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.ICDT.2019.9
URN: urn:nbn:de:0030-drops-103115
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10311/
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Ganguly, Arnab ; Munro, J. Ian ; Nekrich, Yakov ; Shah, Rahul ; Thankachan, Sharma V.

Categorical Range Reporting with Frequencies

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LIPIcs-ICDT-2019-9.pdf (0.8 MB)

Abstract

In this paper, we consider a variant of the color range reporting problem called color reporting with frequencies. Our goal is to pre-process a set of colored points into a data structure, so that given a query range Q, we can report all colors that appear in Q, along with their respective frequencies. In other words, for each reported color, we also output the number of times it occurs in Q. We describe an external-memory data structure that uses O(N(1+log^2D/log N)) words and answers one-dimensional queries in O(1 +K/B) I/Os, where N is the total number of points in the data structure, D is the total number of colors in the data structure, K is the number of reported colors, and B is the block size.
Next we turn to an approximate version of this problem: report all colors sigma that appear in the query range; for every reported color, we provide a constant-factor approximation on its frequency. We consider color reporting with approximate frequencies in two dimensions. Our data structure uses O(N) space and answers two-dimensional queries in O(log_B N +log^*B + K/B) I/Os in the special case when the query range is bounded on two sides. As a corollary, we can also answer one-dimensional approximate queries within the same time and space bounds.

BibTeX - Entry

@InProceedings{ganguly_et_al:LIPIcs:2019:10311,
  author =	{Arnab Ganguly and J. Ian Munro and Yakov Nekrich and Rahul Shah and Sharma V. Thankachan},
  title =	{{Categorical Range Reporting with Frequencies}},
  booktitle =	{22nd International Conference on Database Theory (ICDT 2019)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-101-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{127},
  editor =	{Pablo Barcelo and Marco Calautti},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10311},
  doi =		{10.4230/LIPIcs.ICDT.2019.9},
  annote =	{Keywords: Data Structures, Range Reporting, Range Counting, Categorical Range Reporting, Orthogonal Range Query}
}

Keywords: Data Structures, Range Reporting, Range Counting, Categorical Range Reporting, Orthogonal Range Query
Collection: 22nd International Conference on Database Theory (ICDT 2019)
Issue Date: 2019
Date of publication: 19.03.2019

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