License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2020.50
URN: urn:nbn:de:0030-drops-122088
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Har-Peled, Sariel ; Jones, Mitchell

Fast Algorithms for Geometric Consensuses

LIPIcs-SoCG-2020-50.pdf (4 MB)


Let P be a set of n points in ℝ^d in general position. A median hyperplane (roughly) splits the point set P in half. The yolk of P is the ball of smallest radius intersecting all median hyperplanes of P. The egg of P is the ball of smallest radius intersecting all hyperplanes which contain exactly d points of P.
We present exact algorithms for computing the yolk and the egg of a point set, both running in expected time O(n^(d-1) log n). The running time of the new algorithm is a polynomial time improvement over existing algorithms. We also present algorithms for several related problems, such as computing the Tukey and center balls of a point set, among others.

BibTeX - Entry

  author =	{Sariel Har-Peled and Mitchell Jones},
  title =	{{Fast Algorithms for Geometric Consensuses}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{50:1--50:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-122088},
  doi =		{10.4230/LIPIcs.SoCG.2020.50},
  annote =	{Keywords: Geometric optimization, centerpoint, voting games}

Keywords: Geometric optimization, centerpoint, voting games
Collection: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue Date: 2020
Date of publication: 08.06.2020

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