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Incremental Cardinality Constraints for MaxSAT

  • Conference paper
Principles and Practice of Constraint Programming (CP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8656))

Abstract

Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are non-incremental in nature, i.e. at each iteration the formula is rebuilt and no knowledge is reused from one iteration to another. In this paper, we exploit the knowledge acquired across iterations using novel schemes to use cardinality constraints in an incremental fashion. We integrate these schemes with several MaxSAT algorithms. Our experimental results show a significant performance boost for these algorithms as compared to their non-incremental counterparts. These results suggest that incremental cardinality constraints could be beneficial for other constraint solving domains.

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References

  1. Abío, I., Stuckey, P.J.: Conflict Directed Lazy Decomposition. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 70–85. Springer, Heidelberg (2012)

    Google Scholar 

  2. Ansótegui, C., Bonet, M.L., Gabàs, J., Levy, J.: Improving WPM2 for (Weighted) Partial MaxSAT. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 117–132. Springer, Heidelberg (2013)

    Google Scholar 

  3. Ansótegui, C., Bonet, M.L., Levy, J.: Solving (Weighted) Partial MaxSAT through Satisfiability Testing. In: Kullmann (ed.) [30], pp. 427–440

    Google Scholar 

  4. Ansótegui, C., Bonet, M.L., Levy, J.: A New Algorithm for Weighted Partial MaxSAT. In: Fox, M., Poole, D. (eds.) AAAI Conference on Artificial Intelligence. AAAI Press (2010)

    Google Scholar 

  5. Argelich, J., Berre, D.L., Lynce, I., Marques-Silva, J., Rapicault, P.: Solving Linux Upgradeability Problems Using Boolean Optimization. In: Workshop on Logics for Component Configuration, pp. 11–22 (2010)

    Google Scholar 

  6. Asín, R., Nieuwenhuis, R.: Curriculum-based course timetabling with SAT and MaxSAT. Annals of Operations Research, 1–21 (2012)

    Google Scholar 

  7. Asín, R., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Cardinality Networks: a theoretical and empirical study. Constraints 16(2), 195–221 (2011)

    MATH  MathSciNet  Google Scholar 

  8. Audemard, G., Lagniez, J.M., Simon, L.: Improving Glucose for Incremental SAT Solving with Assumptions: Application to MUS Extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 309–317. Springer, Heidelberg (2013)

    Google Scholar 

  9. Bailleux, O., Boufkhad, Y.: Efficient CNF Encoding of Boolean Cardinality Constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 108–122. Springer, Heidelberg (2003)

    Google Scholar 

  10. Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB Standard: Version 2.0. Tech. rep., Department of Computer Science, The University of Iowa (2010), www.SMT-LIB.org

  11. Büttner, M., Rintanen, J.: Satisfiability Planning with Constraints on the Number of Actions. In: Biundo, S., Myers, K.L., Rajan, K. (eds.) International Conference on Automated Planning and Scheduling, pp. 292–299 (2005)

    Google Scholar 

  12. Chen, Y., Safarpour, S., Marques-Silva, J., Veneris, A.G.: Automated Design Debugging With Maximum Satisfiability. IEEE Transactions on CAD of Integrated Circuits and Systems 29(11), 1804–1817 (2010)

    Google Scholar 

  13. Cheng, K.C.K., Yap, R.H.C.: Maintaining Generalized Arc Consistency on Ad-Hoc n-Ary Boolean Constraints. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) European Conference on Artificial Intelligence. Frontiers in Artificial Intelligence and Applications, vol. 141, pp. 78–82. IOS Press (2006)

    Google Scholar 

  14. Cimatti, A., Sebastiani, R. (eds.): SAT 2012. LNCS, vol. 7317, pp. 2012–2015. Springer, Heidelberg (2012)

    MATH  Google Scholar 

  15. Davies, J., Bacchus, F.: Exploiting the Power of mip Solvers in maxsat. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 166–181. Springer, Heidelberg (2013)

