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DOI: 10.4230/LIPIcs.ESA.2018.25
URN: urn:nbn:de:0030-drops-94886
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9488/
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El-Zein, Hicham ; He, Meng ; Munro, J. Ian ; Sandlund, Bryce

Improved Time and Space Bounds for Dynamic Range Mode

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LIPIcs-ESA-2018-25.pdf (0.5 MB)


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}
}

Keywords: dynamic data structures, range query, range mode, range least frequent, range k-frequency
Seminar: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 08.08.2018


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