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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/
Chan, Timothy M. ;
Tsakalidis, Konstantinos
Dynamic Planar Orthogonal Point Location in Sublogarithmic Time
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: |
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dynamic data structures, point location, word RAM |
Collection: |
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34th International Symposium on Computational Geometry (SoCG 2018) |
Issue Date: |
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2018 |
Date of publication: |
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08.06.2018 |