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On the Quality of Partitions based on SpaceFilling Curves
, 2002
"... This paper presents bounds on the quality of partitions induced by spacefilling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times ..."
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This paper presents bounds on the quality of partitions induced by spacefilling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times worse with respect to the length of the surface. The Lebesgue indexing gives better results than the Hilbert indexing in worst case analysis. Furthermore, the surface of partitions based on the Lebesgue indexing are at most 3 times larger than the optimal in average case.
Definition of a New Circular SpaceFilling Curve  βΩIndexing
"... This technical report presents the definition of a circular Hilbertlike spacefilling curve. Preliminary evaluations in a simulation environment have shown good locality preserving properties. The results are compared with known bounds for other indexing schemes: Hilbert, Lebesgue, and HInde ..."
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This technical report presents the definition of a circular Hilbertlike spacefilling curve. Preliminary evaluations in a simulation environment have shown good locality preserving properties. The results are compared with known bounds for other indexing schemes: Hilbert, Lebesgue, and HIndexing. We evaluated partitions induced by the indexing schemes and uses the diameter and the surface as measures. For both we present worst case and average case results.