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

Date and Time: Thursday, October 18, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Robin Moser

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

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, Millius (Master's thesis), 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.

In this talk, I will suggest a generalization of the PPSZ algorithm to (d,k)-ClSP and sketch 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 is largely based on the Bachelor's thesis by May Szedlák.

In the follow-up talk next week, Sebastian Millius will explain the result of his Master's thesis where he establishes 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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