License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2023.5
URN: urn:nbn:de:0030-drops-178559
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17855/
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Agarwal, Pankaj K. ; Ezra, Esther

Line Intersection Searching Amid Unit Balls in 3-Space

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LIPIcs-SoCG-2023-5.pdf (0.8 MB)

Abstract

Let ℬ be a set of n unit balls in ℝ³. We present a linear-size data structure for storing ℬ that can determine in O^*(n^{1/2}) time whether a query line intersects any ball of ℬ and report all k such balls in additional O(k) time. The data structure can be constructed in O(n log n) time. (The O^*(⋅) notation hides subpolynomial factors, e.g., of the form O(n^ε), for arbitrarily small ε > 0, and their coefficients which depend on ε.)
We also consider the dual problem: Let ℒ be a set of n lines in ℝ³. We preprocess ℒ, in O^*(n²) time, into a data structure of size O^*(n²) that can determine in O^*(1) time whether a query unit ball intersects any line of ℒ, or report all k such lines in additional O(k) time.

BibTeX - Entry

@InProceedings{agarwal_et_al:LIPIcs.SoCG.2023.5,
  author =	{Agarwal, Pankaj K. and Ezra, Esther},
  title =	{{Line Intersection Searching Amid Unit Balls in 3-Space}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17855},
  URN =		{urn:nbn:de:0030-drops-178559},
  doi =		{10.4230/LIPIcs.SoCG.2023.5},
  annote =	{Keywords: Intersection searching, cylindrical range searching, partition trees, union of cylinders}
}

Keywords: Intersection searching, cylindrical range searching, partition trees, union of cylinders
Collection: 39th International Symposium on Computational Geometry (SoCG 2023)
Issue Date: 2023
Date of publication: 09.06.2023

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