Advertisement

Best possible approximation algorithm for MAX SAT with cardinality constraint

  • Maxim I. Sviridenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1444)

Abstract

In this work we consider the MAX SAT problem with the additional constraint that at most p variables have a true value. We obtain (1 — e −1)-approximation algorithm for this problem. Feige [5] proves that for the MAX SAT with cardinality constraint with clauses without negations this is the best possible performance guarantee unless P=NP.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alon, N., Spencer, J.H.: Probabilistic Method. Wiley, 1992.Google Scholar
  2. 2.
    Asano, T.: Approximation algorithms for MAX SAT: Yannakakis vs. Goemans-Williamson. In Proceedings of the 5nd Israel Symposium on Theory and Computing Systems (1997) 182–189Google Scholar
  3. 3.
    Goemans, M., Williamson, D.: New 3/4-approximation algorithms for the maximum satisfiability problem. SIAM Journal on Discrete Mathematics 7 (1994) 656–666MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Goemans M., Williamson, D.: Imroved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming Journal of ACM 42 (1995) 1115–1145MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Feige, U.: A threshold of Inn for approximating set cover. Journal of ACM (to appear)Google Scholar
  6. 6.
    Feige, U., Goemans, M.: Approximating the value of two-prover proof systems, with applications to MAX 2-SAT and MAX-DICUT. In Proceedings of the 3nd Israel Symposium on Theory and Computing Systems (1995) 182–189Google Scholar
  7. 7.
    Feller, W.: An Introduction to Probability Theory and Its Applications. John Wiley & Sons New York (1968)Google Scholar
  8. 8.
    Hastad, J.: Some optimal inapproximability results. In Proceedings of the 28 Annual ACM Symp. on Theory of Computing (1996) 1–10Google Scholar
  9. 9.
    Karloff, H., Zwick, U.: A 7/8-approximation algorithm for MAX 3SAT? In Proceedings of the 38th FOCS (1997) 406–415Google Scholar
  10. 10.
    Khanna, S., Motwani, R.: Towards syntactic characterization of PTAS. In Proceedings of the 28 Annual ACM Symp. on Theory of Computing (1996) 329–337Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Maxim I. Sviridenko
    • 1
  1. 1.Sobolev Institute of MathematicsRussia

Personalised recommendations