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.2018.25
URN: urn:nbn:de:0030-drops-87382
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8738/
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Chan, Timothy M. ; Tsakalidis, Konstantinos

Dynamic Planar Orthogonal Point Location in Sublogarithmic Time

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LIPIcs-SoCG-2018-25.pdf (0.4 MB)

Abstract

We study a longstanding problem in computational geometry: dynamic 2-d orthogonal point location, i.e., vertical ray shooting among n horizontal line segments. We present a data structure achieving O(log n / log log n) optimal expected query time and O(log^{1/2+epsilon} n) update time (amortized) in the word-RAM model for any constant epsilon>0, under the assumption that the x-coordinates are integers bounded polynomially in n. This substantially improves previous results of Giyora and Kaplan [SODA 2007] and Blelloch [SODA 2008] with O(log n) query and update time, and of Nekrich (2010) with O(log n / log log n) query time and O(log^{1+epsilon} n) update time. Our result matches the best known upper bound for simpler problems such as dynamic 2-d dominance range searching.
We also obtain similar bounds for orthogonal line segment intersection reporting queries, vertical ray stabbing, and vertical stabbing-max, improving previous bounds, respectively, of Blelloch [SODA 2008] and Mortensen [SODA 2003], of Tao (2014), and of Agarwal, Arge, and Yi [SODA 2005] and Nekrich [ISAAC 2011].

BibTeX - Entry

@InProceedings{chan_et_al:LIPIcs:2018:8738,
  author =	{Timothy M. Chan and Konstantinos Tsakalidis},
  title =	{{Dynamic Planar Orthogonal Point Location in Sublogarithmic Time}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{25:1--25:15},
  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/2018/8738},
  URN =		{urn:nbn:de:0030-drops-87382},
  doi =		{10.4230/LIPIcs.SoCG.2018.25},
  annote =	{Keywords: dynamic data structures, point location, word RAM}
}

Keywords: dynamic data structures, point location, word RAM
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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