Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k- SAT

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Abstract

We apply techniques from the theory of approximation algorithms to the problem of deciding whether a random k-SAT formula is satisfiable. Let Form n,k,m denote a random k-SAT instance with n variables and m clauses. Using known approximation algorithms for MAX CUT or MIN BISECTION, we show how to certify that Form n,4,m is unsatisfiable efficiently, provided that m≥Cn 2 for a sufficiently large constant C> 0. In addition, we present an algorithm based on the Lovász θ function that decides within polynomial expected time whether Form n,k,m , is satisfiable, provided that k is even and m≥ C. 4 k n k/2 . Finally, we present an algorithm that approximates random MAX 2-SAT on input Form n,2,m within a factor of 1 - O(n/m) 1/2 in expected polynomial time, for m≥Cn.© 2004 Elsevier B.V. All rights reserved.

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Coja-Oghlan, A., Goerdt, A., Lanka, A., & Schädlich, F. (2004). Techniques from combinatorial approximation algorithms yield efficient algorithms for random 2k- SAT. Theoretical Computer Science, 329(1–3), 1–45. https://doi.org/10.1016/j.tcs.2004.07.01

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