A Non-linear Lower Bound for Planar Epsilon-nets

Noga Alon

doi:10.1007/s00454-010-9323-7

A Non-linear Lower Bound for Planar Epsilon-nets

Noga Alon

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

32 Scopus citations

Abstract

We show that the minimum possible size of an ε-net for point objects and line (or rectangle)-ranges in the plane is (slightly) bigger than linear in 1/ε. This settles a problem raised by Matoušek, Seidel and Welzl (Proc. 6th Annu. ACM Sympos. Comput. Geom., pp. 16-22, 1990).

Original language	English (US)
Pages (from-to)	235-244
Number of pages	10
Journal	Discrete and Computational Geometry
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/s00454-010-9323-7
State	Published - Mar 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Keywords

Epsilon nets
VC-dimension
Weak epsilon nets

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10.1007/s00454-010-9323-7

Cite this

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abstract = "We show that the minimum possible size of an ε-net for point objects and line (or rectangle)-ranges in the plane is (slightly) bigger than linear in 1/ε. This settles a problem raised by Matou{\v s}ek, Seidel and Welzl (Proc. 6th Annu. ACM Sympos. Comput. Geom., pp. 16-22, 1990).",

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AB - We show that the minimum possible size of an ε-net for point objects and line (or rectangle)-ranges in the plane is (slightly) bigger than linear in 1/ε. This settles a problem raised by Matoušek, Seidel and Welzl (Proc. 6th Annu. ACM Sympos. Comput. Geom., pp. 16-22, 1990).

KW - Epsilon nets

KW - VC-dimension

KW - Weak epsilon nets

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AN - SCOPUS:84855590895

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EP - 244

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

A Non-linear Lower Bound for Planar Epsilon-nets

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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