Discrete & Computational Geometry

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

Randomized Complexity Lower Bound for Arrangements and Polyhedra

  • D. Grigoriev


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.


Knapsack Problem Computation Tree Multiplicative Complexity Randomize Complexity Distinctness Problem 
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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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