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.2017.28
URN: urn:nbn:de:0030-drops-72291
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7229/
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Chan, Timothy M. ; Tsakalidis, Konstantinos

Dynamic Orthogonal Range Searching on the RAM, Revisited

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LIPIcs-SoCG-2017-28.pdf (0.5 MB)

Abstract

We study a longstanding problem in computational geometry: 2-d dynamic orthogonal range reporting. We present a new data structure achieving O(log n / log log n + k) optimal query time and O(log^{2/3+o(1)}n) update time (amortized) in the word RAM model, where n is the number of data points and k is the output size. This is the first improvement in over 10 years of Mortensen's previous result [SIAM J. Comput., 2006], which has O(log^{7/8+epsilon}n) update time for an arbitrarily small constant epsilon.

In the case of 3-sided queries, our update time reduces to O(log^{1/2+epsilon}n), improving Wilkinson's previous bound [ESA 2014] of O(log^{2/3+epsilon}n).

BibTeX - Entry

@InProceedings{chan_et_al:LIPIcs:2017:7229,
  author =	{Timothy M. Chan and Konstantinos Tsakalidis},
  title =	{{Dynamic Orthogonal Range Searching on the RAM, Revisited}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{28:1--28:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7229},
  URN =		{urn:nbn:de:0030-drops-72291},
  doi =		{10.4230/LIPIcs.SoCG.2017.28},
  annote =	{Keywords: dynamic data structures, range searching, computational geometry}
}

Keywords: dynamic data structures, range searching, computational geometry
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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