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International Conference on Combinatorial Optimization and Applications

COCOA 2017: Combinatorial Optimization and Applications pp 94–108Cite as

An Improved Branching Algorithm for (n, 3)-MaxSAT Based on Refined Observations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10628))

Abstract

In the MaxSAT problem, we are given a CNF formula (conjunctive normal form) and seek an assignment satisfying the maximum number of clauses. In the parameterized (n, 3)-MaxSAT problem we are given an integer k and a CNF formula such that each variable appears in at most 3 clauses, and are asked to find an assignment that satisfies at least k clauses. Based on refined observations, we propose a branching algorithm for the (n, 3)-MaxSAT problem with significant improvement over the previous results. More precisely, the running time of our algorithm can be bounded by \(O^*(1.175^k)\) and \(O^*(1.194^n)\), respectively, where n is the number of variables in the given CNF formula. Prior to our study, the running time of the best known exact algorithm can be bounded by \(O^*(1.194^k)\) and \(O^*(1.237^n)\), respectively.

This work is supported by the National Natural Science Foundation of China (Grants No. 61672536, 61502054, 61702557, 61420106009), the Natural Science Foundation of Hunan Province, China (Grant No. 2017JJ3333), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 17C0047), and the China Postdoctoral Science Foundation (Grant No. 2017M612584).

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References

  1. Argelich, J., Manyà, F.: Exact Max-SAT solvers for over-constrained problems. J. Heuristics 12(4–5), 375–392 (2006)

    Article  MATH  Google Scholar 

  2. Bansal, N., Raman, V.: Upper bounds for MaxSat: further improved. ISAAC 1999. LNCS, vol. 1741, pp. 247–258. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-46632-0_26

    Chapter  Google Scholar 

  3. Berg, J., Hyttinen, A., Jrvisalo, M.: Applications of MaxSAT in data analysis. In: Pragmatics of SAT Workshop (2015)

    Google Scholar 

  4. Bliznets, I., Golovnev, A.: A new algorithm for parameterized MAX-SAT. In: Thilikos, D.M., Woeginger, G.J. (eds.) IPEC 2012. LNCS, vol. 7535, pp. 37–48. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33293-7_6

    Chapter  Google Scholar 

  5. Bliznets, I.A.: A new upper bound for \((n, 3)\)-MAX-SAT. J. Math. Sci. 188(1), 1–6 (2013)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen, J., Kanj, I.A.: Improved exact algorithms for Max-Sat. Discret. Appl. Math. 142(1–3), 17–27 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, J., Kanj, I.A., Xia, G.: Improved upper bounds for vertex cover. Theoret. Comput. Sci. 411(40–42), 3736–3756 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  9. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fomin, F.V., Kratsch, D.: Exact exponential algorithms. In: Texts in Theoretical Computer Science. An EATCS Series, Chap. 2, pp. 13–30. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16533-7

  11. Hochbaum, D.: Approximation Algorithms for NP-Hard Problems. PWS Publishing Company, Boston (1997)

    MATH  Google Scholar 

  12. Hutter, F., Lindauer, M., Balint, A., Bayless, S., Hoos, H., Leyton-Brown, K.: The Configurable SAT Solver Challenge (CSSC). Artif. Intell. 243, 1–25 (2017)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kulikov, A.S.: Automated generation of simplification rules for SAT and MAXSAT. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 430–436. Springer, Heidelberg (2005). https://doi.org/10.1007/11499107_35

    Chapter  Google Scholar 

  14. Lokshtanov, D.: New methods in parameterized algorithms and complexity. Ph.D. thesis, University of Bergen (2009)

    Google Scholar 

  15. Niedermeier, R., Rossmanith, P.: New upper bounds for maximum satisfiability. J. Algorithms 36(1), 63–88 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. 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)

    Article  MATH  MathSciNet  Google Scholar 

  17. Raman, V., Ravikumar, B., Rao, S.S.: A simplified NP-complete MAXSAT problem. Inf. Process. Lett. 65(1), 1–6 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  18. Saikko, P., Malone, B., Järvisalo, M.: MaxSAT-based cutting planes for learning graphical models. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 347–356. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18008-3_24

    Google Scholar 

  19. Shen, H., Zhang, H.: Improving exact algorithms for MAX-2-SAT. Ann. Math. Artif. Intell. 44(4), 419–436 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. Xiao, M., Nagamochi, H.: An exact algorithm for maximum independent set in degree-5 graphs. Discret. Appl. Math. 199, 137–155 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  21. Xu, C., Chen, J., Wang, J.: Resolution and linear CNF formulas: improved \((n, 3)\)-MaxSAT algorithms. Theor. Comput. Sci. (2016)

    Google Scholar 

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Authors and Affiliations

  1. Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation, Changsha University of Science and Technology, Changsha, China

    Wenjun Li

  2. School of Information Science and Engineering, Central South University, Changsha, China

    Chao Xu, Jianxin Wang & Yongjie Yang

  3. Chair of Economic Theory, Universität des Saarlandes, Saarbrücken, Germany

    Yongjie Yang

Authors
  1. Wenjun Li
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  2. Chao Xu
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  3. Jianxin Wang
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  4. Yongjie Yang
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Correspondence to Yongjie Yang .

Editor information

Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Li, W., Xu, C., Wang, J., Yang, Y. (2017). An Improved Branching Algorithm for (n, 3)-MaxSAT Based on Refined Observations. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-71147-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71146-1

  • Online ISBN: 978-3-319-71147-8

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