Improving PPSZ for 3-SAT using Critical Variables

Details Improving PPSZ for 3-SAT using Critical Variables Improving PPSZ for 3-SAT using Critical Variables

2010-09-24

arxiv.org/abs/1009.4830v3

Computer Science

Data Structures and Algorithms

12 pages, 2 figures, corrected a typo in the title, added appendix with bound O(1.32065^n)

Scientific paper

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].

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