Abstract
We show that for any finite point set P in the plane and ϵ > 0 there exist O(1/ϵ3/2+γ) points, for arbitrary small γ > 0, that pierce every convex set K with |K ∩ P| ≥ ϵ|P|. This is the first improvement of the bound of O (1/ϵ 2 ) that was obtained in 1992 by Alon, Bárány, Füredi and Kleitman for general point sets in the plane.
Original language | English |
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Title of host publication | Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 |
Editors | Mikkel Thorup |
Publisher | Institute of Electrical and Electronics Engineers |
Pages | 224-235 |
Number of pages | 12 |
ISBN (Electronic) | 9781538642306 |
DOIs | |
State | Published - 30 Nov 2018 |
Event | 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, France Duration: 7 Oct 2018 → 9 Oct 2018 |
Conference
Conference | 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 |
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Country/Territory | France |
City | Paris |
Period | 7/10/18 → 9/10/18 |
Keywords
- Arrangements of lines
- Convex sets
- Epsilon-nets
- Piercing numbers
- Transversals
- VC-dimension
ASJC Scopus subject areas
- General Computer Science