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An efficient solver for weighted Max-SAT

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Abstract

We present a new branch and bound algorithm for weighted Max-SAT, called Lazy which incorporates original data structures and inference rules, as well as a lower bound of better quality. We provide experimental evidence that our solver is very competitive and outperforms some of the best performing Max-SAT and weighted Max-SAT solvers on a wide range of instances.

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References

  1. Alber, J., Gramm, J., Niedermeier, R.: Faster exact algorithms for hard problems: a parameterized point of view. In: Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics. LNCS, pp. 168–185. Springer, Berlin (1998)

  2. Alsinet, T., Manyà, F., Planes, J.: Improved branch and bound algorithms for Max-SAT. In: Proceedings of the 6th International Conference on the Theory and Applications of Satisfiability Testing. S. Margherita Ligure – Portofino, Italy (2003).

  3. Battiti, R., Protasi, M.: Reactive search, a history-sensitive heuristic for MAX-SAT. ACM J. Exp. Algorithms, 2, Art. 2(1997)

  4. Borchers B. and Furman J. (1999). A two-phase exact algorithm for MAX-SAT and weighted MAX-SAT problems. J. Combi. Optim 2: 299–306

    Article  Google Scholar 

  5. Cheriyan, J., Cunningham, W., Tunçel, L., Wang, Y.: A linear programming and rounding approach to MAX-2-SAT. In: Johnson D., Trick M. (eds.), Cliques, Coloring and Satisfiability, Vol. 26 of DIMACS, pp. 395–414. American Mathematical Society, Providence, USA (1996)

  6. Davis M., Logemann G. and Loveland D. (1962). A machine program for theorem-proving. Commun. ACM 5: 394–397

    Article  Google Scholar 

  7. Feige, U., Goemans, M.: Approximating the value of two proper proof systems, with applications to MAX-2SAT and MAX-DICUT. In: Proceedings of the 3rd Israel Symposium on Theory of Computing and Systems, pp. 182–189. Tel Aviv, Israel (1995)

  8. de Givry, S., Larrosa, J., Meseguer, P., Schiex, T.: Solving Max-SAT as weighted CSP. In: Proceedings of the 9th International Conference on Principles and Practice of Constraint Programming, CP-2003, Kinsale, Ireland, LNCS 2833, pp. 363–376. Springer, Berlin (2003)

  9. Goemans M. and Williamson D. (1995). Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. Assoc. Comput. Mach 42(6): 1115–1145

    Google Scholar 

  10. Hansen P. and Jaumard B. (1990). Algorithms for the maximum satisfiability problem. Computing 44: 279–303

    Article  Google Scholar 

  11. Johnson, D., Trick, M. (eds): Cliques, coloring, and Satisfiability: second DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, Providence, USA (1996)

  12. Jeroslow R.G. and Wang J. (1990). Solving propositional satisfiability problems. Ann. Math. Artif. Intell. 1: 167–187

    Article  Google Scholar 

  13. Joy, S., Mitchell, J., Borchers, B.: A branch and cut algorithm for MAX-SAT and weighted MAX-SAT. In: Proceedings of the DIMACS Workshop on Satisfiability: theory and Applications, Rutgers University, NJ, USA (1996)

  14. Warners J.P. and Klerk E. (1998). Semidefinite programming approaches for MAX-2-SAT and MAX-3-SAT: computational perspectives. Technical report, Delft, The Netherlands

    Google Scholar 

  15. Li, C.M., Anbulagan, A.: 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, Berlin (1997)

  16. Loveland, D.W.: Automated Theorem Proving. A Logical Basis, volume 6 of Fundamental Studies in Computer Science. North-Holland, Amsterdam (1978)

  17. Mitchell, D., Selman, B., Levesque, H.: Hard and easy distributions of SAT problems. In: Proceedings of the 10th National Conference on Artificial Intelligence, AAAI’92, San Jose, CA, USA, pp. 459–465. AAAI Press (1992)

  18. Niedermeier R. and Rossmanith P. (2000). New upper bounds for maximum satisfiability. J. Algorithms 36: 63–88

    Article  Google Scholar 

  19. Pretolani, D.: Efficiency and stability of hypergraph SAT algorithms. In: Proceedings of the DIMACS Challenge II Workshop. Rutgers University, NJ, USA (1993)

  20. Resende, M., Pitsoulis, L., Pardalos, P.: Approximate solutions of weighted MAX-SAT problems using GRASP. In: Du, D.-Z., Gu, J., Pardalos, P. (eds) Satisfiability Problem: theory and aplications, vol. 35 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 393–405. American Mathematical Society, Providence, USA (1997)

  21. Resende M., Pitsoulis L. and Pardalos P. (2000). FORTRAN subroutines for computing approximate solutions of weighted MAX-SAT problems using GRASP. Discrete Appl. Math. 100(1.2): 95–113

    Article  Google Scholar 

  22. Selman, B., Kautz, H., Cohen, B.: Noise Strategies for Improving Local Search. In: Proceedings of the 12th National Conference on Artificial Intelligence, AAAI’94, Seattle, WA, USA, pp. 337–343. AAAI Press (1994)

  23. 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’92, San Jose/CA, USA, pp. 440–446. AAAI Press (1992)

  24. Stützle, T., Hoos, H., Roli, A.: A review of the literature on local search algorithms for MAX-SAT. Technical Report AIDA-01-02, FG Intellektik, FB Informatik, TU Darmstadt, Germany (2001)

  25. 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. American Mathematical Society. Providence, USA (1996)

  26. Xing, Z., Zhang, W.: Efficient strategies for (weighted) maximum satisfiability. In: Proceedings of CP-2004, pp. 690–705. Toronto, Canada (2004)

  27. Zhang, H.: SATO: an efficient propositional prover. In: Proceedings of the Conference on Automated Deduction (CADE-97), pp. 272–275 (1997)

  28. Zhang, H., Shen, H., Manyà, F.: Exact algorithms for MAX-SAT. Electron. Notes Theor. Comput. Sci. 86(1) 190–203 (2003)

    Google Scholar 

  29. Zhang, L., Madigan, C., Moskewicz, M., Malik, S.: Efficient conflict driven learning in a Boolean satisfiability solver. In: Proceedings of the International Conference on Computer Aided Design, ICCAD-2001, San Jose/CA, USA, pp. 279–285 (2001)

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Correspondence to Felip Manyà.

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Alsinet, T., Manyà, F. & Planes, J. An efficient solver for weighted Max-SAT. J Glob Optim 41, 61–73 (2008). https://doi.org/10.1007/s10898-007-9166-9

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