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Counting Satisfying Assignments in 2-SAT and 3-SAT

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Book cover Computing and Combinatorics (COCOON 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2387))

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Abstract

We present an O(1.3247n) algorithm for counting the number of satisfying assignments for instances of 2-SAT and an O(1.6894n) algorithm for instances of 3-SAT. This is an improvement compared to the previously best known algorithms running in O(1.381n) and O(1.739n) time, respectively.

The research is supported by CUGS — National Graduate School in Computer Science, Sweden.

The research is partially supported by the Swedish Research Council (VR) under grant 221-2000-361.

The research is supported by CUGS — National Graduate School in Computer Science, Sweden.

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References

  1. R. J. Bayardo, Jr. and J. Pehoushek. Counting models using connected components. In Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI-2000), pages 157–162. AAAI Press, 2000.

    Google Scholar 

  2. E. Birnbaum and E. L. Lozinskii. The good old Davis-Putnam procedure helps counting models. Journal of Artificial Intelligence Research, 10:457–477, 1999.

    MATH  MathSciNet  Google Scholar 

  3. V. Dahllöf and P. Jonsson. An algorithm for counting maximum weighted independent sets and its applications. In Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-2002), pages 292–298, 2002.

    Google Scholar 

  4. O. Dubois. Counting the number of solutions for instances of satisfiability. Theoretical Computer Science, 81(1):49–64, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Goldberg and M. Jerrum. Counting unlabelled subtrees of a tree is #P-complete. LMS Journal of Computation and Mathematics, 3:117–124, 2000.

    MATH  MathSciNet  Google Scholar 

  6. R. L. Graham, D. E. Knuth, and O. Patashnik. Concrete Mathematics. Addison-Wesley, Reading, MA, USA, second edition, 1994.

    MATH  Google Scholar 

  7. C. S. Greenhill. The complexity of counting colourings and independent sets in sparse graphs and hypergraphs. Computational Complexity, 9(1):52–72, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  8. H. B. Hunt III, M. V. Marathe, V. Radhakrishnan, and R. E. Stearns. The complex-ity of planar counting problems. SIAM Journal on Computing, 27(4):1142–1167, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  9. D. Kozen. The design and analysis of algorithms. Springer-Verlag, 1992.

    Google Scholar 

  10. M. L. Littman, T. Pitassi, and R. Impagliazzo. On the complexity of counting satisfying assignments. Unpublished manuscript.

    Google Scholar 

  11. D. Roth. On the hardness of approximate reasoning. Artificial Intelligence, 82(1–2):273–302, 1996.

    Article  MathSciNet  Google Scholar 

  12. S. P. Vadhan. The complexity of counting in sparse, regular, and planar graphs. SIAM Journal on Computing, 31(2):398–427, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  13. L. Valiant. The complexity of enumeration and reliability problems. SIAM Journal on Computing, 8(3):410–421, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  14. W. Zhang. Number of models and satisfiability of sets of clauses. Theoretical Computer Science, 155(1):277–288, 1996.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, Linköping University, SE-581 83, Linköping, Sweden

    Vilhelm Dahllöf, Peter Jonsson & Magnus Wahlström

Authors
  1. Vilhelm Dahllöf
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  2. Peter Jonsson
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  3. Magnus Wahlström
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, California, 93106, USA

    Oscar H. Ibarra

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore, 117543

    Louxin Zhang

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© 2002 Springer-Verlag Berlin Heidelberg

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Dahllöf, V., Jonsson, P., Wahlström, M. (2002). Counting Satisfying Assignments in 2-SAT and 3-SAT. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_57

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  • DOI: https://doi.org/10.1007/3-540-45655-4_57

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43996-7

  • Online ISBN: 978-3-540-45655-1

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