Skip to main content
SpringerLink
Log in
Book cover

Annual Symposium on Theoretical Aspects of Computer Science

STACS 2002: STACS 2002 pp 192–202Cite as

A Probabilistic 3—SAT Algorithm Further Improved

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

Abstract

In [Sch99], Schöning proposed a simple yet efficient randomized algorithm for solving the k-SAT problem. In the case of 3-SAT, the algorithm has an expected running time of poly(n)·E(4/3)n = O(1.3334n) when given a formula F on n variables. This was the up to now best running time known for an algorithm solving 3-SAT. Here, we describe an algorithm which improves upon this time bound by combining an improved version of the above randomized algorithm with other randomized algorithms. Our new expected time bound for 3-SAT is O(1.3302n).

Supported in part by DFG grant Sch 302/5-2.

Supported in part by JSPS/NSF cooperative research: Complexity Theory for Strategic Goals, 1998–2001.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Aspvall, M.F. Plass, R.E. Tarjan, A linear-time algorithm for testing the truth of certain quantified Boolean formulas, Information Processing Letters, 8(3), 121–123, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  2. E. Dantsin, A. Goerdt, E.A. Hirsch, and U. Schöning, Deterministic algorithms for k-SAT based on covering codes and local search, in Proc. 27th International Colloquium on Automata, Languages and Programming, ICALP’00, Lecture Notes in Comp. Sci. 1853, 236–247, 2000.

    Google Scholar 

  3. E.A. Hirsch, New worst-case upper bounds for SAT, Journal of Automated Reasoning, 24(4), 397–420, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  4. O. Kullmann, New methods for 3-SAT decision and worst-case analysis, Theoretical Computer Science, 223(1/2), 1–72, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Monien and E. Speckenmeyer, Solving satisfiability in less than 2n steps, Discrete Applied Mathematics, 10, 287–295, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Paturi, P. Pudlák, M.E. Saks, and F. Zane, An improved exponentialtime algorithm for k-SAT, in Proc. of the 39th Ann. IEEE Sympos. on Foundations of Comp. Sci. (FOCS’98), IEEE, 628–637, 1998.

    Google Scholar 

  7. U. Schöning, A probabilistic algorithm for k-SAT and constraint satisfaction problems, in Proc. of the 40th Ann. IEEE Sympos. on Foundations of Comp. Sci. (FOCS’99), IEEE, 410–414, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität Dortmund, Informatik 2, 44221, Dortmund, Germany

    Thomas Hofmeister

  2. Abt. Theoretische Informatik, Universität Ulm, 89069, Oberer Eselsberg, Ulm, Germany

    Uwe Schöning & Rainer Schuler

  3. Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro-ku Ookayama, 152-8552, Tokyo, Japan

    Osamu Watanabe

Authors
  1. Thomas Hofmeister
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Uwe Schöning
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rainer Schuler
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Osamu Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hofmeister, T., Schöning, U., Schuler, R., Watanabe, O. (2002). A Probabilistic 3—SAT Algorithm Further Improved. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-45841-7_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation