An improved bound for k-sets in three dimensions

M. Sharir; S. Smorodinsky; G. Tardos

doi:10.1007/s00454-001-0005-3

An improved bound for k-sets in three dimensions

M. Sharir, S. Smorodinsky, G. Tardos

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

58 Scopus citations

Abstract

We prove that the maximum number of k-sets in a set S of n points in ℝ 3 is O(nk^3/2). This improves substantially the previous best known upper bound of O(nk^5/3) (see [7] and [1]).

Original language	English
Pages (from-to)	195-204
Number of pages	10
Journal	Discrete and Computational Geometry
Volume	26
Issue number	2
DOIs	https://doi.org/10.1007/s00454-001-0005-3
State	Published - 1 Jan 2001
Externally published	Yes

ASJC Scopus subject areas

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

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10.1007/s00454-001-0005-3

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title = "An improved bound for k-sets in three dimensions",

abstract = "We prove that the maximum number of k-sets in a set S of n points in ℝ 3 is O(nk3/2). This improves substantially the previous best known upper bound of O(nk5/3) (see [7] and [1]).",

author = "M. Sharir and S. Smorodinsky and G. Tardos",

year = "2001",

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doi = "10.1007/s00454-001-0005-3",

language = "English",

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T1 - An improved bound for k-sets in three dimensions

AU - Sharir, M.

AU - Smorodinsky, S.

AU - Tardos, G.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - We prove that the maximum number of k-sets in a set S of n points in ℝ 3 is O(nk3/2). This improves substantially the previous best known upper bound of O(nk5/3) (see [7] and [1]).

AB - We prove that the maximum number of k-sets in a set S of n points in ℝ 3 is O(nk3/2). This improves substantially the previous best known upper bound of O(nk5/3) (see [7] and [1]).

UR - https://www.scopus.com/pages/publications/0035612718

U2 - 10.1007/s00454-001-0005-3

DO - 10.1007/s00454-001-0005-3

M3 - Article

AN - SCOPUS:0035612718

SN - 0179-5376

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SP - 195

EP - 204

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

An improved bound for k-sets in three dimensions

Abstract

ASJC Scopus subject areas

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