Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Friday, November 16, 2012, 12:15 pm

Duration: 30 minutes

Location: HG D3.2

Speaker: Dominik Scheder (Aarhus University)

Exponential Lower Bounds for the PPSZ k-SAT Algorithm

In 1998, Paturi, Pudlak, Saks, and Zane presented PPSZ, an elegant randomized algorithm for k-SAT. Fourteen years on, this algorithm is still the fastest known worst-case algorithm. They proved that its expected running time on k-CNF formulas with n variables is at most 2^{(1 - ε_k)n}, where ε_k = Ω(1/k). So far, no exponential lower bounds at all have been known. In this paper, we construct hard instances for PPSZ. That is, we construct satisfiable k-CNF formulas over n variables on which the expected running time is at least 2^{(1 - ε_k)n}, for ε_k in O( log²(k) / k).

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