Improved Bound for the PPSZ/Schöning-Algorithm for 3-SAT

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 $O ({1.3071}^{n})$ . Its bound degenerates when the number of solutions increases. In 1999, Schöning proved an $O ({1.3334}^{n})$ bound for 3-SAT. In 2003, Iwama and Tamaki combined both algorithms to yield an $O ({1.3238}^{n})$ bound. We tweak the PPSZ-Bound to get a slightly better contribution to the combined algorithm and prove an $O ({1.32216}^{n})$ bound.

Keywords

3-SAT worst case bound bounded resolution randomized local search