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Multidimensional Range Selection

  • Timothy M. Chan
  • Gelin Zhou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9472)

Abstract

We study the problem of supporting (orthogonal) range selection queries over a set of n points in constant-dimensional space. Under the standard word-RAM model with word size \(w = \varOmega (\lg n)\), we present data structures that occupy \(O(n \cdot (\lg n / \lg \lg n)^{d - 1})\) words of space and support d-dimensional range selection queries using \(O((\lg n / \lg \lg n)^d)\) query time. This improves the best known data structure by a factor of \(\lg \lg n\) in query time. To develop our data structures, we generalize the “parallel counting” technique of Brodal, Gfeller, Jørgensen, and Sanders (2011) for one-dimensional range selection to higher dimensions.

As a byproduct, we design data structures to support d-dimensional range counting queries within \(O(n \cdot (\lg n / \lg w + 1)^{d - 2})\) words of space and \(O((\lg n / \lg w + 1)^{d - 1})\) query time, for any word size \(w = \varOmega (\lg n)\). This improves the best known result of JaJa, Mortensen, and Shi (2004) when \(\lg w\gg \lg \lg n\).

Keywords

Query Range Query Time Word Size Range Tree Parallel Counting 
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.

Notes

Acknowledgements

We thank the anonymous reviewers for their fruitful comments and suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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