Algorithms for satisfiability using independent sets of variables

  • Authors:

  • Ravi Gummadi;N. S. Narayanaswamy;R. Venkatakrishnan

  • Affiliations:

  • Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India;Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India;Department of Information Technology, Crescent Engineering College, Vandalur, Chennai, India

  • Venue:
  • SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
  • Year:
  • 2004

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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 $(\frac{2k-3}{k-1})^{n-i}$.