3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General
Computational Complexity
2011-05-06 v2 Data Structures and Algorithms
Abstract
The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane [1998] is the fastest known algorithm for Unique k-SAT, where the input formula does not have more than one satisfying assignment. For k>=5 the same bounds hold for general k-SAT. We show that this is also the case for k=3,4, using a slightly modified PPSZ algorithm. We do the analysis by defining a cost for satisfiable CNF formulas, which we prove to decrease in each PPSZ step by a certain amount. This improves our previous best bounds with Moser and Scheder [2011] for 3-SAT to O(1.308^n) and for 4-SAT to O(1.469^n).
Cite
@article{arxiv.1103.2165,
title = {3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General},
author = {Timon Hertli},
journal= {arXiv preprint arXiv:1103.2165},
year = {2011}
}
Comments
12 pages, no figures; critical variables are now called frozen, added reference to Makino et al., shortened some proofs and fixed typos