A note about weak ε-nets for axis-parallel boxes in d-space

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Abstract

We show the existence of weak ε-nets of size O(1/εloglog(1/ ε)) for point sets and axis-parallel boxes in ℝd, for d≥4. Our analysis uses a non-trivial variant of the recent technique of Aronov et al. (2009) [3] that yields (strong) ε-nets, whose size have the above asymptotic bound, for d=2,3.

Original languageEnglish
Pages (from-to)835-840
Number of pages6
JournalInformation Processing Letters
Volume110
Issue number18-19
DOIs
StatePublished - 15 Sep 2010
Externally publishedYes

Bibliographical note

Funding Information:
✩ Part of the work on this paper has been supported by NSF under grants CNS-05-40347, CFF-06-35000, and DEB-04-25465, by ARO grants W911NF-07-1-0376 and W911NF-08-1-0452, and by an NIH grant 1P50-GM-08183-01. E-mail address: esther@courant.nyu.edu.

Keywords

  • Computational geometry
  • Geometric range spaces
  • d-Layer range-trees
  • ε-Nets

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