Points and triangles in the plane and halving planes in space

Boris Aronov; Leonidas J. Guibas; Bernard Chazelle; Micha Sharir; Herbert Edelsbrunner; Rephael Wenger

doi:10.1145/98524.98548

Points and triangles in the plane and halving planes in space

Boris Aronov^*
, Leonidas J. Guibas
, Bernard Chazelle
, Micha Sharir
, Herbert Edelsbrunner
, Rephael Wenger

^*Corresponding author for this work

Rutgers University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We prove that for any set S of n points in the plane and n^3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n^3-3α/(512 log²⁵ n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n^8/3 log^5/3 n halving planes.

Original language	English
Title of host publication	Proc Sixth Annu Symp Comput Geom
Publisher	Association for Computing Machinery (ACM)
Pages	112-115
Number of pages	4
ISBN (Print)	0897913620, 9780897913621
DOIs	https://doi.org/10.1145/98524.98548
State	Published - 1990
Externally published	Yes
Event	Proceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA Duration: 6 Jun 1990 → 8 Jun 1990

Publication series

Name	Proc Sixth Annu Symp Comput Geom

Conference

Conference	Proceedings of the Sixth Annual Symposium on Computational Geometry
City	Berkeley, CA, USA
Period	6/06/90 → 8/06/90

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10.1145/98524.98548

Cite this

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title = "Points and triangles in the plane and halving planes in space",

abstract = "We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.",

author = "Boris Aronov and Guibas, \{Leonidas J.\} and Bernard Chazelle and Micha Sharir and Herbert Edelsbrunner and Rephael Wenger",

year = "1990",

doi = "10.1145/98524.98548",

language = "אנגלית",

isbn = "0897913620",

series = "Proc Sixth Annu Symp Comput Geom",

publisher = "Association for Computing Machinery (ACM)",

pages = "112--115",

booktitle = "Proc Sixth Annu Symp Comput Geom",

address = "ארצות הברית",

note = "Proceedings of the Sixth Annual Symposium on Computational Geometry ; Conference date: 06-06-1990 Through 08-06-1990",

}

Aronov, B, Guibas, LJ, Chazelle, B, Sharir, M, Edelsbrunner, H & Wenger, R 1990, Points and triangles in the plane and halving planes in space. in Proc Sixth Annu Symp Comput Geom. Proc Sixth Annu Symp Comput Geom, Association for Computing Machinery (ACM), pp. 112-115, Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, USA, 6/06/90. https://doi.org/10.1145/98524.98548

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AU - Aronov, Boris

AU - Guibas, Leonidas J.

AU - Chazelle, Bernard

AU - Sharir, Micha

AU - Edelsbrunner, Herbert

AU - Wenger, Rephael

PY - 1990

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AB - We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.

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PB - Association for Computing Machinery (ACM)

T2 - Proceedings of the Sixth Annual Symposium on Computational Geometry

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ER -

Points and triangles in the plane and halving planes in space

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