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.ESA.2018.25
URN: urn:nbn:de:0030-drops-94886
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9488/
El-Zein, Hicham ;
He, Meng ;
Munro, J. Ian ;
Sandlund, Bryce
Improved Time and Space Bounds for Dynamic Range Mode
Abstract
Given an array A of n elements, we wish to support queries for the most frequent and least frequent element in a subrange [l, r] of A. We also wish to support updates that change a particular element at index i or insert/ delete an element at index i. For the range mode problem, our data structure supports all operations in O(n^{2/3}) deterministic time using only O(n) space. This improves two results by Chan et al. [Timothy M. Chan et al., 2014]: a linear space data structure supporting update and query operations in O~(n^{3/4}) time and an O(n^{4/3}) space data structure supporting update and query operations in O~(n^{2/3}) time. For the range least frequent problem, we address two variations. In the first, we are allowed to answer with an element of A that may not appear in the query range, and in the second, the returned element must be present in the query range. For the first variation, we develop a data structure that supports queries in O~(n^{2/3}) time, updates in O(n^{2/3}) time, and occupies O(n) space. For the second variation, we develop a Monte Carlo data structure that supports queries in O(n^{2/3}) time, updates in O~(n^{2/3}) time, and occupies O~(n) space, but requires that updates are made independently of the results of previous queries. The Monte Carlo data structure is also capable of answering k-frequency queries; that is, the problem of finding an element of given frequency in the specified query range. Previously, no dynamic data structures were known for least frequent element or k-frequency queries.
BibTeX - Entry
@InProceedings{elzein_et_al:LIPIcs:2018:9488,
author = {Hicham El-Zein and Meng He and J. Ian Munro and Bryce Sandlund},
title = {{Improved Time and Space Bounds for Dynamic Range Mode}},
booktitle = {26th Annual European Symposium on Algorithms (ESA 2018)},
pages = {25:1--25:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-081-1},
ISSN = {1868-8969},
year = {2018},
volume = {112},
editor = {Yossi Azar and Hannah Bast and Grzegorz Herman},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9488},
URN = {urn:nbn:de:0030-drops-94886},
doi = {10.4230/LIPIcs.ESA.2018.25},
annote = {Keywords: dynamic data structures, range query, range mode, range least frequent, range k-frequency}
}
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Keywords: |
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dynamic data structures, range query, range mode, range least frequent, range k-frequency |
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Collection: |
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26th Annual European Symposium on Algorithms (ESA 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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14.08.2018 |
