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Point Selections and Weak ε-Nets for Convex Hulls

Published online by Cambridge University Press:  12 September 2008

Noga Alon ,
Imre Bárány ,
Zoltán Füredi  and
Daniel J. Kleitman
Noga Alon
Affiliation:
Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel, and Bellcore, Morristown, NJ 07960, USA. e-mail: noga@math.tau.ac.il
Imre Bárány
Affiliation:
Cowles Foundation, Yale University, New Haven, CT 06520, USA, and Courant Institute, New York University, New York, NY 10009, USA. e-mail: h2923bar@ella.hu
Zoltán Füredi
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences POB 127, 1364 Budapest, Hungary, and Department of Mathematics, University of Illinois, Urbana, IL 61801, USA. e-mail: zoltan@math.uiuc.edu
Daniel J. Kleitman
Affiliation:
Department of Mathematics, MIT, Cambridge, MA 02139, USA. e-mail: djk@math.mit.edu
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Abstract

One of our results: let X be a finite set on the plane, 0 < ε < 1, then there exists a set F (a weak ε-net) of size at most 7/ε2 such that every convex set containing at least ε|X| elements of X intersects F. Note that the size of F is independent of the size of X.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 3 , September 1992 , pp. 189 - 200
Copyright
Copyright © Cambridge University Press 1992

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