Colored Range Searching in Linear Space

  • Roberto Grossi
  • Søren Vind
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)


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.


Linear Space Query Range Query Time Distinct Color Query Answer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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