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Clustering Analyses of Two-Dimensional Space-Filling Curves

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Future Data and Security Engineering (FDSE 2021)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 13076))

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Abstract

A discrete space-filling curve provides a linear traversal or indexing of a multi-dimensional grid space. This paper presents two analytical studies on clustering analyses of the 2-dimensional Hilbert and z-order curve families. The underlying measure is the mean number of cluster over all identically shaped subgrids. We derive the exact formulas for the clustering statistics for the 2-dimensional Hilbert and z-order curve families. The exact results allow us to compare their relative performances with respect to this measure: when the grid-order is sufficiently larger than the subgrid-order (typical scenario for most applications), Hilbert curve family performs significantly better than z-order curve family.

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Author information

Authors and Affiliations

  1. Computer Science Department, Oklahoma State University, Stillwater, OK, 74078, USA

    H. K. Dai

  2. Department of Computer Science, Arkansas State University, Jonesboro, AR, 72401, USA

    H. C. Su

Authors
  1. H. K. Dai
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  2. H. C. Su
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Correspondence to H. K. Dai .

Editor information

Editors and Affiliations

  1. HCMC University of Technology, Ho Chi Minh City, Vietnam

    Tran Khanh Dang

  2. Johannes Kepler University of Linz, Linz, Austria

    Josef Küng

  3. Sungkyunkwan University, Suwon, Korea (Republic of)

    Tai M. Chung

  4. Hosei University, Koganei-shi, Tokyo, Japan

    Makoto Takizawa

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Dai, H.K., Su, H.C. (2021). Clustering Analyses of Two-Dimensional Space-Filling Curves. In: Dang, T.K., Küng, J., Chung, T.M., Takizawa, M. (eds) Future Data and Security Engineering. FDSE 2021. Lecture Notes in Computer Science(), vol 13076. Springer, Cham. https://doi.org/10.1007/978-3-030-91387-8_24

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  • DOI: https://doi.org/10.1007/978-3-030-91387-8_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-91386-1

  • Online ISBN: 978-3-030-91387-8

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