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Algorithmica

, Volume 16, Issue 4–5, pp 415–433 | Cite as

On deterministic approximation of DNF

  • M. Luby
  • B. Veličković
Article

Abstract

We develop several quasi-polynomial-time deterministic algorithms for approximating the fraction of truth assignments that satisfy a disjunctive normal form formula. The most efficient algorithm computes for a given DNF formulaF onn variables withm clauses and ε > 0 an estimateY such that ¦Pr[F] −Y¦≤ε in time which is\((m\log (n))^{\exp (O(\sqrt {\log \log (m)} ))}\), for any constantε. Although the algorithms themselves are deterministic, their analysis is probabilistic and uses the notion of limited independence between random variables.

Key words

Approximation algorithms #P-complete Derandomization DNF formula Small sample spaces 

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Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • M. Luby
    • 1
    • 2
  • B. Veličković
    • 3
  1. 1.International Computer Science InstituteBerkeley
  2. 2.University of CaliforniaBerkeleyUSA
  3. 3.Equipe de LogiqueUniversité Paris VIIParisFrance

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