Clique Is Hard to Approximate within n1-o(1)

  • Lars Engebretsen
  • Jonas Holmerin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1853)

Abstract

It was previously known that Max Clique cannot be approximated in polynomial time within n1-ε, for any constant ε > 0, unless NP = ZPP. In this paper, we extend the reductions used to prove this result and combine the extended reductions with a recent result of Samorodnitsky and Trevisan to show that clique cannot be approximated within \( n^{1 - O} \left( {1/\sqrt {\log \log n} } \right) \) unless NPZPTIMENP ⊆ ZPTIME(2O(log n(log log n)3/2)).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Lars Engebretsen
    • 1
  • Jonas Holmerin
    • 1
  1. 1.Department of Numerical Analysis and Computing ScienceRoyal Institute of TechnologyStockholmSweden

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