New inference rules for max-SAT

Journal of Artificial Intelligence Research

Volumn 30, Issue , 2007, Pages 321-359

  Li, Chu Min ^a   Manyà, Felip ^b   Planes, Jordi ^c  

^a UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^b CSIC   (Spain)

^c UNIVERSITY OF LLEIDA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BENCHMARKING; INTEGER PROGRAMMING; MATHEMATICAL TRANSFORMATIONS; RANDOM VARIABLES;

INFERENCE RULES; INTEGER PROGRAMMING TRANSFORMATIONS;

PROBLEM SOLVING;

EID: 38149129628     PISSN: None     EISSN: 10769757     Source Type: Journal    
DOI: 10.1613/jair.2215     Document Type: Article

References (54)

1. Alber, J., Gramm, J., & Niedermeier, R. (2001). Faster exact algorithms for hard problems: A parameterized point of view. Discrete Mathematics, 229(1-3), 3-27.
2. Alsinet, T., Manyà, F., & Planes, J. (2003a). Improved branch and bound algorithms for Max-2-SAT and weighted Max-2-SAT. In Proceedings of the Catalonian Conference on Artificial Intelligence (CCIA-03), P. Mallorca, Spain, Vol. 100 of Frontiers in Artificial Intelligence and Applications, pp. 435-442. IOS Press.
3. Alsinet, T., Manyà, F., & Planes, J. (2003b). Improved branch and bound algorithms for Max-SAT. In Proceedings of the 6th International Conference on the Theory and Applications of Satisfiability Testing (SAT-03), Portofino, Italy, pp. 408-415.
4. Alsinet, T., Manyà, F., & Planes, J. (2004). A Max-SAT solver with lazy data structures. In Proceedings of the 9th Ibero-American Conference on Artificial Intelligence (IBERAMIA-04), Puebla, México, LNCS 3315, pp. 334-342. Springer.
5. Alsinet, T., Manyà, F., & Planes, J. (2005). Improved exact solver for weighted Max-SAT. In Proceedings of the 8th International Conference on Theory and Applications of Satisfiability Testing (SAT-05), St. Andrews, Scotland, LNCS 3569, pp. 371-377. Springer.
6. Ansótegui, C., Bonet, M. L., Levy, J., & Manyà, F. (2007a). Inference rules for high-order consistency in weighted CSP. In Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI-07), Vancouver, Canada, pp. 167-172. AAAI Press.
7. Ansótegui, C., Bonet, M. L., Levy, J., & Manyà, F. (2007b). The logic behind weighted CSP. In Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI-07), Hyderabad, India, pp. 32-37. AAAI Press.
8. Argelich, J., & Manyà, F. (2005). Solving over-constrained problems with SAT technology. In Proceedings of the 8th International Conference on Theory and Applications of Satisfiability Testing (SAT-05), St. Andrews, Scotland, LNCS 3569, pp. 1-15. Springer.
9. Argelich, J., & Manyà, F. (2006). Exact Max-SAT solvers for over-constrained problems. Journal of Heuristics, 12(4-5), 375-392.
10. Argelich, J., & Manyà, F. (2007). Partial Max-SAT solvers with clause learning. In Proceedings of the 10th International Conference on Theory and Applications of Satisfiability Testing (SAT-07), Lisbon, Portugal, LNCS 4501, pp. 28-40. Springer.
11. Bansal, N., & Raman, V. (1999). Upper bounds for MaxSat: Further improved. In Proceedings of 10th International Symposium on Algorithms and Computation (ISAAC-99), Chennai, India, LNCS 1741, pp. 247-260. Springer.
12. Beame, P., Kautz, H., & Sabharwal, A. (2003). Understanding the power of clause learning. In Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI-03), Acapulco, México, pp. 94-99. Morgan Kaufman.
13. Bonet, M. L., Levy, J., & Manyà, F. (2006). A complete calculus for Max-SAT. In Proceedings of the 9th International Conference on Theory and Applications of Satisfiability Testing (SAT-06), Seattle, USA, LNCS 4121, pp. 240-251. Springer.
