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

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

2008-06-29

arxiv.org/abs/0806.4787v2

Computer Science

Computational Geometry

24 pages, full version of paper to appear in ESA. Difference with first version: minor editing; Fig. 2(m) corrected

Scientific paper

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 space-filling curves are for this purpose. We give general lower bounds on the bounding-box quality measures and on locality according to Gotsman and Lindenbaum for a large class of space-filling 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 the bounding-box quality of several known and new space-filling curves. Surprisingly, some curves with relatively 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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