Colored Range Searching in Linear Space

  • Roberto Grossi
  • Søren Vind
Conference paper

DOI: 10.1007/978-3-319-08404-6_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)
Cite this paper as:
Grossi R., Vind S. (2014) Colored Range Searching in Linear Space. In: Ravi R., Gørtz I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham

Abstract

In colored range searching, we are given a set of n colored points in d ≥ 2 dimensions to store, and want to support orthogonal range queries taking colors into account. In the colored range counting problem, a query must report the number of distinct colors found in the query range, while an answer to the colored range reporting problem must report the distinct colors in the query range.

We give the first linear space data structure for both problems in two dimensions (d = 2) with o(n) worst case query time. We also give the first data structure obtaining almost-linear space usage and o(n) worst case query time for points in d > 2 dimensions. Finally, we present the first dynamic solution to both counting and reporting with o(n) query time for d ≥ 2 and d ≥ 3 dimensions, respectively.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Roberto Grossi
    • 1
  • Søren Vind
    • 2
  1. 1.Dipartimento di InformaticaUniversità di PisaItaly
  2. 2.Technical University of Denmark, DTU ComputeDenmark

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