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On the zone of a surface in a hyperplane arrangement

  • Boris Aronov
  • Micha Sharir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)

Abstract

Let H be a collection of n hyperplanes in ℝ d , let A denote the arrangement of H, and let σ be a (d - 1)-dimensional algebraic surface of low degree, or the boundary of a convex body in ℝd. The zone of σ in A is the collection of cells of A crossed by σ. We show that the total number of faces bounding the cells of the zone of σ is O(nd−1 log n).

Keywords

Convex Body General Position Algebraic Surface Hyperplane Arrangement Simple Arrangement 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Boris Aronov
    • 1
  • Micha Sharir
    • 2
    • 1
  1. 1.Department of Computer SciencePolytechnic UniversityBrooklynUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityUSA

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