: Stochastic Local Search — Methods, Models, Applications. PhD thesis, CS Department, TU Darmstadt (1998)
Iwama, K., Miyazaki, S.: SAT-Variable Complexity of Hard Combinatorial Problems. In: IFIP World Computer Congress, pp. 253–258. Elsevier Science B.V., North-Holland (1994)
Kasif, S.: On the Parallel Complexity of Discrete Relaxation in Constraint Satisfaction Networks. In: Artificial Intelligence, vol. 45, pp. 275–286. Elsevier, Amsterdam (1990)
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proceedings of the Thirty Ninth Design Automation Conference, Las Vegas (June 2001)
Parkes, J.: Lifted Search Engines for Satisfiability. PhD dissertation, University of Oregon (June 1999)
Prestwich, S.D.: Negative Effects of Modeling Techniques on Search Performance. Annals of Operations Research 18, 137–150 (2003)
Prestwich, S.D.: Maintaining Arc-Consistency in Stochastic Local Search. In: Workshop on Techniques for Implementing Constraint Programming Systems, Ithaca, NY (2002)
Prestwich, S.D., Higgins, D., O’Sullivan, O.: A SAT-Based Approach to Multiple Sequence Alignment. In: Poster, Ninth International Conference on Principles and Practice of Constraint Programming, Kinsale, Ireland (2003)
Prestwich, S.D., Bressan, S.: A SAT Approach to Query Optimization in Mediator Systems. In: Fifth International Symposium on the Theory and Applications of Satisfiability Testing, University of Cincinnati, pp. 252–259 (2002); Submitted to Annals of Mathematics and Artificial Intelligence
Sabin, D., Freuder, G.: Contradicting Conventional Wisdom in Constraint Satisfaction. In: Eleventh European Conference on Artificial Intelligence, pp. 125–129 (1994)
Selman, B., Kautz, H., Cohen, B.: Noise Strategies for Improving Local Search. In: Twelfth National Conference on Artificial Intelligence, pp. 337–343. AAAI Press, Menlo Park (1994)
Selman, B., Levesque, H., Mitchell, D.: A New Method for Solving Hard Satisfiability Problems. In: Tenth National Conference on Artificial Intelligence, pp. 440–446. MIT Press, Cambridge (1992)
Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)
Yokoo, M.: Why Adding More Constraints Makes a Problem Easier for Hill-climbing Algorithms: Analyzing Landscapes of CSPs. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 356–370. Springer, Heidelberg (1997)
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Prestwich, S. (2004). Local Search on SAT-encoded Colouring Problems. In: Giunchiglia, E., Tacchella, A. (eds) Theory and Applications of Satisfiability Testing. SAT 2003. Lecture Notes in Computer Science, vol 2919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24605-3_9
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DOI: https://doi.org/10.1007/978-3-540-24605-3_9
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