CIKM '93 Proceedings of the second international conference on Information and knowledge management
Space-filling curves and their use in the design of geometric data structures
Theoretical Computer Science - Special issue: Latin American theoretical informatics
Implementing the hierarchical PRAM on the 2D mesh: analyses and experiments
SPDP '95 Proceedings of the 7th IEEE Symposium on Parallel and Distributeed Processing
R-Trees: Theory and Applications (Advanced Information and Knowledge Processing)
R-Trees: Theory and Applications (Advanced Information and Knowledge Processing)
Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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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 qualityof 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.