Observed lower bounds for random 3-SAT phase transition density using linear programming

Authors:
Marijn Heule;Hans van Maaren
Affiliations:
Department of Software Technology, Faculty of Electrical Engineering, Mathematics and Computer Sciences, Delft University of Technology;Department of Software Technology, Faculty of Electrical Engineering, Mathematics and Computer Sciences, Delft University of Technology
Venue:
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Year:
2005

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Abstract

We introduce two incomplete polynomial time algorithms to solve satisfiability problems which both use Linear Programming (LP) techniques. First, the FlipFlop LP attempts to simulate a Quadratic Program which would solve the CNF at hand. Second, the WeightedLinearAutarky LP is an extended variant of the LinearAutarky LP as defined by Kullmann [6] and iteratively updates its weights to find autarkies in a given formula. Besides solving satisfiability problems, this LP could also be used to study the existence of autark assignments in formulas. Results within the experimental domain (up to 1000 variables) show a considerably sharper lower bound for the uniform random 3-Sat phase transition density than the proved lower bound of the myopic algorithm ( 3.26) by Achlioptas [1] and even than that of the greedy algorithm ( 3.52) proposed by Kaporis [5].