Certifying Unsatisfiability of Random 2k-SAT Formulas Using Approximation Techniques

  • Amin Coja-Oghlan
  • Andreas Goerdt
  • André Lanka
  • Frank Schädlich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2751)


Let k be an even integer. We investigate the applicability of approximation techniques to the problem of deciding whether a random k-SAT formula is satisfiable. Let n be the number of propositional variables under consideration. First we show that if the number m of clauses satisfies mCn k/2 for a certain constant C, then unsatisfiability can be certified efficiently using (known) approximation algorithms for MAX CUT or MIN BISECTION. In addition, we present an algorithm based on the Lovász ϑ function that within polynomial expected time decides whether the input formula is satisfiable, provided mCn k/2. These results improve previous work by Goerdt and Krivelevich [14]. Finally, we present an algorithm that approximates random MAX 2-SAT within expected polynomial time.


Random Graph Label Edge Satisfying Assignment Independence Number Negligible Discrepancy 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Amin Coja-Oghlan
    • 1
  • Andreas Goerdt
    • 2
  • André Lanka
    • 2
  • Frank Schädlich
    • 2
  1. 1.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Fakultät für InformatikTechnische Universität ChemnitzChemnitzGermany

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