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 \((\frac{2k-3}{k-1})^{n-i}\).
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Gummadi, R., Narayanaswamy, N.S., Venkatakrishnan, R. (2005). Algorithms for Satisfiability Using Independent Sets of Variables. In: Hoos, H.H., Mitchell, D.G. (eds) Theory and Applications of Satisfiability Testing. SAT 2004. Lecture Notes in Computer Science, vol 3542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527695_11
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DOI: https://doi.org/10.1007/11527695_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27829-0
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