Improving PPSZ for 3-SAT using Critical Variables
Abstract
A critical variable of a satisfiable CNF formula is a variable that has the same value in all satisfying assignments. Using a simple case distinction on the fraction of critical variables of a CNF formula, we improve the running time for 3-SAT from O(1.32216^n) by Rolf [2006] to O(1.32153^n). Using a different approach, Iwama et al. [2010] very recently achieved a running time of O(1.32113^n). Our method nicely combines with theirs, yielding the currently fastest known algorithm with running time O(1.32065^n). We also improve the bound for 4-SAT from O(1.47390^n) [Iwama, Tamaki 2004] to O(1.46928^n), where O(1.46981^n) can be obtained using the methods of [Iwama, Tamaki 2004] and [Rolf 2006].
Keywords
Cite
@article{arxiv.1009.4830,
title = {Improving PPSZ for 3-SAT using Critical Variables},
author = {Timon Hertli and Robin A. Moser and Dominik Scheder},
journal= {arXiv preprint arXiv:1009.4830},
year = {2011}
}
Comments
12 pages, 2 figures, corrected a typo in the title, added appendix with bound O(1.32065^n)