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Algorithms for Weighted Boolean Optimization

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Theory and Applications of Satisfiability Testing - SAT 2009 (SAT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5584))

Abstract

The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT, despite the existence of straightforward mappings from PBO to MaxSAT, and vice-versa. This papers proposes Weighted Boolean Optimization (WBO), a new unified framework that aggregates and extends PBO and MaxSAT. In addition, the paper proposes a new unsatisfiability-based algorithm for WBO, based on recent unsatisfiability-based algorithms for MaxSAT. Besides standard MaxSAT, the new algorithm can also be used to solve weighted MaxSAT and PBO, handling pseudo-Boolean constraints either natively or by translation to clausal form. Experimental results illustrate that unsatisfiability-based algorithms for MaxSAT can be orders of magnitude more efficient than existing dedicated algorithms. Finally, the paper illustrates how other algorithms for either PBO or MaxSAT can be extended to WBO.

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References

  1. Aloul, F., Ramani, A., Markov, I., Sakallah, K.A.: Generic ILP versus specialized 0-1 ILP: An update. In: International Conference on Computer-Aided Design, pp. 450–457 (2002)

    Google Scholar 

  2. Amgoud, L., Cayrol, C., Berre, D.L.: Comparing arguments using preference ordering for argument-based reasoning. In: International Conference on Tools with Artificial Intelligence, pp. 400–403 (1996)

    Google Scholar 

  3. Argelich, J., Li, C.M., Manà, F.: An improved exact solver for partial max-sat. In: International Conference on Nonconvex Programming: Local and Global Approaches, pp. 230–231 (2007)

    Google Scholar 

  4. Argelich, J., Li, C.M., Manyà, F., Planes, J.: Third Max-SAT evaluation (2008), http://www.maxsat.udl.cat/08/

  5. Bailleux, O., Boufkhad, Y., Roussel, O.: A translation of pseudo Boolean constraints to SAT. Journal on Satisfiability, Boolean Modeling and Computation 2, 191–200 (2006)

    MATH  Google Scholar 

  6. Barth, P.: A Davis-Putnam Enumeration Algorithm for Linear Pseudo-Boolean Optimization. Technical Report MPI-I-95-2-003, Max Plank Institute for Computer Science (1995)

    Google Scholar 

  7. Berre, D.L.: SAT4J library, http://www.sat4j.org

  8. Biere, A.: PicoSAT essentials. Journal on Satisfiability, Boolean Modeling and Computation 2, 75–97 (2008)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Borchers, B., Furman, J.: A two-phase exact algorithm for MAX-SAT and weighted MAX-SAT problems. Journal of Combinatorial Optimization 2, 299–306 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chai, D., Kuehlmann, A.: A fast pseudo-Boolean constraint solver. In: Design Automation Conference, pp. 830–835 (2003)

    Google Scholar 

  12. Coudert, O.: On Solving Covering Problems. In: Design Automation Conference, pp. 197–202 (1996)

    Google Scholar 

  13. Darras, S., Dequen, G., Devendeville, L., Li, C.M.: On inconsistent clause-subsets for Max-SAT solving. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 225–240. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Edmonds, J.: Paths, trees and flowers. Canadian Journal of Mathematics 17, 449–467 (1965)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  16. 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)

    Chapter  Google Scholar 

  17. Heras, F., Larrosa, J., Oliveras, A.: MiniMaxSat: a new weighted Max-SAT solver. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 41–55. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Heras, F., Larrosa, J., Oliveras, A.: MiniMaxSAT: An efficient weighted Max-SAT solver. Journal of Artificial Intelligence Research 31, 1–32 (2008)

    MathSciNet  MATH  Google Scholar 

  19. Larrosa, J., Heras, F., de Givry, S.: A logical approach to efficient Max-SAT solving. Artificial Intelligence 172(2-3), 204–233 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  21. Liao, S., Devadas, S.: Solving Covering Problems Using LPR-Based Lower Bounds. In: Design Automation Conference, pp. 117–120 (1997)

    Google Scholar 

  22. Lin, H., Su, K.: Exploiting inference rules to compute lower bounds for MAX-SAT solving. In: International Joint Conference on Artificial Intelligence, pp. 2334–2339 (2007)

    Google Scholar 

  23. Manquinho, V., Marques-Silva, J.: Search pruning techniques in SAT-based branch-and-bound algorithms for the binate covering problem. IEEE Transactions on Computer-Aided Design 21(5), 505–516 (2002)

    Article  Google Scholar 

  24. Manquinho, V., Marques-Silva, J.: Effective lower bounding techniques for pseudo-boolean optimization. In: Design, Automation and Test in Europe Conference, pp. 660–665 (2005)

    Google Scholar 

  25. Marques-Silva, J., Manquinho, V.: Towards more effective unsatisfiability-based maximum satisfiability algorithms. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 225–230. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  26. Marques-Silva, J., Planes, J.: On using unsatisfiability for solving maximum satisfiability. Computing Research Repository, abs/0712.0097 (December 2007)

    Google Scholar 

  27. Marques-Silva, J., Planes, J.: Algorithms for maximum satisfiability using unsatisfiable cores. In: Design, Automation and Testing in Europe Conference, pp. 408–413 (2008)

    Google Scholar 

  28. Nieuwenhuis, R., Oliveras, A.: On SAT modulo theories and optimization problems. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 156–169. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  29. Pipatsrisawat, K., Palyan, A., Chavira, M., Choi, A., Darwiche, A.: Solving weighted Max-SAT problems in a reduced search space: A performance analysis. Journal on Satisfiability Boolean Modeling and Computation (JSAT) 4, 191–217 (2008)

    MATH  Google Scholar 

  30. Ramírez, M., Geffner, H.: Structural relaxations by variable renaming and their compilation for solving MinCostSAT. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 605–619. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  31. Safarpour, S., Mangassarian, H., Veneris, A., Liffiton, M.H., Sakallah, K.A.: Improved design debugging using maximum satisfiability. In: Formal Methods in Computer-Aided Design (2007)

    Google Scholar 

  32. Sheini, H., Sakallah, K.A.: Pueblo: A hybrid pseudo-Boolean SAT solver. Journal on Satisfiability, Boolean Modeling and Computation 2, 165–189 (2006)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  34. Xu, H., Rutenbar, R.A., Sakallah, K.A.: sub-SAT: a formulation for relaxed boolean satisfiability with applications in routing. IEEE Transactions on CAD of Integrated Circuits and Systems 22(6), 814–820 (2003)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. IST/UTL - INESC-ID, Portugal

    Vasco Manquinho

  2. University College Dublin, Ireland

    Joao Marques-Silva

  3. Universitat de Lleida, Spain

    Jordi Planes

Authors
  1. Vasco Manquinho
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  2. Joao Marques-Silva
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  3. Jordi Planes
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Editor information

Editors and Affiliations

  1. Computer Science Department, Swansea University, Faraday Building, Singleton Park, SA2 8PP, Swansea, UK

    Oliver Kullmann

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Manquinho, V., Marques-Silva, J., Planes, J. (2009). Algorithms for Weighted Boolean Optimization. In: Kullmann, O. (eds) Theory and Applications of Satisfiability Testing - SAT 2009. SAT 2009. Lecture Notes in Computer Science, vol 5584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02777-2_45

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  • DOI: https://doi.org/10.1007/978-3-642-02777-2_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02776-5

  • Online ISBN: 978-3-642-02777-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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