Skip to main content
SpringerLink
Log in
Book cover

Italian Conference on Algorithms and Complexity

CIAC 2006: Algorithms and Complexity pp 50–59Cite as

Counting All Solutions of Minimum Weight Exact Satisfiability

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3998))

Abstract

We show that the number of all solutions of minimum weight exact satisfiability can be found in O(n 2.||C||+20.40567 n) time, for a CNF formula C containing n propositional variables equipped with arbitrary real-valued weights. In recent years merely the unweighted counterpart of this problem has been studied [2, 3, 7].

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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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. Aspvall, B., Plass, M.R., Tarjan, R.E.: A linear-time algorithm for testing the truth of certain quantified Boolean formulas. Inform. Process. Lett. 8, 121–123 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dahllöf, V., Jonsson, P.: An Algorithm for Counting Maximum Weighted Independent Sets and its Applications. In: Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms, pp. 292–298 (2002)

    Google Scholar 

  3. Dahllöf, V., Jonsson, P., Beigel, R.: Algorithms for four variants of the exact satisfiability problem. Theoretical Comp. Sci. 320, 373–394 (2004)

    Article  MATH  Google Scholar 

  4. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco (1979)

    MATH  Google Scholar 

  5. Johnson, D.S., Yannakakis, M., Papadimitriou, C.H.: On Generating All Maximal Independent Sets. Inform. Process. Lett. 27, 119–123 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  6. Monien, B., Speckenmeyer, E., Vornberger, O.: Upper Bounds for Covering Problems. Methods of Operations Research 43, 419–431 (1981)

    MATH  MathSciNet  Google Scholar 

  7. Porschen, S.: On Some Weighted Satisfiability and Graph Problems. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds.) SOFSEM 2005. LNCS, vol. 3381, pp. 278–287. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Porschen, S.: Solving Minimum Weight Exact Satisfiability in Time O(20.2441n). In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 654–664. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Schaefer, T.J.: The complexity of satisfiability problems. In: Proceedings of the 10th ACM Symposium on Theory of Computing, pp. 216–226 (1978)

    Google Scholar 

  10. Valiant, L.: The complexity of enumeration and reliability problems. SIAM J. Comput. 9, 410–421 (1979)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität zu Köln, Pohligstr. 1, D-50969, Köln, Germany

    Stefan Porschen

Authors
  1. Stefan Porschen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rome, ”Sapienza”, Italy

    Tiziana Calamoneri

  2. Computer Science Department, Sapienza University of Rome, Via Salaria, 113, 00198, Rome, Italy

    Irene Finocchi

  3. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Roma, Italy

    Giuseppe F. Italiano

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Porschen, S. (2006). Counting All Solutions of Minimum Weight Exact Satisfiability. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds) Algorithms and Complexity. CIAC 2006. Lecture Notes in Computer Science, vol 3998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758471_8

Download citation

  • DOI: https://doi.org/10.1007/11758471_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34375-2

  • Online ISBN: 978-3-540-34378-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation