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International Symposium on Parameterized and Exact Computation

IPEC 2012: Parameterized and Exact Computation pp 37–48Cite as

A New Algorithm for Parameterized MAX-SAT

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7535))

Abstract

We show how to check whether at least k clauses of an input formula in CNF can be satisfied in time O *(1.358k). This improves the bound O *(1.370k) proved by Chen and Kanj more than 10 years ago. Though the presented algorithm is based on standard splitting techniques its core are new simplification rules that often allow to reduce the size of case analysis. Our improvement is based on a simple algorithm for a special case of MAX-SAT where each variable appears at most 3 times.

Research is partially supported by Federal Target Program “Scientific and scientific-pedagogical personnel of the innovative Russia” 2009–2013 and Russian Foundation for Basic Research.

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References

  1. Chen, J., Kanj, I.A.: Improved Exact Algorithms for MAX-SAT. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 341–355. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Mahajan, M., Raman, V.: Parameterizing above guaranteed values: MaxSat and MaxCut. J. Algorithms 31(2), 335–354 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Niedermeier, R., Rossmanith, P.: New Upper Bounds for MaxSat. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 575–584. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  4. Bansal, N., Raman, V.: Upper Bounds for MaxSat: Further Improved. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 247–258. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Alon, N., Gutin, G., Kim, E., Szeider, S., Yeo, A.: Solving MAX-r-SAT Above a Tight Lower Bound. Algorithmica 61, 638–655 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Crowston, R., Gutin, G., Jones, M., Yeo, A.: A New Lower Bound on the Maximum Number of Satisfied Clauses in Max-SAT and Its Algorithmic Applications. Algorithmica 64(1), 56–68 (2012)

    Article  MathSciNet  Google Scholar 

  7. van Rooij, J.M., Bodlaender, H.L.: Exact algorithms for dominating set. Discrete Applied Mathematics 159(17), 2147–2164 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kulikov, A., Kutzkov, K.: New Bounds for MAX-SAT by Clause Learning. In: Diekert, V., Volkov, M.V., Voronkov, A. (eds.) CSR 2007. LNCS, vol. 4649, pp. 194–204. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Bliznets: A New Upper Bound for (n,3)-MAX-SAT. Zapiski Nauchnikh Seminarov POMI, 5–14 (2012)

    Google Scholar 

  10. Lieberherr, K.J., Specker, E.: Complexity of Partial Satisfaction. J. ACM 28, 411–421 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yannakakis, M.: On the approximation of maximum satisfiability. In: SODA 1992, pp. 1–9 (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. St. Petersburg University of the Russian Academy of Sciences, St. Petersburg, Russia

    Ivan Bliznets & Alexander Golovnev

Authors
  1. Ivan Bliznets
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  2. Alexander Golovnev
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Editor information

Editors and Affiliations

  1. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece

    Dimitrios M. Thilikos

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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© 2012 Springer-Verlag Berlin Heidelberg

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Bliznets, I., Golovnev, A. (2012). A New Algorithm for Parameterized MAX-SAT. In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33293-7_6

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  • DOI: https://doi.org/10.1007/978-3-642-33293-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33292-0

  • Online ISBN: 978-3-642-33293-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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