Unit distances in three dimensions

Haim Kaplan; Jiří Matoušek; Zuzana Safernová; Micha Sharir

doi:10.1017/S0963548312000144

Unit distances in three dimensions

Haim Kaplan, Jiří Matoušek, Zuzana Safernová, Micha Sharir

School of Computer Science

Tel Aviv University

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

Abstract

We show that the number of unit distances determined by n points in R ³ is O(n ^3/2), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [28].

Original language	English
Pages (from-to)	597-610
Number of pages	14
Journal	Combinatorics Probability and Computing
Volume	21
Issue number	4
DOIs	https://doi.org/10.1017/S0963548312000144
State	Published - Jul 2012

All Science Journal Classification (ASJC) codes

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

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Cite this

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abstract = "We show that the number of unit distances determined by n points in R 3 is O(n 3/2), slightly improving the bound of Clarkson, Edelsbrunner, Guibas, Sharir and Welzl [5], established in 1990. The new proof uses the recently introduced polynomial partitioning technique of Guth and Katz [12]. While this paper was still in a draft stage, a similar proof of our main result was posted to the arXiv by Joshua Zahl [28].",

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JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

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ER -

Unit distances in three dimensions

Abstract

All Science Journal Classification (ASJC) codes

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