    Google Scholar 

  16. Davies, J., Bacchus, F.: Postponing Optimization to Speed Up MAXSAT Solving. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 247–262. Springer, Heidelberg (2013)

    Google Scholar 

  17. Debruyne, R.: Arc-Consistency in Dynamic CSPs Is No More Prohibitive. In: International Conference on Tools with Artificial Intelligence, pp. 299–307. IEEE (1996)

    Google Scholar 

  18. Dechter, R., Dechter, A.: Belief Maintenance in Dynamic Constraint Networks. In: Shrobe, H.E., Mitchell, T.M., Smith, R.G. (eds.) AAAI Conference on Artificial Intelligence, pp. 37–42. AAAI Press / The MIT Press (1988)

    Google Scholar 

  19. Dutertre, B., de Moura, L.M.: A Fast Linear-Arithmetic Solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)

    Google Scholar 

  20. Eén, N., Sörensson, N.: Translating Pseudo-Boolean Constraints into SAT. Journal on Satisfiability, Boolean Modeling and Computation 2, 1–26 (2006)

    MATH  Google Scholar 

  21. Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)

    Google Scholar 

  22. Eén, N., Sörensson, N.: Temporal induction by incremental SAT solving. Electronic Notes in Theoretical Computer Science 89(4), 543–560 (2003)

    Google Scholar 

  23. Fu, Z., Malik, S.: On Solving the Partial MAX-SAT Problem. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 252–265. Springer, Heidelberg (2006)

    Google Scholar 

  24. Graça, A., Lynce, I., Marques-Silva, J., Oliveira, A.L.: Efficient and Accurate Haplotype Inference by Combining Parsimony and Pedigree Information. In: Horimoto, K., Nakatsui, M., Popov, N. (eds.) ANB 2010. LNCS, vol. 6479, pp. 38–56. Springer, Heidelberg (2012)

    Google Scholar 

  25. Heras, F., Morgado, A., Marques-Silva, J.: Core-guided binary search algorithms for maximum satisfiability. In: Burgard, W., Roth, D. (eds.) AAAI Conference on Artificial Intelligence. AAAI Press (2011)

    Google Scholar 

  26. Hooker, J.N.: Solving the incremental satisfiability problem. Journal of Logic Programming 15(1&2), 177–186 (1993)

    MATH  MathSciNet  Google Scholar 

  27. Jose, M., Majumdar, R.: Cause clue clauses: error localization using maximum satisfiability. In: Hall, M.W., Padua, D.A. (eds.) Programming Language Design and Implementation, pp. 437–446. ACM (2011)

    Google Scholar 

  28. Kadioglu, S., Malitsky, Y., Sellmann, M.: Non-Model-Based Search Guidance for Set Partitioning Problems. In: Hoffmann, J., Selman, B. (eds.) AAAI Conference on Artificial Intelligence. AAAI Press (2012)

    Google Scholar 

  29. Koshimura, M., Zhang, T., Fujita, H., Hasegawa, R.: QMaxSAT: A Partial Max-SAT Solver. Journal on Satisfiability, Boolean Modeling and Computation 8, 95–100 (2012)

    MathSciNet  Google Scholar 

  30. Kullmann, O. (ed.): SAT 2009. LNCS, vol. 5584. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  31. Lagerkvist, M.Z., Schulte, C.: Advisors for Incremental Propagation. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 409–422. Springer, Heidelberg (2007)

    Google Scholar 

  32. Le Berre, D., Parrain, A.: The Sat4j library, release 2.2. Journal on Satisfiability, Boolean Modeling and Computation 7(2-3), 59–66 (2010)

    Google Scholar 

  33. Li, C.M., Manyà, F.: MaxSAT, Hard and Soft Constraints. In: Handbook of Satisfiability, pp. 613–631. IOS Press (2009)

    Google Scholar 

  34. Liffiton, M.H., Sakallah, K.A.: Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints. Journal Automated Reasoning 40(1), 1–33 (2008)

