On Multi-dimensional Hilbert Indexings

  • Jochen Alber
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jochen Alber
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenFed. Rep. of Germany

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