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.SWAT.2018.17
URN: urn:nbn:de:0030-drops-88438
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8843/
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El-Zein, Hicham ; Munro, J. Ian ; Nekrich, Yakov

Succinct Dynamic One-Dimensional Point Reporting

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LIPIcs-SWAT-2018-17.pdf (0.4 MB)


Abstract

In this paper we present a succinct data structure for the dynamic one-dimensional range reporting problem. Given an interval [a,b] for some a,b in [m], the range reporting query on an integer set S subseteq [m] asks for all points in S cap [a,b]. We describe a data structure that answers reporting queries in optimal O(k+1) time, where k is the number of points in the answer, and supports updates in O(lg^epsilon m) expected time. Our data structure uses B(n,m) + o(B(n,m)) bits where B(n,m) is the minimum number of bits required to represent a set of size n from a universe of m elements. This is the first dynamic data structure for this problem that uses succinct space and achieves optimal query time.

BibTeX - Entry

@InProceedings{elzein_et_al:LIPIcs:2018:8843,
  author =	{Hicham El-Zein and J. Ian Munro and Yakov Nekrich},
  title =	{{Succinct Dynamic One-Dimensional Point Reporting}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm  Theory (SWAT 2018)},
  pages =	{17:1--17:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{David Eppstein},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8843},
  URN =		{urn:nbn:de:0030-drops-88438},
  doi =		{10.4230/LIPIcs.SWAT.2018.17},
  annote =	{Keywords: Succinct Data Structures, Range Searching, Computational Geometry}
}

Keywords: Succinct Data Structures, Range Searching, Computational Geometry
Collection: 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)
Issue Date: 2018
Date of publication: 04.06.2018


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