Improving the first selection lemma in ℝ3

Abdul Basit; Nabil H. Mustafa; Saurabh Ray; Sarfraz Raza

doi:10.1145/1810959.1811017

Improving the first selection lemma in ℝ³

Abdul Basit, Nabil H. Mustafa, Saurabh Ray, Sarfraz Raza

Computer Science

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

Abstract

We present new bounds on the first selection lemma in ℝ³. This makes progress on the open problems of Bukh, Matoušek and Nivash [6] and Boros-Füredi [4] for the three-dimensional case, improving the previously best result of Wagner [8]. While our results narrow the gap between the current best lower and upper bounds, they do not settle this question. However, they indicate that it is the current lower-bounds that are not tight, and we conjecture that the lower-bounds can be further improved to match the current upper bound.

Original language	English (US)
Title of host publication	Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10
Pages	354-357
Number of pages	4
DOIs	https://doi.org/10.1145/1810959.1811017
State	Published - 2010
Event	26th Annual Symposium on Computational Geometry, SoCG 2010 - Snowbird, UT, United States Duration: Jun 13 2010 → Jun 16 2010

Publication series

Name	Proceedings of the Annual Symposium on Computational Geometry

Other

Other	26th Annual Symposium on Computational Geometry, SoCG 2010
Country/Territory	United States
City	Snowbird, UT
Period	6/13/10 → 6/16/10

Keywords

Centerpoints
First selection lemma
Hitting simplices
Location depth

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Mathematics

Access to Document

10.1145/1810959.1811017

Cite this

Basit, A, Mustafa, NH, Ray, S & Raza, S 2010, Improving the first selection lemma in ℝ³. in Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10. Proceedings of the Annual Symposium on Computational Geometry, pp. 354-357, 26th Annual Symposium on Computational Geometry, SoCG 2010, Snowbird, UT, United States, 6/13/10. https://doi.org/10.1145/1810959.1811017

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abstract = "We present new bounds on the first selection lemma in ℝ3. This makes progress on the open problems of Bukh, Matou{\v s}ek and Nivash [6] and Boros-F{\"u}redi [4] for the three-dimensional case, improving the previously best result of Wagner [8]. While our results narrow the gap between the current best lower and upper bounds, they do not settle this question. However, they indicate that it is the current lower-bounds that are not tight, and we conjecture that the lower-bounds can be further improved to match the current upper bound.",

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AU - Raza, Sarfraz

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AB - We present new bounds on the first selection lemma in ℝ3. This makes progress on the open problems of Bukh, Matoušek and Nivash [6] and Boros-Füredi [4] for the three-dimensional case, improving the previously best result of Wagner [8]. While our results narrow the gap between the current best lower and upper bounds, they do not settle this question. However, they indicate that it is the current lower-bounds that are not tight, and we conjecture that the lower-bounds can be further improved to match the current upper bound.

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KW - Location depth

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