@inproceedings{1fb28294f85c4ba49b6e405f11389dab,
title = "Improving the first selection lemma in ℝ3",
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.",
keywords = "Centerpoints, First selection lemma, Hitting simplices, Location depth",
author = "Abdul Basit and Mustafa, {Nabil H.} and Saurabh Ray and Sarfraz Raza",
year = "2010",
month = jun,
day = "13",
doi = "10.1145/1810959.1811017",
language = "English",
isbn = "9781450300162",
series = "Proceedings of the Annual Symposium on Computational Geometry",
pages = "354--357",
booktitle = "Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10",
note = "26th Annual Symposium on Computational Geometry, SoCG 2010 ; Conference date: 13-06-2010 Through 16-06-2010",
}