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An improved bound on weak epsilon nets in the plane Rubin, Natan
Description
We show that for any set $P$ of $n$ points in the plane and $\eps>0$ there exists a set of $o\left(\frac{1}{\eps^{1.7}}\right)$ points in the plane that pierce every convex set $K$ with $|K\cap P|\geq \eps |P|$. This is the first improvement of the 1992 upper bound $O\left(\frac{1}{\eps^2}\right)$ of Alon, Bárány, Füredi, and Kleitman.
Item Metadata
| Title |
An improved bound on weak epsilon nets in the plane
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2018-02-06T15:48
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| Description |
We show that for any set $P$ of $n$ points in the plane and $\eps>0$ there exists a set of $o\left(\frac{1}{\eps^{1.7}}\right)$ points in
the plane that pierce every convex set $K$ with $|K\cap P|\geq \eps |P|$. This is the first improvement of the 1992 upper bound $O\left(\frac{1}{\eps^2}\right)$ of Alon,
Bárány, Füredi, and Kleitman.
|
| Extent |
62 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Ben-Gurion University
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| Series | |
| Date Available |
2018-08-06
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0369718
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
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Item Media
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International