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Approximable minimization problems and optimal solutions on random inputs

  • Erich Grädel
  • Anders Malmström
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 832)

Abstract

In this paper we extend recent work about logical criteria for approximation properties of optimization problems. We focus on the relationship between logical expressibility and expected asymptotic growth of optimal solutions on random inputs. This further develops a probabilistic approach due to Behrendt, Compton and Grädel showing that expected optimal solutions for any problem in the class Max1 grows essentially like a polynomial. We show that there is a similar result for MinF+ II1, a syntactic class of minimization problems which provides a logical criterion for approximability. As a consequence, we show that some important problems do not belong to MinF+II1.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Erich Grädel
    • 1
  • Anders Malmström
    • 1
  1. 1.Lehrgebiet Mathematische Grundlagen der InformatikRWTH AachenAachen

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