on Mathematical and Computing Sciences : TR - C 146 title : An Improved Randomized Algorithm for 3 - SAT author :

Schöning [Sch99] proposed a simple yet efficient randomized algorithm for solving the k-SAT problem. His analysis showed that for 3-SAT, finding a satisfying assignment of any satisfiable formula F with n variables can be achieved in poly(n) · (4/3) (= poly(n) · (1.3333)) expected time, which is optimal up to now. In this paper, we improve this expected time bound by using a combination of a deterministic algorithm for 3-SAT and an improvement of the above randomized algorithm. Our new bound for the above task is poly(n) · (1.3303) .