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 language | English |
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Pages (from-to) | 835-840 |
Number of pages | 6 |
Journal | Information Processing Letters |
Volume | 110 |
Issue number | 18-19 |
DOIs | |
State | Published - 15 Sep 2010 |
Externally published | Yes |
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: [email protected].
Funding
✩ 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: [email protected].
Funders | Funder number |
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National Science Foundation | CNS-05-40347, DEB-04-25465, CFF-06-35000 |
National Institutes of Health | 1P50-GM-08183-01 |
Army Research Office | W911NF-07-1-0376, W911NF-08-1-0452 |
Keywords
- Computational geometry
- Geometric range spaces
- d-Layer range-trees
- ε-Nets