Algorithms for Satisfiability Using Independent Sets of Variables

Ravi Gummadi, N. S. Narayanaswamy, Venkatakrishnan Ramaswamy

Abstract: An independent set of variables is one in which no two variables occur in the same clause in a given instance of k-SAT. Instances of k-SAT with an independent set of size i can be solved in time, within a polynomial factor of 2\(^{n-{\it i}}\). In this paper, we present an algorithm for k-SAT based on a modification of the Satisfiability Coding Lemma. Our algorithm runs within a polynomial factor of \(2^{(n-i)(1- \frac{1}{2k-2})}\), where i is the size of an independent set. We also present a variant of Schöning’s randomized local-search algorithm for k-SAT that runs in time which is with in a polynomial factor of \((\frac{2k-3}{k-1})^{n-i}\).