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Approximating MIN k-SAT

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Algorithms and Computation (ISAAC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2518))

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Abstract

We obtain substantially improved approximation algorithms for the MIN k-SAT problem, for k = 2,3. More specifically, we obtain a 1.1037-approximation algorithm for the MIN 2-SAT problem, improving a previous 1.5-approximation algorithm, and a 1.2136-approximation algorithm for the MIN 3-SAT problem, improving a previous 1.75-approximation algorithm for the problem. These results are obtained by adapting techniques that were previously used to obtain approximation algorithms for the MAX k-SAT problem. We also obtain some hardness of approximation results.

This research was supported by the Israel Science Foundation (grant no. 246/01).

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References

  1. C. Bazgan and W. Fernandez de la Vega. A polynomial time approximation scheme for dense min2sat. In Proc. 12th Int. Symp. on Fundamentals of Computation Theory, Lecture Notes in Comput. Sci. 1684, pages 91–99. Springer-Verlag, 1999.

    Chapter  Google Scholar 

  2. P. Berman and T. Fujito. On approximation properties of the independent set problem for low degree graphs. Theory of Computing Systems, 32(2): 115–132, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Berman and M. Karpinski. On some tighter inapproximability results (extended abstract). In Proceedings ofICALP’99, pages 200–209, 1999.

    Google Scholar 

  4. D. Bertsimas, C. Teo, and R. Vohra. On dependent randomized rounding algorithms. Oper. Res. Lett., 24(3): 105–114, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  5. YE81]_R. Bar-Yehuda and S. Even. A linear-time approximation algorithm for the weighted vertex cover problem. Journal of Algorithms, 2(2):198–203, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Bar-Yehuda and S. Even. A local-ratio theorem for approximating the weighted vertex cover problem. Annals of Discrete Mathematics, 25:27–45, 1985.

    MathSciNet  Google Scholar 

  7. I. Dinur and S. Safra. The importance of being biased. In Proceedings ofSTOC’02, pages 33–42, 2002.

    Google Scholar 

  8. U. Feige and M.X. Goemans. Approximating the value of two prover proof systems, with applications to MAX-2SAT and MAX-DICUT. In Proceedings ofISTCS’95, pages 182–189, 1995.

    Google Scholar 

  9. M.X. Goemans and D.P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM, 42:1115–1145, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  10. E. Halperin. Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs. In Proceedings ofSODA’00, pages 329–337, 2000.

    Google Scholar 

  11. J. Håstad. Some optimal inapproximability results. Journal of the ACM, 48:798–859, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  12. D.S. Hochbaum. Approximation algorithms for the set covering and vertex cover problems. SIAM Journal on Computing, 11(3):555–556, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  13. D.S. Hochbaum. Efficient bounds for the stable set, vertex cover and set packing problems. Discrete Applied Mathematics, 6(3):243–254, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  14. D.S. Hochbaum. Instant recognition of polynomial time solvability, half itegrality and 2-approximations. In Proceedongs ofAPPROX’00, pages 2–14, 2000.

    Google Scholar 

  15. D. Hochbaum and A. Pathria. Approximating a generalization of MAX 2S AT and MIN2SAT. Discrete Applied Mathematics, 107(1–3):41–59, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  16. R. Kohli, R. Krishnamurti, and P. Mirchandani. The minimum satisfiability problem. Discrete Mathematics, 7:275–283, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  17. M. Lewin, D. Livnat, and U. Zwick. Improved rounding techniques for the MAX 2-SAT and MAX DI-CUT problems. In Proceedings of IP CO’02, pages 67–82, 2002.

    Google Scholar 

  18. S. Matuura and T. Matsui. 0.863-approximation algorithm for MAX DICUT. In Proceedongs ofAPPROX-RANDOM’01, pages 138–146, 2001.

    Google Scholar 

  19. S. Matuura and T. Matsui. 0.935-approximation randomized algorithm for MAX 2SAT and its derandomization. Technical Report METR 2001-03, Department of Mathematical Engineering and Information Physics, the University of Tokyo, Japan, September 2001.

    Google Scholar 

  20. M.V. Marathe and S.S. Ravi. On approximation algorithms for the minimum satisfiability problem. Information Processing Letters, 58:23–29, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  21. S. Mahajan and H. Ramesh. Derandomizing approximation algorithms based on semidefinite programming. SIAM Journal on Computing, 28:1641–1663, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  22. 85]_B. Monien and E. Speckenmeyer. Ramsey numbers and an approximation algorithm for the vertex cover problem. Acta Informatica, 22(1): 115–123, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  23. L. Trevisan, G.B. Sorkin, M. Sudan, and D.P. Williamson. Gadgets, approximation, and linear programming. SIAM Journal on Computing, 29:2074–2097, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  24. U. Zwick. Computer assisted proof of optimal approximability results. In Proceedings ofSODA’02, pages 496–505, 2002.

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Adi Avidor & Uri Zwick

Authors
  1. Adi Avidor
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  2. Uri Zwick
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6

    Prosenjit Bose  & Pat Morin  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Avidor, A., Zwick, U. (2002). Approximating MIN k-SAT. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_41

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  • DOI: https://doi.org/10.1007/3-540-36136-7_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00142-3

  • Online ISBN: 978-3-540-36136-7

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