Skip to main content
SpringerLink
Log in

Parallel Maximum Satisfiability

  • Chapter
  • First Online:
Handbook of Parallel Constraint Reasoning

Abstract

Developments in parallel Boolean Satisfiability (SAT) have motivated developments in parallel Maximum Satisfiability (MaxSAT), where MaxSAT is the optimization counterpart of SAT. Although many of the techniques implemented in parallel SAT can be extended to parallel MaxSAT, additional techniques are required to deal with the optimization part. This chapter provides an overview of the state of the art in parallel Maximum Satisfiability. The required background is first provided, namely the characteristics of the different MaxSAT algorithms. Solutions to parallel MaxSAT solving include portfolio approaches and search space splitting. Clause sharing is a key issue and so conditions for safe clause sharing are described. Deterministic parallel MaxSAT is another contribution in the field, having the additional challenge of synchronization strategies. Finally, future research directions are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Achá, R.J.A., Nieuwenhuis, R.: Curriculum-based course timetabling with SAT and MaxSAT. Annals of Operations Research 218(1), 71–91 (2014)

    Google Scholar 

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

    Google Scholar 

  3. Ansótegui, C., Bonet, M.L., Gabàs, J., Levy, J.: Improving WPM2 for (Weighted) Partial MaxSAT. In: Proc. International Conference on Principles and Practice of Constraint Programming, pp. 117–132. Springer (2013)

    Google Scholar 

  4. Ansótegui, C., Bonet, M.L., Levy, J.: On Solving MaxSAT Through SAT. In: Proc. International Conference of the Catalan Association for Artificial Intelligence, pp. 284–292. IOS Press (2009)

    Google Scholar 

  5. Ansótegui, C., Bonet, M.L., Levy, J.: Solving (Weighted) Partial MaxSAT through Satisfiability Testing. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 427–440. Springer (2009)

    Google Scholar 

  6. Ansótegui, C., Bonet, M.L., Levy, J.: A New Algorithm for Weighted Partial MaxSAT. In: Proc. AAAI Conference on Artificial Intelligence, pp. 3–8. AAAI Press (2010)

    Google Scholar 

  7. Ansótegui, C., Gabàs, J.: Solving (Weighted) Partial MaxSAT with ILP. In: Proc. International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, pp. 403–409. Springer (2013)

    Google Scholar 

  8. Ansótegui, C., Manyà, F.: Mapping problems with finite-domain variables into problems with Boolean variables. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 1–15. Springer (2004)

    Google Scholar 

  9. 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. Conference Proceedings (2010)

    Google Scholar 

  10. Argelich, J., Li, C.M., Manyà, F.: An improved exact solver for Partial Max-SAT. In: Proc. of the International Conference on Nonconvex Programming: Local and Global Approaches, pp. 230–231. Conference Proceedings (2007)

    Google Scholar 

  11. Argelich, J., Manyà, F.: Partial Max-SAT Solvers with Clause Learning. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 28–40. Springer (2007)

    Google Scholar 

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

    Google Scholar 

  13. Audemard, G., Hoessen, B., Jabbour, S., Lagniez, J.M., Piette, C.: Revisiting Clause Exchange in Parallel SAT Solving. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 200–213. Springer (2012)

    Google Scholar 

  14. Audemard, G., Lagniez, J.M., Mazure, B., Sais, L.: On Freezing and Reactivating Learnt Clauses. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 188–200. Springer (2011)

    Google Scholar 

  15. Audemard, G., Simon, L.: Predicting Learnt Clauses Quality in Modern SAT Solvers. In: Proc. International Joint Conferences on Artificial Intelligence, pp. 399–404. IJCAI/AAAI Press (2009)

    Google Scholar 

  16. Bailleux, O., Boufkhad, Y.: Efficient CNF Encoding of Boolean Cardinality Constraints. In: Proc. International Conference on Principles and Practice of Constraint Programming, pp. 108–122. Springer (2003)

    Google Scholar 

  17. Bailleux, O., Boufkhad, Y., Roussel, O.: New Encodings of Pseudo-Boolean Constraints into CNF. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 181–194. Springer (2009)

    Google Scholar 

  18. Berre, D.L., Parrain, A.: The Sat4j library, release 2.2. JSAT 7(2-3), 59–6 (2010)

    Google Scholar 

  19. Bjørner, N., Phan, A., Fleckenstein, L.: \( {\nu Z} \) - An Optimizing SMT Solver. In: Proc. Tools and Algorithms for Construction and Analysis of Systems, pp. 194–199. Springer (2015)

    Google Scholar 

  20. Böhm, M., Speckenmeyer, E.: A Fast Parallel SAT-Solver - Efficient Workload Balancing. Annals of Mathematics and Artificial Intelligence 17, 381–400 (1996)

