Weak ε-nets for Axis-Parallel Boxes in d-Space
نویسنده
چکیده
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-04-25465, by ARO grants W911NF-07-1-0376 and W911NF-08-1-0452, and by an NIH grant 1P50-GM-08183-01. Department of Computer Science, Duke University, Durham, NC 27708-0129, USA; [email protected]. 1
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A Note about Weak ε-nets for Axis-Parallel Boxes in d-space
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تاریخ انتشار 2009