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

Date and Time: Thursday, October 25, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Sebastian Millius

Towards a Generalization of the PPSZ Algorithm to Larger Domains, Part II

Since Timon Hertli's improved analysis (you recall his mittagsseminar talk of May 19, 2011), the PPSZ algorithm due to Paturi, Pudlák, Saks and Zane is the fastest known randomized algorithm for the k-SAT problem. In joint work with Hertli, Moser, Scheder and Szedlák (Bachelors's thesis), we demonstrate that the PPSZ approach can be generalized to the case of (d,k)-ClSP which is the variant of k-SAT where the variables can take any number d of values, rather than just two. For many cases of d and k, we thereby obtain the fastest known (d,k)-ClSP algorithm.

Last week, Robin Moser suggested a generalization of the PPSZ algorithm to (d,k)-ClSP and sketched an analysis in the simpler case where we assume the ClSP to have exactly one satisfying assignment. For this case, we obtain the fastest known algorithm for all d and k. This was largely based on the Bachelor's thesis by May Szedlák.

In this follow-up talk, I will explain the result of my Master's thesis where we establish that for many important cases of d and k, the aforementioned analysis can be generalized so as to hold without the uniqueness assumption, by means of similar proof techniques as provided by Hertli.

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