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Discrete & Computational Geometry

, Volume 21, Issue 3, pp 329–344 | Cite as

Randomized Complexity Lower Bound for Arrangements and Polyhedra

  • D. Grigoriev

Abstract.

The complexity lower bound Ω (log N ) for randomized computation trees is proved for recognizing an arrangement or a polyhedron with N faces. This provides, in particular, the randomized lower bound Ω (n log n ) for the DISTINCTNESS problem and generalizes [11] where the randomized lower bound Ω (n 2 ) was ascertained for the KNAPSACK problem. The core of the method is an extension of the lower bound from [8] on the multiplicative complexity of a polynomial.

Keywords

Knapsack Problem Computation Tree Multiplicative Complexity Randomize Complexity Distinctness Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • D. Grigoriev
    • 1
  1. 1.IMR Université de Rennes-1, Beaulieu 35042, Rennes, France dima@maths.univ-rennes1.frFR

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