    Google Scholar 

  21. Bonet, M.L., Levy, J., Manyà, F.: Resolution for Max-SAT. Artificial Intelligence 171(8–9), 606–618 (2007)

    Google Scholar 

  22. 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 

  23. Darras, S., Dequen, G., Devendevill, L., Li, C.M.: On Inconsistent Clause-Subsets for Max-SAT Solving. In: Proc. International Conference on Principles and Practice of Constraint Programming, pp. 225–240. Springer (2007)

    Google Scholar 

  24. Davies, J., Bacchus, F.: Solving MAXSAT by Solving a Sequence of Simpler SAT Instances. In: Proc. International Conference on Principles and Practice of Constraint Programming, pp. 225–239. Springer (2011)

    Google Scholar 

  25. Davies, J., Bacchus, F.: Postponing optimization to speed up MAXSAT solving. In: Proc. International Conference on Principles and Practice of Constraint Programming, pp. 247–262. Springer (2013)

    Google Scholar 

  26. Eén, N., Sörensson, N.: An extensible SAT-solver. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 502–518. Springer (2003)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  29. Feng, Y., Bastani, O., Martins, R., Dillig, I., Anand, S.: Automated Synthesis of Semantic Malware Signatures using Maximum Satisfiability. In: Network and Distributed System Security Symposium. The Internet Society (2017)

    Google Scholar 

  30. Frisch, A.M., Peugniez, T.J., Doggett, A.J., Nightingale, P.: Solving Non-Boolean Satisfiability Problems with Stochastic Local Search: A Comparison of Encodings. Journal of Automated Reasoning 35(1-3), 143–179 (2005)

    Google Scholar 

  31. Fu, Z., Malik, S.: On solving the partial MAX-SAT problem. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 252–265. Springer (2006)

    Google Scholar 

  32. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)

    Google Scholar 

  33. Gent, I.P., Nightingale, P.: A new encoding of All Different into SAT. In: International Workshop on Modelling and Reformulating Constraint Satisfaction Problems. Conference Proceedings (2004)

    Google Scholar 

  34. Graça, A., Lynce, I., Marques-Silva, J., Oliveira, A.L.: Efficient and Accurate Haplotype Inference by Combining Parsimony and Pedigree Information. In: Algebraic and Numeric Biology, pp. 38–56. Springer (2010)

    Google Scholar 

  35. Hamadi, Y., Jabbour, S., Piette, C., Sais, L.: Deterministic Parallel DPLL. Journal on Satisfiability, Boolean Modeling and Computation 7(4), 127–132 (2011)

    Google Scholar 

  36. Hamadi, Y., Jabbour, S., Sais, L.: Control-Based Clause Sharing in Parallel SAT Solving. In: Proc. International Joint Conferences on Artificial Intelligence, pp. 499–504. IJCAI/AAAI Press (2009)

    Google Scholar 

  37. Hamadi, Y., Jabbour, S., Sais, L.: ManySAT: a Parallel SAT Solver. Journal on Satisfiability, Boolean Modeling and Computation 6(4), 245–262 (2009)

    Google Scholar 

  38. Heras, F., Morgado, A., Marques-Silva, J.: Core-Guided Binary Search Algorithms for Maximum Satisfiability. In: Proc. AAAI Conference on Artificial Intelligence, pp. 36–41. AAAI Press (2011)

    Google Scholar 

  39. Heule, M.J., Kullmann, O.,Wieringa, S., Biere, A.: Cube and Conquer: Guiding CDCL SAT Solvers by Lookaheads. In: Hardware and Software: Verification and Testing, pp. 50–65. Springer (2012)

    Google Scholar 

  40. Hölldobler, S., Manthey, N., Steinke, P.: A compact encoding of pseudo-Boolean constraints into SAT. In: KI 2013: Advances in Artificial Intelligence, pp. 107–118. Springer (2012)

    Google Scholar 

  41. Jose, M., Majumdar, R.: Cause clue clauses: error localization using maximum satisfiability. In: Proc. Conference on Programming Language Design and Implementation, pp. 437–446. ACM Press (2011)

    Google Scholar 

  42. Joshi, S., Martins, R., Manquinho, V.: Generalized Totalizer Encoding for Pseudo-Boolean Constraints. In: International Conference on Principles and Practice of Constraint Programming, pp. 200–209. Springer (2015)

    Google Scholar 

  43. Klieber, W., Kwon, G.: Efficient CNF Encoding for Selecting 1 from N Objects. In: International Workshop on Constraints in Formal Verification. Conference Proceedings (2007)

    Google Scholar 

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

    Google Scholar 

  45. Li, C.M., Manyà, F., Planes, J.: Exploiting unit propagation to compute lower bounds in branch and bound Max-SAT solvers. In: Proc. International Conference on Principles and Practice of Constraint Programming, pp. 403–414. Springer (2005)

