Abstract
In this paper, we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm, GO-MOCE, is based on the Method of Conditional Expectations (MOCE, also known as Johnson’s Algorithm), and applies a greedy variable ordering to it. We conduct an extensive empirical evaluation on two collections of instances – instances from a past Max Sat competition and random instances. We show that GO-MOCE reduces the number of unsatisfied clauses by tens of percents as compared to MOCE. We prove that, using tailored data structures we designed, GO-MOCE retains the linear time complexity. Moreover, its runtime overhead in our experiments is at most 10%. We combine GO-MOCE with CCLS, a state-of-the-art solver, and show that the combined solver improves CCLS on the above mentioned collections.
We thank David Gamarnik, MohammadTaghi Hajiaghayi, Dmitry Panchenko, and Gregory Sorkin for helpful information and correspondence regarding bounds on the optimum of Max \(r\)-Sat. This research was partially supported by the Milken Families Foundation Chair in Mathematics, by the Lynne and William Frankel Foundation for Computer Science, and by the Israeli Council for Higher Education (CHE) via the Data Science Research Center, Ben-Gurion University of the Negev.
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References
Ansótegui, C., Bonet, M.L., Gabàs, J., Levy, J.: Improving SAT-based weighted MaxSAT solvers. In: Milano, M. (ed.) CP 2012. LNCS, pp. 86–101. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33558-7_9
Ansótegui, C., Bonet, M.L., Levy, J.: Solving (weighted) partial MaxSAT through satisfiability testing. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 427–440. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_39
Ansótegui, C., Bonet, M.L., Levy, J.: SAT-based MaxSAT algorithms. Artif. Intell. 196, 77–105 (2013)
Argelich, J., Li, C.M., Manyá, F., Planes, J.: MaxSAT Evaluations. http://www.maxsat.udl.cat/
Ausiello, G., et al.: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, 2nd edn. Springer-Verlag, Heidelberg (2003). https://doi.org/10.1007/978-3-642-58412-1
Avellaneda, F.: A short description of the solver EvalMaxSAT. MaxSAT Eval. 2020, 8 (2020)
Berend, D., Twitto, Y.: Effect of initial assignment on local search performance for Max Sat. In: Faro, S., Cantone, D. (eds.) 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), vol. 160, pp. 8:1–8:14 (2020)
Berg, J., Korhonen, T., Järvisalo, M.: Loandra: PMRES extended with preprocessing entering MaxSAT evaluation 2017. MaxSAT Evaluation 2017, p. 13 (2017)
Biere, A., Heule, M., van Maaren, H.: Handbook of Satisfiability, vol. 185. IOS Press, Amsterdam (2009)
Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): MaxSAT, Hard and Soft Constraints, vol. 185, pp. 613–631. IOS Press, Amsterdam (2009)
de Boer, P.T., Kroese, D.P., Mannor, S., Rubinstein, R.Y.: A tutorial on the cross-entropy method. Ann. Oper. Res. 134(1), 19–67 (2005). https://doi.org/10.1007/s10479-005-5724-z
Chen, J., Friesen, D.K., Zheng, H.: Tight bound on Johnson’s algorithm for maximum satisfiability. J. Comput. Syst. Sci. 58(3), 622–640 (1999)
Coppersmith, D., Gamarnik, D., Hajiaghayi, M., Sorkin, G.B.: Random MAX SAT, random MAX CUT, and their phase transitions. Random Struct. Algorithms 24(4), 502–545 (2004)
Crawford, J.M., Auton, L.D.: Experimental results on the crossover point in random 3-SAT. Artif. Intell. 81(1–2), 31–57 (1996)
Davies, J.: Solving MaxSAT by decoupling optimization and satisfaction. Ph.D. thesis, University of Toronto (2013)
Erdős, P., Selfridge, J.L.: On a combinatorial game. J. Comb. Theory Ser. A 14(3), 298–301 (1973)
Guerreiro, A.P., Terra-Neves, M., Lynce, I., Figueira, J.R., Manquinho, V.: Constraint-based techniques in stochastic local search MaxSAT solving. In: Schiex, T., de Givry, S. (eds.) CP 2019. LNCS, vol. 11802, pp. 232–250. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30048-7_14
Håstad, J.: Some optimal inapproximability results. J. ACM (JACM) 48(4), 798–859 (2001)
Koshimura, M., Zhang, T., Fujita, H., Hasegawa, R.: QMaxSAT: a partial max-sat solver. J. Satisf. Boolean Model. Comput. 8(1–2), 95–100 (2012)
Le Berre, D., Parrain, A.: The SAT4J library, release 22. J. Satisf. Boolean Model. Comput. 7(2–3), 59–64 (2010)
Li, C.M., Manya, F., Planes, J.: New inference rules for max-sat. J. Artif. Intell. Res. 30, 321–359 (2007)
Luo, C., Cai, S., Wu, W., Jie, Z., Su, K.W.: CCLS: an efficient local search algorithm for weighted Maximum Satisfiability. IEEE Trans. Comput. 64(7), 1830–1843 (2014)
Mertens, S., Mézard, M., Zecchina, R.: Threshold values of random \(k\)-SAT from the cavity method. Random Struct. Algorithms 28(3), 340–373 (2006)
Nadel, A.: TT-open-WBO-Inc: tuning polarity and variable selection for anytime SAT-based optimization. In: Proceedings of the MaxSAT Evaluations (2019)
Narodytska, N., Bacchus, F.: Maximum satisfiability using core-guided MaxSAT resolution. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, pp. 2717–2723. AAAI Press (2014)
Paxian, T., Reimer, S., Becker, B.: Pacose: an iterative sat-based MaxSAT solver. MaxSAT Eval. 2018, 20 (2018)
Pipatsrisawat, K., Darwiche, A.: Clone: solving weighted Max-SAT in a reduced search space. In: Orgun, M.A., Thornton, J. (eds.) AI 2007. LNCS (LNAI), vol. 4830, pp. 223–233. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76928-6_24
Poloczek, M.: Bounds on greedy algorithms for MAX SAT. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 37–48. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23719-5_4
Poloczek, M., Schnitger, G.: Randomized variants of Johnson’s algorithm for MAX SAT. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 656–663. SIAM (2011)
Poloczek, M., Schnitger, G., Williamson, D.P., Van Zuylen, A.: Greedy algorithms for the maximum satisfiability problem: simple algorithms and inapproximability bounds. SIAM J. Comput. 46(3), 1029–1061 (2017)
Poloczek, M., Williamson, D.P.: An experimental evaluation of fast approximation algorithms for the maximum satisfiability problem. In: Goldberg, A.V., Kulikov, A.S. (eds.) SEA 2016. LNCS, vol. 9685, pp. 246–261. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-38851-9_17
Raab, M., Steger, A.: “Balls into Bins’’ — a simple and tight analysis. In: Luby, M., Rolim, J.D.P., Serna, M. (eds.) RANDOM 1998. LNCS, vol. 1518, pp. 159–170. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-49543-6_13
Selman, B., Kautz, H.A., Cohen, B.: Local search strategies for satisfiability testing. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 521–532 (1996)
Selman, B., Levesque, H., Mitchell, D.: A new method for solving hard satisfiability problems. In: Proceedings of the Tenth National Conference on Artificial Intelligence, pp. 440–446. AAAI Press (1992)
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Berend, D., Golan, S., Twitto, Y. (2021). A Novel Algorithm for Max Sat Calling MOCE to Order. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_25
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