    MATH  MathSciNet  Google Scholar 

  35. Lonsing, F., Egly, U.: Incremental QBF Solving. Computing Research Repository - arXiv abs/1402.2410 (2014)

    Google Scholar 

  36. Mahajan, Y.S., Fu, Z., Malik, S.: Zchaff2004: An efficient sat solver. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 360–375. Springer, Heidelberg (2005)

    Google Scholar 

  37. Manolios, P., Papavasileiou, V.: Pseudo-Boolean Solving by incremental translation to SAT. In: Bjesse, P., Slobodová, A. (eds.) International Conference on Formal Methods in Computer-Aided Design, pp. 41–45. FMCAD Inc. (2011)

    Google Scholar 

  38. Manquinho, V., Marques-Silva, J., Planes, J.: Algorithms for Weighted Boolean Optimization. In: Kullmann (ed.) [30], pp. 495–508

    Google Scholar 

  39. Marin, P., Miller, C., Lewis, M.D.T., Becker, B.: Verification of partial designs using incremental QBF solving. In: Rosenstiel, W., Thiele, L. (eds.) Design, Automation, and Test in Europe Conference, pp. 623–628. IEEE (2012)

    Google Scholar 

  40. Marques-Silva, J., Planes, J.: On using unsatisfiability for solving Maximum Satisfiability. Tech. rep., Computing Research Repository, abs/0712.0097 (2007)

    Google Scholar 

  41. Martins, R., Manquinho, V., Lynce, I.: Parallel Search for Maximum Satisfiability. AI Communications 25(2), 75–95 (2012)

    MathSciNet  Google Scholar 

  42. 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, Heidelberg (2014)

    Google Scholar 

  43. Morgado, A., Heras, F., Liffiton, M., Planes, J., Marques-Silva, J.: Iterative and core-guided MaxSAT solving: A survey and assessment. Constraints 18(4), 478–534 (2013)

    MathSciNet  Google Scholar 

  44. Morgado, A., Heras, F., Marques-Silva, J.: Improvements to Core-Guided Binary Search for MaxSAT. In: Cimatti, Sebastiani (eds.) [14], pp. 284–297

    Google Scholar 

  45. Nadel, A., Ryvchin, V.: Efficient SAT Solving under Assumptions. In: Cimatti, Sebastiani (eds.) [14], pp. 242–255

    Google Scholar 

  46. Sinz, C.: Towards an Optimal CNF Encoding of Boolean Cardinality Constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005)

    Google Scholar 

  47. Shtrichman, O.: Pruning Techniques for the SAT-Based Bounded Model Checking Problem. In: Margaria, T., Melham, T.F. (eds.) CHARME 2001. LNCS, vol. 2144, pp. 58–70. Springer, Heidelberg (2001)

    Google Scholar 

  48. van Beek, P.: Backtracking Search Algorithms. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, ch. 4. Elsevier (2006)

    Google Scholar 

  49. van Hoeve, W.J., Katriel, I.: Global constraints. In: Rossi, F., van Beek, P., Walsh, T. (eds.) Handbook of Constraint Programming, ch. 6. Elsevier (2006)

    Google Scholar 

  50. Whittemore, J., Kim, J., Sakallah, K.A.: SATIRE: A New Incremental Satisfiability Engine. In: Design Automation Conference, pp. 542–545. ACM (2001)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Oxford, UK

    Ruben Martins & Saurabh Joshi

  2. INESC-ID / Instituto Superior Técnico, Universidade de Lisboa, Portugal

    Vasco Manquinho & Inês Lynce

Authors
  1. Ruben Martins
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  2. Saurabh Joshi
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  3. Vasco Manquinho
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  4. Inês Lynce
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Editors and Affiliations

  1. Insight Centre for Data Analytics, School of Computer Science and IT, University College Cork, Western Road, Cork, Ireland

    Barry O’Sullivan

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Martins, R., Joshi, S., Manquinho, V., Lynce, I. (2014). Incremental Cardinality Constraints for MaxSAT. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_39

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  • DOI: https://doi.org/10.1007/978-3-319-10428-7_39

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10427-0

  • Online ISBN: 978-3-319-10428-7

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