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

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.