Improving the first selection lemma in ℝ3

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

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publicationProceedings of the 26th Annual Symposium on Computational Geometry, SCG'10
Pages354-357
Number of pages4
DOIs
StatePublished - Jul 30 2010
Event26th Annual Symposium on Computational Geometry, SoCG 2010 - Snowbird, UT, United States
Duration: Jun 13 2010Jun 16 2010

Other

Other26th Annual Symposium on Computational Geometry, SoCG 2010
CountryUnited States
CitySnowbird, UT
Period6/13/106/16/10

Fingerprint

Lemma
Lower bound
Upper and Lower Bounds
Open Problems
Upper bound
Three-dimensional

Keywords

  • Centerpoints
  • First selection lemma
  • Hitting simplices
  • Location depth

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Basit, A., Mustafa, N. H., Ray, S., & Raza, S. (2010). Improving the first selection lemma in ℝ3 In Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10 (pp. 354-357) https://doi.org/10.1145/1810959.1811017

Improving the first selection lemma in ℝ3 . / Basit, Abdul; Mustafa, Nabil H.; Ray, Saurabh; Raza, Sarfraz.

Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10. 2010. p. 354-357.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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. 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
Basit A, Mustafa NH, Ray S, Raza S. Improving the first selection lemma in ℝ3 In Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10. 2010. p. 354-357 https://doi.org/10.1145/1810959.1811017
Basit, Abdul ; Mustafa, Nabil H. ; Ray, Saurabh ; Raza, Sarfraz. / Improving the first selection lemma in ℝ3 Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10. 2010. pp. 354-357
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