Skip to main content
Springer Nature Link
Log in

Bounds on Greedy Algorithms for MAX SAT

  • Conference paper
Algorithms – ESA 2011 (ESA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6942))

Included in the following conference series:

Abstract

We study adaptive priority algorithms for MAX SAT and show that no such deterministic algorithm can reach approximation ratio \(\frac{3}{4}\), assuming an appropriate model of data items. As a consequence we obtain that the Slack–Algorithm of [13] cannot be derandomized. Moreover, we present a significantly simpler version of the Slack–Algorithm and also simplify its analysis. Additionally, we show that the algorithm achieves a ratio of \(\frac{3}{4}\) even if we compare its score with the optimal fractional score.

Partially supported by DFG SCHN 503/5-1.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alekhnovich, M., Borodin, A., Buresh-Oppenheim, J., Impagliazzo, R., Magen, A.: Toward a model for backtracking and dynamic programming. Electronic Colloquium on Computational Complexity (ECCC) 16, 38 (2009)

    MATH  Google Scholar 

  2. Angelopoulos, S., Borodin, A.: Randomized priority algorithms. Theor. Comput. Sci. 411(26-28), 2542–2558 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Avidor, A., Berkovitch, I., Zwick, U.: Improved approximation algorithms for MAX NAE-SAT and MAX SAT. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 27–40. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Azar, Y., Gamzu, I., Roth, R.: Submodular Max-SAT. In: ESA (2011)

    Google Scholar 

  5. Borodin, A., Boyar, J., Larsen, K.S., Mirmohammadi, N.: Priority algorithms for graph optimization problems. Theor. Comput. Sci. 411(1), 239–258 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Borodin, A., Nielsen, M.N., Rackoff, C.: (Incremental) priority algorithms. Algorithmica 37(4), 295–326 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen, J., Friesen, D.K., Zheng, H.: Tight bound on Johnson’s algorithm for maximum satisfiability. J. Comput. Syst. Sci. 58(3), 622–640 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Costello, K.P., Shapira, A., Tetali, P.: Randomized greedy: new variants of some classic approximation algorithms. In: SODA, pp. 647–655 (2011)

    Google Scholar 

  9. Davis, S., Impagliazzo, R.: Models of greedy algorithms for graph problems. Algorithmica 54(3), 269–317 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Goemans, M.X., Williamson, D.P.: New 3/4-approximation algorithms for the maximum satisfiability problem. SIAM J. Discrete Math. 7(4), 656–666 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9(3), 256–278 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  12. Poloczek, M.: Bounds on greedy algorithms for MAX SAT, http://www.thi.cs.uni-frankfurt.de/poloczek/maxsatesa11.pdf

  13. Poloczek, M., Schnitger, G.: Randomized variants of Johnson’s algorithm for MAX SAT. In: SODA, pp. 656–663 (2011)

    Google Scholar 

  14. van Zuylen, A.: Simpler 3/4 approximation algorithms for MAX SAT (submitted)

    Google Scholar 

  15. Yao, A.C.-C.: Lower bounds by probabilistic arguments. In: FOCS, pp. 420–428. IEEE, Los Alamitos (1983)

    Google Scholar 

  16. Yung, C.K.: Inapproximation result for exact Max-2-SAT (unpublished manuscript)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Frankfurt, Frankfurt, Germany

    Matthias Poloczek

Authors
  1. Matthias Poloczek
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, University of Rome " La Sapienza", via Ariosto 25, 00185, Roma, Italy

    Camil Demetrescu

  2. School of Computer Science, Reykjavik University, Menntavegur 1, 101, Reykjavik, Iceland

    Magnús M. Halldórsson

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Poloczek, M. (2011). Bounds on Greedy Algorithms for MAX SAT. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-23719-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23718-8

  • Online ISBN: 978-3-642-23719-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics