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Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves

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Algorithms - ESA 2008 (ESA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5193))

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Abstract

Space-filling curves can be used to organise points in the plane into bounding-box hierarchies (such as R-trees). We develop measures of the bounding-box quality of space-filling curves that express how effective different curves are for this purpose. We give general lower bounds on the bounding-box quality and on locality according to Gotsman and Lindenbaum for a large class of curves. We describe a generic algorithm to approximate these and similar quality measures for any given curve. Using our algorithm we find good approximations of the locality and bounding-box quality of several known and new space-filling curves. Surprisingly, some curves with bad locality by Gotsman and Lindenbaum’s measure, have good bounding-box quality, while the curve with the best-known locality has relatively bad bounding-box quality.

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Authors and Affiliations

  1. Dept. of Computer Science, Eindhoven University of Technology, the Netherlands

    Herman Haverkort & Freek van Walderveen

Authors
  1. Herman Haverkort
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  2. Freek van Walderveen
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Dan Halperin Kurt Mehlhorn

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© 2008 Springer-Verlag Berlin Heidelberg

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Haverkort, H., van Walderveen, F. (2008). Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_43

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  • DOI: https://doi.org/10.1007/978-3-540-87744-8_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87743-1

  • Online ISBN: 978-3-540-87744-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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