    Google Scholar 

  46. Li, C.M., Manyà, F., Planes, J.: New inference rules for Max-SAT. Journal of Artificial Intelligence Research 30, 321–359 (2007)

    Google Scholar 

  47. Lin, H., Su, K.: Exploiting inference rules to compute lower bounds for MAXSAT solving. In: Proc. International Joint Conferences on Artificial Intelligence, pp. 2334–2339. IJCAI/AAAI Press (2007)

    Google Scholar 

  48. Lin, H., Su, K., Li, C.M.: Within-problem Learning for Efficient Lower Bound Computation in Max-SAT Solving. In: Proc. AAAI Conference on Artificial Intelligence, pp. 351–356. AAAI Press (2008)

    Google Scholar 

  49. Mancinelli, F., Boender, J., Cosmo, R.D., Vouillon, J., Durak, B., Leroy, X., Treinen, R.: Managing the Complexity of Large Free and Open Source Package-Based Software Distributions. In: Proc. International Conference on Automated Software Engineering, pp. 199–208. IEEE Computer Society Press (2006)

    Google Scholar 

  50. Manquinho, V., Marques-Silva, J., Planes, J.: Algorithms for Weighted Boolean Optimization. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 495–508. Springer (2009)

    Google Scholar 

  51. Manquinho, V., Martins, R., Lynce, I.: Improving Unsatisfiability-Based Algorithms for Boolean Optimization. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 181–193. Springer (2010)

    Google Scholar 

  52. Marques-Silva, J., Planes, J.: On using unsatisfiability for solving maximum satisfiability. CoRR. http://arXiv.org/abs/0712.1097 (2007)

  53. Marques-Silva, J., Sakallah, K.: GRASP: A New Search Algorithm for Satisfiability. In: Proc. International Conference on Computer-Aided Design, pp. 220–227. IEEE Computer Society Press (1996)

    Google Scholar 

  54. Marques-Silva, J., Sakallah, K.: GRASP: A Search Algorithm for Propositional Satisfiability. IEEE Transactions on Computers 48(5), 506–521 (1999)

    Google Scholar 

  55. Martins, R., Joshi, S., Manquinho, V., Lynce, I.: Incremental Cardinality Constraints for MaxSAT. In: Proc. International Conference on Principles and Practice of Constraint Programming, pp. 531–548. Springer (2014)

    Google Scholar 

  56. Martins, R., Joshi, S., Manquinho, V., Lynce, I.: On Using Incremental Encodings in Unsatisfiability-based MaxSAT Solving. Journal on Satisfiability, Boolean Modeling and Computation 9, 59–81 (2015)

    Google Scholar 

  57. Martins, R., Manquinho, V., Lynce, I.: Exploiting Cardinality Encodings in Parallel Maximum Satisfiability. In: Proc. International Conference on Tools with Artificial Intelligence, pp. 313–320. IEEE Computer Society Press (2011)

    Google Scholar 

  58. Martins, R., Manquinho, V., Lynce, I.: Clause Sharing in Deterministic Parallel Maximum Satisfiability. In: RCRA International Workshop on Experimental Evaluation of Algorithms for solving problems with combinatorial explosion. Conference Proceedings (2012)

    Google Scholar 

  59. Martins, R., Manquinho, V., Lynce, I.: Clause Sharing in Parallel MaxSAT. In: Proc. Learning and Intelligent Optimization Conference, pp. 455–460. Springer (2012)

    Google Scholar 

  60. Martins, R., Manquinho, V., Lynce, I.: On Partitioning for Maximum Satisfiability. In: Proc. European Conference on Artificial Intelligence, pp. 913–914. IOS Press (2012)

    Google Scholar 

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

    Google Scholar 

  62. Martins, R., Manquinho, V., Lynce, I.: Community-based Partitioning for MaxSAT Solving. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 182–191. Springer (2013)

    Google Scholar 

  63. Martins, R., Manquinho, V., Lynce, I.: Deterministic Parallel MaxSAT Solving. International Journal on Artificial Intelligence Tools 24(3) (2015)

    Google Scholar 

  64. Martins, R., Manquinho, V.M., Lynce, I.: Open-WBO: A Modular MaxSAT Solver. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 438–445. Springer (2014)

    Google Scholar 

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

    Google Scholar 

  66. Morgado, A., Ignatiev, A., Marques-Silva, J.: MSCG: Robust Core-Guided MaxSAT Solving. Journal on Satisfiability, Boolean Modeling and Computation 9, 129–134 (2015)

    Google Scholar 

  67. Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Design Automation Conference, pp. 530–535. ACM (2001)

