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.2018.4
URN: urn:nbn:de:0030-drops-87175
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8717/
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Agarwal, Pankaj K. ; Arge, Lars ; Staals, Frank

Improved Dynamic Geodesic Nearest Neighbor Searching in a Simple Polygon

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LIPIcs-SoCG-2018-4.pdf (0.6 MB)

Abstract

We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set S of point sites in a static simple polygon P. Our data structure allows us to insert a new site in S, delete a site from S, and ask for the site in S closest to an arbitrary query point q in P. All distances are measured using the geodesic distance, that is, the length of the shortest path that is completely contained in P. Our data structure achieves polylogarithmic update and query times, and uses O(n log^3n log m + m) space, where n is the number of sites in S and m is the number of vertices in P. The crucial ingredient in our data structure is an implicit representation of a vertical shallow cutting of the geodesic distance functions. We show that such an implicit representation exists, and that we can compute it efficiently.

BibTeX - Entry

@InProceedings{agarwal_et_al:LIPIcs:2018:8717,
  author =	{Pankaj K. Agarwal and Lars Arge and Frank Staals},
  title =	{{Improved Dynamic Geodesic Nearest Neighbor Searching in a Simple Polygon}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8717},
  URN =		{urn:nbn:de:0030-drops-87175},
  doi =		{10.4230/LIPIcs.SoCG.2018.4},
  annote =	{Keywords: data structure, simple polygon, geodesic distance, nearest neighbor searching, shallow cutting}
}

Keywords: data structure, simple polygon, geodesic distance, nearest neighbor searching, shallow cutting
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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