Abstract
We introduce a framework for studying and solving a class of CSP formulations. The framework allows constraints to be expressed as linear and non-linear equations, then compiles them into SAT instances via Boolean logic circuits. While in general reduction to SAT may lead to the loss of structure, we specifically detect several types of structure in high-level input and use them in compilation. Linearity is preserved by the use of pseudo-Boolean (PB) constraints in conjunction with a 0-1 ILP solver that extends common SAT-solving techniques. Symmetries are detected in high-level constraints by solving the graph automorphism problem on parse trees. Symmetry-breaking predicates are added during compilation. Our system generalizes earlier work on symmetries in SAT and 0-1 ILP problems. Empirical evaluation is performed on instances of the social golfers and Hamming code generation problems. We show substantial speedups with symmetry-breaking, especially on unsatisfiable instances. In general, our runtimes with the specialized 0-1 ILP solver Pueblo are competitive with results recently reported for ILOG Solver.
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References
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving Difficult SAT Instances In The Presence of Symmetry. IEEE Transactions on CAD 22(9), 1117–1137 (2003)
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Generic ILP versus Specialized 0-1 ILP: An Update. In: Proceedings of the International Conference on Computer-Aided Design, pp. 450–457 (2002)
Aloul, F.A., Markov, I.L., Sakallah, K.A.: Shatter: Efficient Symmetry-Breaking for Boolean Satisfiability. In: Proc. Intl. Joint Conf. on AI, pp. 271–282 (2003)
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Symmetry-Breaking for Pseudo- Boolean Formulas. In: Proceedings of the Asia-South Pacific Design Automation Conference, pp. 884–887 (2004)
Bailleux, O., Boufkhad, Y.: Efficient CNF Encoding of Boolean Cardinality Constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 108–122. Springer, Heidelberg (2003)
Bailleux, O., Boufkhad, Y.: Full CNF Encoding: The Counting Constraints Case. In: 7th Intl. Conf. on Theory and Applications of SAT Testing (2004)
Chai, D., Kuehlmann, A.: A fast pseudo-boolean constraint solver. In: Proceedings of the Design Automation Conference, pp. 830–835 (2003)
Colbourn, C.H., Dinitz, J.H.: The CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton (1996)
Crawford, J., Ginsburg, M., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: Proc. of the Intl. Conf. on Principles of Knowledge Representation and Reasoning, pp. 148–159 (1996)
Darga, P.: SAUCY Man Page, http://vlsicad.eecs.umich.edu/BK/SAUCY/
Frisch, A.M., Miguel, I., Walsh, T.: Cgrass: A System for Transforming Constraint Satisfaction Problems. In: Jt. Workshop of ERCIM/CologNet area on Constr. Solving and Constr. Logic Prog., pp. 23–26 (2002)
Gent, I.P., Harvey, W., Kelsey, T., Linton, S.: Generic SBDD using Computational Group Theory. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 333–347. Springer, Heidelberg (2003)
Gent, I.P., Walsh, T., Selman, B.: CSPLib Problem Library for Constraints, http://www.csplib.org
Kiziltan, Z.: Symmetry Breaking Ordering Constraints, Doctoral Thesis, Uppsala University (2004)
Lal, A., Choueiry, B.: Dynamic Detection and Exploitation of Value Symmetries for Non- Binary Finite CSPs. In: Workshop on Symmetry in CSPs (2003)
McKay, B.: Practical Graph Isomorphism. Congressus Numerantium 30, 45–87 (1981)
Margot, F.: Exploiting Orbits in Symmetric ILP. Mathematical Programming Ser. B 98, 3–21 (2003)
Meseguer, P., Torras, C.: Solving strategies for highly symmetric CSPs. In: Proceedings IJCAI, pp. 400–405 (1999)
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proc. Design Automation Conf., pp. 530–535 (2001)
Nam, G., Aloul, F., Sakallah, K., Rutenbar, R.: A Comparative Study of Two Boolean Formulations of FPGA Detailed Routing Constraints. In: Proc. of the Intl. Symposium on Physical Design, pp. 222–227 (2001)
van Hentenryck, P.: The OPL Optimization Programming Language. The MIT Press, Cambridge (1999)
The ECLiPSe Team, The ECLiPSe Constraint Logic Programming System, http://www.icparc.ic.ac.uk/eclipse/
Prestwich, S.D.: Balanced Incomplete Block Design as Satisfiability. In: 12th Irish Conference on Artificial Intelligence and Cognitive Science (2001)
Puget, J.F.: Symmetry Breaking Using Stabilizers. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 585–599. Springer, Heidelberg (2003)
Sheini, H.: The Pueblo solver, http://www.eecs.umich.edu/~hsheini/pueblo
Ramani, A., Markov, I.L.: GSymEx: Generic Symmetry Extraction for Constraint Programming Problems, http://vlsicad.eecs.umich.edu/BK/GSymEx/
ILOG Solver, http://www.ilog.com/products/solver/
Warners, J.P.: A Linear-Time Transformation of Linear Inequalities into Conjunctive Normal Form. Information Proc. Letters 68(2), 63–69 (1998)
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Ramani, A., Markov, I.L. (2005). Automatically Exploiting Symmetries in Constraint Programming. In: Faltings, B.V., Petcu, A., Fages, F., Rossi, F. (eds) Recent Advances in Constraints. CSCLP 2004. Lecture Notes in Computer Science(), vol 3419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11402763_8
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DOI: https://doi.org/10.1007/11402763_8
Publisher Name: Springer, Berlin, Heidelberg
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