    Google Scholar 

  68. Narodytska, N., Bacchus, F.: Maximum Satisfiability Using Core-Guided MaxSAT Resolution. In: Proc. AAAI Conference on Artificial Intelligence, pp. 2717–2723. AAAI Press (2014)

    Google Scholar 

  69. Neves, M., Lynce, I., Manquinho, V.: DistMS: A Non-Portfolio Distributed Solver for Maximum Satisfiability. In: Proc. International Conference on Tools with Artificial Intelligence. IEEE Computer Society Press (2016)

    Google Scholar 

  70. Neves, M., Martins, R., Janota, M., Lynce, I., Manquinho, V.M.: Exploiting resolution-based representations for MaxSAT solving. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 272–286. Springer (2015)

    Google Scholar 

  71. Ogawa, T., Liu, Y., Hasegawa, R., Koshimura, M., Fujita, H.: Modulo Based CNF Encoding of Cardinality Constraints and Its Application to MaxSAT Solvers. In: Proc. International Conference on Tools with Artificial Intelligence, pp. 9–17. IEEE Computer Society (2013)

    Google Scholar 

  72. Papadimitriou, C.M.: Computational complexity. Addison-Wesley, Reading, Massachusetts (1994)

    Google Scholar 

  73. Plaza, S., Kountanis, I., Andraus, Z., Bertacco, V., Mudge, T.: Advances and Insights into Parallel SAT Solving. In: Internacional Workshop on Logic & Synthesis, pp. 188–194. Conference Proceedings (2006)

    Google Scholar 

  74. Prestwich, S.: Variable Dependency in Local Search: Prevention is Better than Cure. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 107–120. Springer (2007)

    Google Scholar 

  75. Saikko, P., Berg, J., Järvisalo, M.: LMHS: A SAT-IP Hybrid MaxSAT Solver. In: Proc. International Conference on Theory and Applications of Satisfiability Testing, pp. 539–546. Springer (2016)

    Google Scholar 

  76. Schubert, T., Lewis, M., Becker, B.: PaMira - A Parallel SAT Solver with Knowledge Sharing. In: Workshop on Microprocessor Test and Verification, pp. 29–36. Conference Proceedings (2005)

    Google Scholar 

  77. Schubert, T., Lewis, M., Becker, B.: PaMiraXT: Parallel SAT Solving with Threads and Message Passing. Journal on Satisfiability, Boolean Modeling and Computation 6, 203–222 (2009)

    Google Scholar 

  78. Singer, D., Monnet, A.: JaCk-SAT: A New Parallel Scheme to Solve the Satisfiability Problem (SAT) Based on Join-and-Check. In: Proc. Parallel Processing and Applied Mathematics, pp. 249–258. Springer (2008)

    Google Scholar 

  79. Sinz, C.: Towards an Optimal CNF Encoding of Boolean Cardinality Constraints. In: Proc. International Conference on Principles and Practice of Constraint Programming, pp. 827–831. Springer (2005)

    Google Scholar 

  80. Stump, A., Sutcliffe, G., Tinelli, C.: StarExec: A Cross-Community Infrastructure for Logic Solving. In: Proc. International Joint Conference on Automated Reasoning, pp. 367–373. Springer (2014)

    Google Scholar 

  81. Warners, J.P.: A linear-time transformation of linear inequalities into conjunctive normal form. Information Processing Letters 68(2), 63–69 (1998)

    Google Scholar 

  82. Zhang, H., Bonacina, M.P., Hsiang, J.: PSATO: a Distributed Propositional Prover and Its Application to Quasigroup Problems. Journal of Symbolic Computation 21, 543–560 (1996)

    Google Scholar 

  83. Zhang, L., Madigan, C.F., Moskewicz, M.W., Malik, S.: Efficient Conflict Driven Learning in Boolean Satisfiability Solver. In: Proc. International Conference on Computer-Aided Design, pp. 279–285. IEEE Computer Society Press (2001)

    Google Scholar 

Download references

Acknowledgments

This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013.

Author information

Authors and Affiliations

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

    Inês Lynce & Vasco Manquinho

  2. University of Texas at Austin, Austin, USA

    Ruben Martins

Authors
  1. Inês Lynce
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vasco Manquinho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruben Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Inês Lynce .

Editor information

Editors and Affiliations

  1. Laboratoire d'informatique (LIX) de l'École polytechnique, Palaiseau, France

    Youssef Hamadi

  2. CRIL, CNRS UMR 8188, Université d'Artois, Lens, France

    Lakhdar Sais

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Lynce, I., Manquinho, V., Martins, R. (2018). Parallel Maximum Satisfiability. In: Hamadi, Y., Sais, L. (eds) Handbook of Parallel Constraint Reasoning. Springer, Cham. https://doi.org/10.1007/978-3-319-63516-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-63516-3_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63515-6

  • Online ISBN: 978-3-319-63516-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation