MAX-SAT for Formulas with Constant Clause Density Can Be Solved Faster Than in \(\mathcal{O}(2^n)\) Time

  • Evgeny Dantsin
  • Alexander Wolpert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4121)


We give an exact deterministic algorithm for MAX-SAT. On input CNF formulas with constant clause density (the ratio of the number of clauses to the number of variables is a constant), this algorithm runs in \({\mathcal{O}}(c^n)\) time where c<2 and n is the number of variables. Worst-case upper bounds for MAX-SAT less than \({\mathcal{O}}(2^n)\) were previously known only for k-CNF formulas and for CNF formulas with small clause density.


Exact Algorithm Conjunctive Normal Form Decision Version Main Algorithm Partial Assignment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Evgeny Dantsin
    • 1
  • Alexander Wolpert
    • 1
  1. 1.Roosevelt UniversityChicagoUSA

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