Approximation Strategies for Incomplete MaxSAT

  • Saurabh JoshiEmail author
  • Prateek Kumar
  • Ruben Martins
  • Sukrut Rao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)


Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental results show that approximation strategies can be used to find better solutions than the best incomplete solvers in the MaxSAT Evaluation 2017.


MaxSAT Incomplete Approximation 



This work is partially funded by ECR 2017 grant from SERB, DST, India, NSF award #1762363 and CMU/AIR/0022/2017 grant. Authors would like to thank the anonymous reviewers for their helpful comments, and Saketha Nath for lending his servers for the experiments.


  1. 1.
    Alviano, M., Dodaro, C., Ricca, F.: A MaxSAT algorithm using cardinality constraints of bounded size. In: Proceedings of International Joint Conference on Artificial Intelligence, pp. 2677–2683. AAAI Press (2015)Google Scholar
  2. 2.
    Ansótegui, C., Bacchus, F., Järvisalo, M., Martins, R.: MaxSAT Evaluation 2017 (2017). Accessed 18 Apr 2017
  3. 3.
    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). Scholar
  4. 4.
    Ansótegui, C., Gabàs, J.: WPM3: an (in)complete algorithm for weighted partial MaxSAT. Artif. Intell. 250, 37–57 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Argelich, J., Le Berre, D., Lynce, I., Marques-Silva, J., Rapicault, P.: Solving linux upgradeability problems using Boolean optimization. In: Proceedings of Workshop on Logics for Component Configuration, pp. 11–22. EPTCS (2010)Google Scholar
  6. 6.
    Argelich, J., Li, C.M., Manyà, F., Planes, J.: MaxSAT Evaluation 2016 (2016). Accessed 18 Apr 2016
  7. 7.
    Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proceedings of International Joint Conference on Artificial Intelligence, pp. 399–404. AAAI Press (2009)Google Scholar
  8. 8.
    Le Berre, D., Parrain, A.: The SAT4J library, release 2.2. JSAT 7(2–3), 59–64 (2010)Google Scholar
  9. 9.
    Cai, S., Luo, C., Thornton, J., Su, K.: Tailoring local search for partial MaxSat. In: Proceedings of AAAI Conference on Artificial Intelligence, pp. 2623–2629. AAAI Press (2014)Google Scholar
  10. 10.
    Cai, S., Luo, C., Zhang, H., From decimation to local search and back: a new approach to MaxSAT. In: Proceedings of AAAI Conference on Artificial Intelligence, pp. 571–577. AAAI Press (2017)Google Scholar
  11. 11.
    Davies, J., Bacchus, F.: Solving MAXSAT by solving a sequence of simpler SAT instances. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 225–239. Springer, Heidelberg (2011). Scholar
  12. 12.
    Eén, N., Sörensson, N.: Translating pseudo-Boolean constraints into SAT. JSAT 2(1–4), 1–26 (2006)zbMATHGoogle Scholar
  13. 13.
    Fan, Y., Ma, Z., Kaile, S., Sattar, A., Li, C.: Ramp: a local search solver based on make-positive variables. In: Proceedings of MaxSAT Evaluation (2016)Google Scholar
  14. 14.
    Feng, Y., Bastani, O., Martins, R., Dillig, I., Anand, S.: Automated synthesis of semantic malware signatures using maximum satisfiability. In: Proceedings of Network and Distributed System Security Symposium (2017)Google Scholar
  15. 15.
    Johnson, S.C.: Hierarchical clustering schemes. Psychometrika 32(3), 241–254 (1967)CrossRefGoogle Scholar
  16. 16.
    Jose, M., Majumdar, R.: Cause clue clauses: error localization using maximum satisfiability. In: Proceedings of Conference on Programming Language Design and Implementation, pp. 437–446. ACM (2011)Google Scholar
  17. 17.
    Joshi, S., Martins, R., Manquinho, V.: Generalized totalizer encoding for pseudo-Boolean constraints. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 200–209. Springer, Cham (2015). Scholar
  18. 18.
    Koshimura, M., Zhang, T., Fujita, H., Hasegawa, R.: QMaxSAT: a partial Max-SAT solver. JSAT 8(1/2), 95–100 (2012)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Luo, C., Cai, S., Kaile, S., Huang, W.: CCEHC: an efficient local search algorithm for weighted partial maximum satisfiability. Artif. Intell. 243, 26–44 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Luo, C., Cai, S., Wei, W., Jie, Z., Kaile, S.: CCLS: an efficient local search algorithm for weighted maximum satisfiability. IEEE Trans. Comput. 64(7), 1830–1843 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Marques-Silva, J., Argelich, J., Graça, A., Lynce, I.: Boolean lexicographic optimization: algorithms & applications. Ann. Math. Artif. Intell. 62(3–4), 317–343 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Martins, R., Joshi, S., Manquinho, V., Lynce, I.: Incremental Cardinality Constraints for MaxSAT. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 531–548. Springer, Cham (2014). Scholar
  23. 23.
    Martins, R., Manquinho, V., Lynce, I.: Open-WBO: a modular MaxSAT solver’. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 438–445. Springer, Cham (2014). Scholar
  24. 24.
    Morgado, A., Dodaro, C., Marques-Silva, J.: Core-guided MaxSAT with soft cardinality constraints. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 564–573. Springer, Cham (2014)Google Scholar
  25. 25.
    Saikko, P., Berg, J., Järvisalo, M.: LMHS: a SAT-IP hybrid MaxSAT solver. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 539–546. Springer, Cham (2016). Scholar
  26. 26.
    Sugawara, T.: MaxRoster: solver description. In: Proceedings MaxSAT Evaluation 2017: Solver and Benchmark Descriptions, vol. B-2017-2, p. 12. University of Helsinki, Department of Computer Science (2017)Google Scholar
  27. 27.
    Warners, J.P.: A linear-time transformation of linear inequalities into conjunctive normal form. Inf. Process. Lett. 68(2), 63–69 (1998)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Saurabh Joshi
    • 1
    Email author
  • Prateek Kumar
    • 1
  • Ruben Martins
    • 2
  • Sukrut Rao
    • 1
  1. 1.Indian Institute of Technology HyderabadSangareddyIndia
  2. 2.Carnegie Mellon UniversityPittsburghUSA

Personalised recommendations