Abstract
We present a new generic problem solving approach for over-constrained problems based on Max-SAT. We first define a clausal form formalism that deals with blocks of clauses instead of individual clauses, and that allows one to declare each block either as hard (i.e., must be satisfied by any solution) or soft (i.e., can be violated by some solution). We then present two Max-SAT solvers that find a truth assignment that satisfies all the hard blocks of clauses and the maximum number of soft blocks of clauses. Our solvers are branch and bound algorithms equipped with original lazy data structures; the first one incorporates static variable selection heuristics while the second one incorporates dynamic variable selection heuristics. Finally, we present an experimental investigation to assess the performance of our approach on a representative sample of instances (random 2-SAT, Max-CSP, and graph coloring).
Research partially supported by projects TIN2004-07933-C03-03 and TIC2003-00950 funded by the Ministerio de Educación y Ciencia. The second author is supported by a grant Ramón y Cajal.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Aloul, F., Ramani, A., Markov, I., Sakallah, K.: PBS: A backtrack search pseudo-Boolean solver. In: Symposium on the Theory and Applications of Satisfiability Testing, SAT 2002 (2002)
Alsinet, T., Manyà, F., Planes, J.: Improved branch and bound algorithms for Max-SAT. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 162–171. Springer, Heidelberg (2004)
Borchers, B., Furman, J.: A two-phase exact algorithm for MAX-SAT and weighted MAX-SAT problems. Journal of Combinatorial Optimization 2, 299–306 (1999)
Cha, B., Iwama, K., Kambayashi, Y., Miyazaki, S.: Local search algorithms for partial MAXSAT. In: Proceedings of the 14th National Conference on Artificial Intelligence, AAAI 1997, Providence/RI, USA, pp. 263–268. AAAI Press, Menlo Park (1997)
Culberson, J.: Graph coloring page: The flat graph generator (1995), See http://web.cs.ualberta.ca/~joe/Coloring/Generators/flat.html
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of the ACM 5, 394–397 (1962)
Gent, I.P.: Arc consistency in SAT. In: Proceedings of the 15th European Conference on Artificial Intelligence (ECAI), Lyon, France, pp. 121–125 (2002)
Jiang, Y., Kautz, H., Selman, B.: Solving problems with hard and soft constraints using a stochastic algorithm for MAX-SAT. In: Proceedings of the 1st International Workshop on Artificial Intelligence and Operations Research (1995)
Kasif, S.: On the parallel complexity of discrete relaxation in constraint satisfaction networks. Artificial Intelligence 45, 275–286 (1990)
Larrosa, J.: Algorithms and Heuristics for Total and Partial Constraint Satisfaction. PhD thesis, FIB, Universitat Politècnica de Catalunya, Barcelona (1998)
Loveland, D.W.: Automated Theorem Proving. A Logical Basis. Fundamental Studies in Computer Science, vol. 6. North-Holland, Amsterdam (1978)
Meseguer, P., Bouhmala, N., Bouzoubaa, T., Irgens, M., Sánchez, M.: Current approaches for solving over-constrained problems. Constraints 8(1), 9–39 (2003)
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an efficient sat solver. In: 39th Design Automation Conference (2001)
Selman, B., Levesque, H., Mitchell, D.: A new method for solving hard satisfiability problems. In: Proceedings of the 10th National Conference on Artificial Intelligence, AAAI 1992, San Jose/CA, USA, pp. 440–446. AAAI Press, Menlo Park (1992)
Shen, H., Zhang, H.: Study of lower bound functions for max-2-sat. In: Proceedings of AAAI 2004, pp. 185–190 (2004)
Smith, B., Dyer, M.: Locating the phase transition in binary constraint satisfaction problems. Artificial Intelligence 81, 155–181 (1996)
Wallace, R., Freuder, E.: Comparative studies of constraint satisfaction and Davis-Putnam algorithms for maximum satisfiability problems. In: Johnson, D., Trick, M. (eds.) Cliques, Coloring and Satisfiability, vol. 26, pp. 587–615 (1996)
Xing, Z., Zhang, W.: Efficient strategies for (weighted) maximum satisfiability. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 690–705. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Argelich, J., Manyà, F. (2005). Solving Over-Constrained Problems with SAT Technology. In: Bacchus, F., Walsh, T. (eds) Theory and Applications of Satisfiability Testing. SAT 2005. Lecture Notes in Computer Science, vol 3569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499107_1
Download citation
DOI: https://doi.org/10.1007/11499107_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26276-3
Online ISBN: 978-3-540-31679-4
eBook Packages: Computer ScienceComputer Science (R0)