MAX SAT approximation beyond the limits of polynomial-time approximation

Evgeny Dantsin, Michael Gavrilovich, Edward A. Hirsch, Boris Konev

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We describe approximation algorithms for (unweighted) MAX SAT with performance ratios arbitrarily close to 1, in particular, when performance ratios exceed the limits of polynomial-time approximation. Namely, given a polynomial-time α-approximation algorithm A0, we construct an (α+ε)-approximation algorithm A. The algorithm A runs in time of the order cεk, where k is the number of clauses in the input formula and c is a constant depending on α. Thus we estimate the cost of improving a performance ratio. Similar constructions for MAX 2SAT and MAX 3SAT are also described. Taking known algorithms as A0 (for example, the Karloff-Zwick algorithm for MAX 3SAT), we obtain particular upper bounds on the running time of A.

Original languageEnglish
Pages (from-to)81-94
Number of pages14
JournalAnnals of Pure and Applied Logic
Issue number1-3
StatePublished - 27 Dec 2001
Externally publishedYes


  • 03B05
  • 03B25
  • 68W25
  • Approximation algorithms
  • Maximum satisfiability problem


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