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DOI: 10.4230/LIPIcs.SoCG.2017.28
URN: urn:nbn:de:0030-drops-72291
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7229/
Chan, Timothy M. ; Tsakalidis, Konstantinos
Dynamic Orthogonal Range Searching on the RAM, Revisited
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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 | |
| Seminar: | 33rd International Symposium on Computational Geometry (SoCG 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 20.06.2017 |
