2 July 2014, Theoretical Computer Science Seminar, Anke van Zuylen

Abstract

Recently a number of randomized 3/4-approximation algorithms for MAX SAT have been proposed that all work in the same way: given a fixed ordering of the variables the algorithm makes a random assignment to each variable in sequence, in which the probability of assigning each variable true or false depends on the current set of satisfied (or unsatisfied) clauses. To our knowledge, the first such algorithm was proposed by Poloczek and Schnitger (2011); Van Zuylen (2011) subsequently gave an algorithm that set the probabilities differently and had a simpler analysis. Buchbinder, Feldman, Naor, and Schwartz (2012), as a special case of their work on maximizing submodular functions, also give a randomized $\frac{3}{4}$-approximation algorithm for MAX SAT with the same structure as these previous algorithms. In this talk, we give an even simpler version of the algorithm and analysis that was proposed by Buchbinder et al and we show that in fact it is equivalent to the algorithm proposed by Van Zuylen. We also show how it extends to a deterministic LP rounding algorithm, and we show that this same algorithm was also given by Van Zuylen. This is based on joint work with Matthias Poloczek and David Williamson. _______________________________________________

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