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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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)
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)
Rolf, D.: \(3\text{-SAT} \in {RTIME}(1.32971^n)\). Diploma thesis, Department of Computer Science, Humboldt University Berlin, Germany (2003)
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)
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)
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)
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)
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)
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)
Alon, N., Spencer, J.: The Probabilistic Method. John Wiley, Chichester (1992)
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)
Paturi, R., Pudlak, P., Zane, F.: Satisfiability coding lemma. Chicago Journal of Theoretical Computer Science (1999)
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Rolf, D. (2005). Derandomization of PPSZ for Unique-k-SAT. In: Bacchus, F., Walsh, T. (eds) Theory and Applications of Satisfiability Testing. SAT 2005. Lecture Notes in Computer Science, vol 3569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499107_16
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DOI: https://doi.org/10.1007/11499107_16
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