Point Selections and Weak ε-Nets for Convex Hulls

Noga Alon; Imre Bárány; Zoltán Füredi; Daniel J. Kleitman

doi:10.1017/S0963548300000225

Point Selections and Weak ε-Nets for Convex Hulls

Noga Alon
, Imre Bárány
, Zoltán Füredi
, Daniel J. Kleitman

Research output: Contribution to journal › Article › peer-review

116 Scopus citations

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.

Original language	English (US)
Pages (from-to)	189-200
Number of pages	12
Journal	Combinatorics, Probability and Computing
Volume	1
Issue number	3
DOIs	https://doi.org/10.1017/S0963548300000225
State	Published - Sep 1992
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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10.1017/S0963548300000225

Cite this

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title = "Point Selections and Weak ε-Nets for Convex Hulls",

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.",

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AU - Alon, Noga

AU - Bárány, Imre

AU - Füredi, Zoltán

AU - Kleitman, Daniel J.

PY - 1992/9

Y1 - 1992/9

N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/84971766257#tab=citedBy

U2 - 10.1017/S0963548300000225

DO - 10.1017/S0963548300000225

M3 - Article

AN - SCOPUS:84971766257

SN - 0963-5483

VL - 1

SP - 189

EP - 200

JO - Combinatorics, Probability and Computing

JF - Combinatorics, Probability and Computing

IS - 3

ER -

Point Selections and Weak ε-Nets for Convex Hulls

Abstract

All Science Journal Classification (ASJC) codes

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