Logik in der Informatik Prof. Dr. Martin Grohe

Institut für Informatik

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