Discrete & Computational Geometry

, Volume 6, Issue 3, pp 307–338 | Cite as

On levels in arrangements and voronoi diagrams

  • Ketan Mulmuley
Article

Abstract

This paper gives efficient, randomized algorithms for the following problems: (1) construction of levels of order 1 tok in an arrangement of hyperplanes in any dimension and (2) construction of higher-order Voronoi diagrams of order 1 tok in any dimension. A new combinatorial tool in the form of a mathematical series, called a θ series, is associated with an arrangement of hyperplanes inR d . It is used to study the combinatorial as well as algorithmic complexity of the geometric problems under consideration.

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Copyright information

© Springer-Verlag New York Inc 1991

Authors and Affiliations

  • Ketan Mulmuley
    • 1
  1. 1.Department of Computer ScienceUniversity of ChicagoChicagoUSA

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