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Orthogonal Subdivisions with Low Stabbing Numbers

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Algorithms and Data Structures (WADS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3608))

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Abstract

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.

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Author information

Authors and Affiliations

  1. MIT, Cambridge, MA, 02139, USA

    Csaba D. Tóth

Authors
  1. Csaba D. Tóth
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Cheriton School of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada

    Alejandro López-Ortiz

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Jörg-Rüdiger Sack

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© 2005 Springer-Verlag Berlin Heidelberg

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Tóth, C.D. (2005). Orthogonal Subdivisions with Low Stabbing Numbers. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_23

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  • DOI: https://doi.org/10.1007/11534273_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28101-6

  • Online ISBN: 978-3-540-31711-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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