Orthogonal Subdivisions with Low Stabbing Numbers

  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3608)


It is shown that for any orthogonal subdivision of size n in a d-dimensional Euclidean space, d ∈ ℕ, d ≥ 2, there is an axis-parallel line that stabs at least Ω(log1/(d − 1) n) boxes. For any integer k, 1≤ k<d, there is also an axis-aligned k-flat that stabs at least Ω(log\(^{\rm 1/ \lfloor (d-1)/k \rfloor }\) n) boxes of the subdivision. These bounds cannot be improved.


Unit Cube Steiner Point Convex Cell Delaunay Tetrahedralizations Convex Subdivision 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Csaba D. Tóth
    • 1
  1. 1.MITCambridgeUSA

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