14. Bonet, M. L., Levy, J., & Manyà, F. (2007). Resolution for Max-SAT. Artificial Intelligence, 171, 606-618.
15. Borchers, B., & Furman, J. (1999). A two-phase exact algorithm for MAX-SAT and weighted MAX-SAT problems. Journal of Combinatorial Optimization, 2, 299-306.
16. Boros, E., & Hammer, P. (2002). Pseudo-Boolean optimization. Discrete Applied Mathematics, 123, 155-225.
17. Cooper, M. C. (2003). Reduction operations in fuzzy or valued constraint satisfaction. Fuzzy Sets and Systems, 134, 311-342.
18. Cooper, M. C. (2005). High-order consistency in valued constraint satisfaction. Constraints, 10, 283-305.
19. Cooper, M. C., & Schiex, T. (2004). Arc consistency for soft constraints. Artificial Intelligence, 154(1-2), 199-227.
20. Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2001). Introduction to Algorithms (second edition). MIT Press.
21. Davis, M., Logemann, G., & Loveland, D. (1962). A machine program for theorem-proving. Communications of the ACM, 5, 394-397.
22. Davis, M., & Putnam, H. (1960). A computing procedure for quantification theory. Journal of the ACM, 7(3), 201-215.
23. de Givry, S., Larrosa, J., Meseguer, P., & Schiex, T. (2003). Solving Max-SAT as weighted CSP. In Proceedings of 9th International Conference on Principles and Practice of Constraint Programming (CP-03), Kinsale, Ireland, LNCS 2833, pp. 363-376. Springer.
24. de Givry, S., Zytnicki, M., Heras, F., & Larrosa, J. (2005). Existential arc consistency: Getting closer to full arc consistency in weighted csps. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI-05), Edinburgh, Scotland, pp. 84-89.
25. Freeman, J. W. (1995). Improvements to Propositions Satisfiability Search Algorithms. Ph.D. thesis, Department of Computer and Information Science, University of Pennsylvania, PA, USA.
26. Goldberg, E., & Novikov, Y. (2001). BerkMin: A fast and robust SAT solver. In Proceedings of Design, Automation and Test in Europe (DATE-02), Paris, France, pp. 142-149. IEEE Computer Society.
27. Heras, F., & Larrosa, J. (2006). New inference rules for efficient Max-SAT solving. In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI-06), Boston, USA. AAAI Press.
28. Huang, W. Q., & Jin, R. C. (1997). Solar: A learning from human algorithm for solving SAT. Science in China (Series E), 27(2), 179-186.
29. Jeroslow, R. G., & Wang, J. (1990). Solving propositional satisfiability problems. Annals of Mathematics and Artificial Intelligence, 1, 167-187.
30. Larrosa, J., & Heras, F. (2005). Resolution in Max-SAT and its relation to local consistency in weighted CSPs. In Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI-05), Edinburgh, Scotland, pp. 193-198. Morgan Kaufmann.
31. Larrosa, J., Heras, F., & de Givry, S. (2007). A logical approach to efficient Max-SAT solving. Artificial Intelligence, (in press).
32. Larrosa, J., & Meseguer, P. (2002). Partition-based lower bound for Max-CSP. Constraints, 7(3-4), 407-419.
33. Larrosa, J., Meseguer, P., & Schiex, T. (1999). Maintaining reversible DAC for Max-CSP. Artificial Intelligence, 107(1), 149-163.
34. Li, C. M. (1999). A constraint-based approach to narrow search trees for satisfiability. Information Processing Letters, 71, 75-80.
35. Li, C. M., & Anbulagan (1997a). Heuristics based on unit propagation for satisfiability problems. In Proceedings of 15th the International Joint Conference on Artificial Intelligence (IJCAI-97), Nagoya, Japan, pp. 366-371. Morgan Kaufmann.
