Abstract
We introduce a new approach to approximating weighted Max-SAT problems that is based on simplifying a given instance, and then tightening the approximation. First, we relax its structure until it is tractable for exact algorithms. Second, we compensate for the relaxation by introducing auxiliary weights. More specifically, we relax equivalence constraints from a given Max-SAT problem, which we compensate for by recovering a weaker notion of equivalence. We provide a simple algorithm for finding these approximations, that is based on iterating over relaxed constraints, compensating for them one-by-one. We show that the resulting Max-SAT instances have certain interesting properties, both theoretical and empirical.
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 subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Pipatsrisawat, K., Palyan, A., Chavira, M., Choi, A., Darwiche, A.: Solving weighted Max-SAT problems in a reduced search space: A performance analysis. Journal on Satisfiability, Boolean Modeling, and Computation 4, 191–217 (2008)
Ramírez, M., Geffner, H.: Structural relaxations by variable renaming and their compilation for solving MinCostSAT. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 605–619. Springer, Heidelberg (2007)
Choi, A., Standley, T., Darwiche, A.: Approximating weighted Max-SAT problems by compensating for relaxations. Technical report, CSD, UCLA (2009)
Li, C.M., Manyà, F.: MaxSAT, hard and soft constraints. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, pp. 613–631. IOS Press, Amsterdam (2009)
Choi, A., Chavira, M., Darwiche, A.: Node splitting: A scheme for generating upper bounds in Bayesian networks. In: UAI, pp. 57–66 (2007)
Siddiqi, S., Huang, J.: Variable and value ordering for MPE search. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence (to appear, 2009)
Dechter, R., Rish, I.: Mini-buckets: A general scheme for bounded inference. J. ACM 50(2), 107–153 (2003)
Rish, I., Dechter, R.: Resolution versus search: Two strategies for SAT. J. Autom. Reasoning 24(1/2), 225–275 (2000)
Darwiche, A.: Decomposable negation normal form. Journal of the ACM 48(4), 608–647 (2001)
Darwiche, A.: On the tractability of counting theory models and its application to belief revision and truth maintenance. Journal of Applied Non-Classical Logics 11(1-2), 11–34 (2001)
Darwiche, A.: New advances in compiling CNF to decomposable negational normal form. In: Proceedings of European Conference on Artificial Intelligence, pp. 328–332 (2004)
Darwiche, A., Marquis, P.: A knowledge compilation map. Journal of Artificial Intelligence Research 17, 229–264 (2002)
Darwiche, A., Marquis, P.: Compiling propositional weighted bases. Artificial Intelligence 157(1-2), 81–113 (2004)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, Inc., San Mateo (1988)
Chavira, M., Darwiche, A.: Compiling Bayesian networks with local structure. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI), pp. 1306–1312 (2005)
Percus, A., Istrate, G., Moore, C.: Where statistical physics meets computation. In: Percus, A., Istrate, G., Moore, C. (eds.) Computational Complexity and Statistical Physics, pp. 3–24. Oxford University Press, Oxford (2006)
Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M.F., Rother, C.: A comparative study of energy minimization methods for Markov random fields. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3952, pp. 16–29. Springer, Heidelberg (2006)
Park, J.D.: Using weighted max-sat engines to solve MPE. In: AAAI/IAAI, pp. 682–687 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Choi, A., Standley, T., Darwiche, A. (2009). Approximating Weighted Max-SAT Problems by Compensating for Relaxations. In: Gent, I.P. (eds) Principles and Practice of Constraint Programming - CP 2009. CP 2009. Lecture Notes in Computer Science, vol 5732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04244-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-04244-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04243-0
Online ISBN: 978-3-642-04244-7
eBook Packages: Computer ScienceComputer Science (R0)