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International Conference on Similarity Search and Applications

SISAP 2017: Similarity Search and Applications pp 234–246Cite as

Practical Space-Efficient Data Structures for High-Dimensional Orthogonal Range Searching

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10609))

Abstract

We consider the orthogonal range search problem: given a point set P in d-dimensional space and an orthogonal query region Q, return some information on \(P\cap Q\). We focus on the counting query to count the number of points of P contained in Q, and the reporting query to enumerate all points of P in Q.

For 2-dimensional case, Bose et al. proposed a space-efficient data structure supporting the counting query in \(\mathrm {O}\mathord {\left(\lg n/\lg \lg n\right)}\) time and the reporting query in \(\mathrm {O}\mathord {\left(k \lg n/\lg \lg n\right)}\) time, where \(n=|P|\) and \(k=|P\cap Q|\). For high-dimensional cases, the KDW-tree [Okajima, Maruyama, ALENEX 2015] and the data structure of [Ishiyama, Sadakane, DCC 2017] have been proposed. These are however not efficient for very large d.

This paper proposes practical space-efficient data structures for the problem. They run fast when the number of dimensions \(d'\) used in queries is smaller than the data dimension d. This kind of queries are typical in database queries.

This work was supported by JST CREST Grant Number JPMJCR1402, Japan.

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Notes

  1. 1.

    Although we don’t store C in the root, we consider that the root corresponds to C.

  2. 2.

    Here, we use zero-based indexing.

  3. 3.

    As we mentioned before, we use zero-base indexing here.

  4. 4.

    From now on we call the d dimensions as 0-th dimension to \((d-1)\)-st dimension.

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Author information

Authors and Affiliations

  1. Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan

    Kazuki Ishiyama & Kunihiko Sadakane

Authors
  1. Kazuki Ishiyama
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  2. Kunihiko Sadakane
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Corresponding author

Correspondence to Kazuki Ishiyama .

Editor information

Editors and Affiliations

  1. Fraunhofer Institute for Applied Information Technology, Sankt Augustin, Germany

    Christian Beecks

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Felix Borutta

  3. Ludwig-Maximilians-Universität München, Munich, Germany

    Peer Kröger

  4. Ludwig-Maximilians-Universität München, Munich, Germany

    Thomas Seidl

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Ishiyama, K., Sadakane, K. (2017). Practical Space-Efficient Data Structures for High-Dimensional Orthogonal Range Searching. In: Beecks, C., Borutta, F., Kröger, P., Seidl, T. (eds) Similarity Search and Applications. SISAP 2017. Lecture Notes in Computer Science(), vol 10609. Springer, Cham. https://doi.org/10.1007/978-3-319-68474-1_16

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  • DOI: https://doi.org/10.1007/978-3-319-68474-1_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68473-4

  • Online ISBN: 978-3-319-68474-1

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