36. Li, C. M., & Anbulagan (1997b). Look-ahead versus look-back for satisfiability problems. In Proceedings of the 3rd International Conference on Principles of Constraint Programming (CP-97), Linz, Austria, LNCS 1330, pp. 341-355. Springer.
37. Li, C. M., & Huang, W. Q. (2005). Diversification and determinism in local search for satisfiability. In Proceedings of the 8th International Conference on Theory and Applications of Satisfiability Testing (SAT-05), St. Andrews, Scotland, LNCS 3569, pp. 158-172. Springer.
38. Li, C. M., Manyà, F., & Planes, J. (2005). Exploiting unit propagation to compute lower bounds in branch and bound Max-SAT solvers. In Proceedings of the 11th International Conference on Principles and Practice of Constraint Programming (CP-05), Sitges, Spain, LNCS 3709, pp. 403-414. Springer.
39. Li, C. M., Manyà, F., & Planes, J. (2006). Detecting disjoint inconsistent subformulas for computing lower bounds for Max-SAT. In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI-06), Boston, USA, pp. 86-91. AAAI Press.
40. Marques-Silva, J. P., & Sakallah, K. A. (1999). GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers, 48(5), 506-521.
41. Niedermeier, R., & Rossmanith, P. (2000). New upper bounds for maximum satisfiability. Journal of Algorithms, 36, 63-88.
42. Régin, J. C., Petit, T., Bessière, C., & Puget, J. F. (2001). New lower bounds of constraint violations for over-constrained problems. In 7th International Conference on Principles and Practice of Constraint Programming (CP-01), Paphos, Cyprus, LNCS 2239, pp. 332-345. Springer.
43. Schiex, T. (2000). Arc consistency for soft constraints. In Proceedings of the 6th International Conference on Principles of Constraint Programming (CP-00), Singapore, LNCS 1894, pp. 411-424. Springer.
44. Shen, H., & Zhang, H. (2004). Study of lower bound functions for max-2-sat. In Proceedings of the National Conference on Artificial Intelligence (AAAI-04), San Jose, USA, pp. 185-190. AAAI Press.
45. Shen, H., & Zhang, H. (2005). Improving exact algorithms for max-2-sat. Annals of Mathematics and Artificial Intelligence, 44, 419-436.
46. Wallace, R. J. (1995). Directed arc consistency preprocessing. In Constraint Processing, Selected Papers, LNCS 923, pp. 121-137. Springer.
47. Wallace, R. J., & Freuder, E. (1996). 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. American Mathematical Society.
48. Xing, Z., & Zhang, W. (2004). Efficient strategies for (weighted) maximum satisfiability. In Proceedings of the 10th International Conference on Principles and Practice of Constraint Programming (CP-04), Toronto, Canada, LNCS 3258, pp. 690-705. Springer.
49. Xing, Z., & Zhang, W. (2005). An efficient exact algorithm for (weighted) maximum satisfiability. Artificial Intelligence, 164(2), 47-80.
50. Xu, K., Boussemart, F., Hemery, F., & Lecoutre, C. (2005). A simple model to generate hard satisfiable instances. In Proceedings of 19th International Joint Conference on Artificial Intelligence (IJCAI-05), Edinburgh, Scotland, pp. 337-342.
51. Xu, K., & Li, W. (2006). Many hard examples in exact phase transitions. Theoretical Computer Science, 355, 291-302.
52. Zhang, H. (1997). SATO: An efficient propositional prover. In Proceedings in the Conference on Automated Deduction (CADE-97), pp. 272-275.
53. Zhang, H., Shen, H., & Manyà, F. (2003). Exact algorithms for MAX-SAT. Electronic Notes in Theoretical Computer Science, 86(1).
54. Zhang, L., Madigan, C., Moskewicz, M., & Malik, S. (2001). Efficient conflict driven learning in a Boolean satisfiability solver. In International Conference on Computer Aided Design (ICCAD-01), San Jose, USA, pp. 279-285.