Approximation algorithm for random MAX-kSAT

Authors:
Yannet Interian
Affiliations:
Center for Applied Mathematics, Cornell University, Ithaca, NY
Venue:
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Year:
2004

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Abstract

We provide a rigorous analysis of a greedy approximation algorithm for the maximum random k-SAT (MAX-R-kSAT) problem. The algorithm assigns variables one at a time in a predefined order. A variable is assigned TRUE if it occurs more often positively than negatively; otherwise, it is assigned FALSE. After each variable assignment, problem instance is simplified and a new variable is selected. We show that this algorithm gives a 10/9.5-approximation, improving over the 9/8-approximation given by de la Vega and Karpinski [7]. The new approximation ratio is achieved by using a different algorithm than the one proposed in [7], along with a new upper bound on the maximum number of clauses that can be satisfied in a random k-SAT formula [2].