Locality and bounding-box quality of two-dimensional space-filling curves

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 th...

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Bibliographic Details
Published in:Computational geometry : theory and applications Vol. 43; no. 2; pp. 131 - 147
Main Authors: Haverkort, Herman, van Walderveen, Freek
Format: Journal Article
Language:English
Published: Elsevier B.V 01.02.2010
Subjects:
R-trees
Space-filling curves
Spatial data structures
Spatial data structures
Space-filling curves
R-trees
ISSN:0925-7721
Online Access:Get full text
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Summary: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.
ISSN:0925-7721
DOI:10.1016/j.comgeo.2009.06.002