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.2021.4
URN: urn:nbn:de:0030-drops-138039
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13803/
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Abdelkader, Ahmed ; Mount, David M.

Approximate Nearest-Neighbor Search for Line Segments

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LIPIcs-SoCG-2021-4.pdf (0.8 MB)

Abstract

Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider nearest-neighbor queries against a set of line segments in ℝ^d, for constant dimension d. Given a set S of n disjoint line segments in ℝ^d and an error parameter ε > 0, the objective is to build a data structure such that for any query point q, it is possible to return a line segment whose Euclidean distance from q is at most (1+ε) times the distance from q to its nearest line segment. We present a data structure for this problem with storage O((n²/ε^d) log (Δ/ε)) and query time O(log (max(n,Δ)/ε)), where Δ is the spread of the set of segments S. Our approach is based on a covering of space by anisotropic elements, which align themselves according to the orientations of nearby segments.

BibTeX - Entry

@InProceedings{abdelkader_et_al:LIPIcs.SoCG.2021.4,
  author =	{Abdelkader, Ahmed and Mount, David M.},
  title =	{{Approximate Nearest-Neighbor Search for Line Segments}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13803},
  URN =		{urn:nbn:de:0030-drops-138039},
  doi =		{10.4230/LIPIcs.SoCG.2021.4},
  annote =	{Keywords: Approximate nearest-neighbor searching, Approximate Voronoi diagrams, Line segments, Macbeath regions}
}

Keywords: Approximate nearest-neighbor searching, Approximate Voronoi diagrams, Line segments, Macbeath regions
Collection: 37th International Symposium on Computational Geometry (SoCG 2021)
Issue Date: 2021
Date of publication: 02.06.2021

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