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Multidimensional Range Selection

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Algorithms and Computation (ISAAC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9472))

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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 \(\lg w\gg \lg \lg n\).

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Notes

  1. 1.

    The conference version claimed \(O(\lg k / \lg w + 1)\) query time but it would require non-standard word operations.

References

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Acknowledgements

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

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Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    Timothy M. Chan & Gelin Zhou

Authors
  1. Timothy M. Chan
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  2. Gelin Zhou
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Corresponding author

Correspondence to Gelin Zhou .

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Editors and Affiliations

  1. Masdar Institute, Abu Dhabi, United Arab Emirates

    Khaled Elbassioni

  2. Kyoto University, Kyoto, Japan

    Kazuhisa Makino

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Chan, T.M., Zhou, G. (2015). Multidimensional Range Selection. In: Elbassioni, K., Makino, K. (eds) Algorithms and Computation. ISAAC 2015. Lecture Notes in Computer Science(), vol 9472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48971-0_8

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  • DOI: https://doi.org/10.1007/978-3-662-48971-0_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48970-3

  • Online ISBN: 978-3-662-48971-0

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