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Derandomization of PPSZ for Unique-k-SAT

  • Daniel Rolf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3569)

Abstract

The PPSZ Algorithm presented by Paturi, Pudlak, Saks, and Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable 3-SAT formula can be found in expected running time at most \(\mathcal{O}(1.3071^n)\). Using the technique of limited independence, we can derandomize this algorithm yielding \(\mathcal{O}(1.3071^n)\) deterministic running time at most.

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References

  1. 1.
    Schöning, U.: A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 410–414 (1999)Google Scholar
  2. 2.
    Schuler, R., Schöning, U., Watanabe, O.: A probabilistic 3-SAT algorithm further improved. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 192–202. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Rolf, D.: \(3\text{-SAT} \in {RTIME}(1.32971^n)\). Diploma thesis, Department of Computer Science, Humboldt University Berlin, Germany (2003)Google Scholar
  4. 4.
    Baumer, S., Schuler, R.: Improving a probabilistic 3-SAT algorithm by dynamic search and independent clause pairs. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 150–161. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Rolf, D.: \(\text{3-SAT} \in {RTIME}(O(1.32793^n))\) - improving randomized local search by initializing strings of 3-clauses. In: Electronic Colloquium on Computational Complexity, ECCC (2003)Google Scholar
  6. 6.
    Iwama, K., Tamaki, S.: Improved upper bounds for 3-SAT. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), p. 328 (2004)Google Scholar
  7. 7.
    Paturi, R., Pudlak, P., Saks, M.E., Zane, F.: An improved exponential-time algorithm for k-SAT. In: Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 628–637 (1998)Google Scholar
  8. 8.
    Calabro, C., Impagliazzo, R., Kabanets, V., Paturi, R.: The complexity of unique k-SAT: An isolation lemma for k-CNFs. In: Proceedings of the 18th Annual IEEE Conference on Computational Complexity (CCC), pp. 135–141 (2003)Google Scholar
  9. 9.
    Dantsin, E., Goerdt, A., Hirsch, E.A., Kannan, R., Kleinberg, J., Papadimitriou, C., Raghavan, P., Schöning, U.: A deterministic (2 − 2/(k + 1))n algorithm for k-SAT based on local search. Theoretical Computer Science 289, 69–83 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Alon, N., Spencer, J.: The Probabilistic Method. John Wiley, Chichester (1992)zbMATHGoogle Scholar
  11. 11.
    Paturi, R., Pudlak, P., Saks, M.E., Zane, F.: An improved exponential-time algorithm for k-SAT. Journal of the Association for Computing Machinery (JACM) (to appear)Google Scholar
  12. 12.
    Paturi, R., Pudlak, P., Zane, F.: Satisfiability coding lemma. Chicago Journal of Theoretical Computer Science (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Daniel Rolf
    • 1
  1. 1.Institut für Informatik, Lehrstuhl für Logik in der InformatikHumboldt-Universität zu BerlinBerlinGermany

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