Abstract
The PPSZ algorithm by Paturi, Pudlák, Saks, and Zane (FOCS 1998) is the fastest known algorithm for (Promise) Unique k-SAT. We give an improved algorithm with exponentially faster bounds for Unique 3-SAT.
For uniquely satisfiable 3-CNF formulas, we do the following case distinction: We call a clause critical if exactly one literal is satisfied by the unique satisfying assignment. If a formula has many critical clauses, we observe that PPSZ by itself is already faster. If there are only few clauses in total, we use an algorithm by Wahlström (ESA 2005) that is faster than PPSZ in this case. Otherwise we have a formula with few critical and many non-critical clauses. Non-critical clauses have at least two literals satisfied; we show how to exploit this to improve PPSZ.
Full version available at http://arxiv.org/abs/1311.2513
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hamza, K.: The smallest uniform upper bound on the distance between the mean and the median of the binomial and poisson distributions. Statistics & Probability Letters 23(1), 21–25 (1995)
Hertli, T.: 3-SAT faster and simpler—unique-SAT bounds for PPSZ hold in general. In: 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, pp. 277–284. IEEE Computer Soc., Los Alamitos (2011)
Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity. J. Comput. System Sci. 63(4), 512–530 (2001); Special issue on FOCS 1998 (Palo Alto, CA)
Iwama, K., Tamaki, S.: Improved upper bounds for 3-SAT. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 328–329 (electronic). ACM Press, New York (2004)
MacWilliams, F.F.J., Sloane, N.N.J.A.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1977)
Paturi, R., Pudlák, P., Saks, M.E., Zane, F.: An improved exponential-time algorithm for k-SAT. J. ACM 52(3), 337–364 (electronic) (2005)
Schöning, U.: A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: Proceedings of the 40th Annual Symposium on Foundations of Computer Science, pp. 410–414. IEEE Computer Society, Los Alamitos (1999)
Wahlström, M.: An algorithm for the SAT problem for formulae of linear length. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 107–118. Springer, Heidelberg (2005)
Welzl, E.: Boolean Satisfiability – Combinatorics and Algorithms (Lecture Notes) (2005), www.inf.ethz.ch/~emo/SmallPieces/SAT.ps
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hertli, T. (2014). Breaking the PPSZ Barrier for Unique 3-SAT. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_50
Download citation
DOI: https://doi.org/10.1007/978-3-662-43948-7_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43947-0
Online ISBN: 978-3-662-43948-7
eBook Packages: Computer ScienceComputer Science (R0)