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On Multi-dimensional Hilbert Indexings

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Computing and Combinatorics (COCOON 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1449))

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Abstract

Indexing schemes for grids based on space-filling curves (e.g., Hilbert indexings) find applications in numerous fields. Hilbert curves yield the most simple and popular scheme. We extend the concept of curves with Hilbert property to arbitrary dimensions and present first results concerning their structural analysis that also simplify their applicability. As we show, Hilbert indexings can be completely described and analyzed by “generating elements of order 1”, thus, in comparison with previous work, reducing their structural complexity decisively.

Work partially supported by a Feodor Lynen fellowship of the Alexander von Humboldt-Stiftung, Bonn, and the Center for Discrete Mathematics, Theoretical Computer Science, and Applications (DIMATIA), Prague.

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References

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Germany

    Jochen Alber & Rolf Niedermeier

Authors
  1. Jochen Alber
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  2. Rolf Niedermeier
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Editor information

Editors and Affiliations

  1. Institute of Information Science, Academia Sinica, 11529, Nankang, Taipei, Taiwan

    Wen-Lian Hsu

  2. Department of Computer Science, Yale University, 51 Prospect Street, New Haven, CT, 06520, USA

    Ming-Yang Kao

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© 1998 Springer-Verlag Berlin Heidelberg

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Alber, J., Niedermeier, R. (1998). On Multi-dimensional Hilbert Indexings. In: Hsu, WL., Kao, MY. (eds) Computing and Combinatorics. COCOON 1998. Lecture Notes in Computer Science, vol 1449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68535-9_37

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  • DOI: https://doi.org/10.1007/3-540-68535-9_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64824-6

  • Online ISBN: 978-3-540-68535-7

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