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Categorical Range Reporting with Frequencies

Authors Arnab Ganguly, J. Ian Munro, Yakov Nekrich, Rahul Shah, Sharma V. Thankachan

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Author Details

Arnab Ganguly
  • Dept. of Computer Science, University of Wisconsin, Whitewater, USA
J. Ian Munro
  • Cheriton School of Computer Science, University of Waterloo, Canada
Yakov Nekrich
  • Cheriton School of Computer Science, University of Waterloo, Canada
Rahul Shah
  • Dept. of Computer Science, Baton Rouge, USA
Sharma V. Thankachan
  • Dept. of Computer Science, University of Central Florida

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Arnab Ganguly, J. Ian Munro, Yakov Nekrich, Rahul Shah, and Sharma V. Thankachan. Categorical Range Reporting with Frequencies. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ICDT.2019.9

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Data Structures
  • Range Reporting
  • Range Counting
  • Categorical Range Reporting
  • Orthogonal Range Query

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