Optimal numberings of an N N array
SIAM Journal on Algebraic and Discrete Methods
Fractals for secondary key retrieval
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Linear clustering of objects with multiple attributes
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
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
Optimal linear arrangement of a rectangular grid
Discrete Mathematics - Special issue on Selected Topics in Discrete Mathematics conferences
Analysis of the Clustering Properties of the Hilbert Space-Filling Curve
IEEE Transactions on Knowledge and Data Engineering
On the Quality of Partitions Based on Space-Filling Curves
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
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)
The priority R-tree: A practically efficient and worst-case optimal R-tree
ACM Transactions on Algorithms (TALG)
Infinite series of generalized Gosper space filling curves
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
Reordering columns for smaller indexes
Information Sciences: an International Journal
Four-dimensional hilbert curves for R-trees
Journal of Experimental Algorithmics (JEA)
Clustering, visualizing, and navigating for large dynamic graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
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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 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.