A Note about Weak ε-nets for Axis-Parallel Boxes in d-space
نویسنده
چکیده
We show the existence of weak ε-nets of size O (1/ε log log (1/ε)) for point sets and axisparallel boxes in R, for d ≥ 4. Our analysis uses a non-trivial variant of the recent technique of Aronov et al. [2] that yields (strong) ε-nets, whose size have the above asymptotic bound, for d = 2, 3.
منابع مشابه
Weak ε-nets for Axis-Parallel Boxes in d-Space
In this note we show the existence of weak ε-nets of size O (1/ε log log (1/ε)) for point sets and axis-parallel boxes in R. Our analysis uses a non-trivial variant for the recent technique of Aronov et al. [AES09] that yields (strong) ε-nets, whose size have the above asymptotic bound, for d = 2, 3. Work on this paper has been supported by NSF under grants CNS-05-40347, CFF-06-35000, and DEB-0...
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تاریخ انتشار 2010