Optimal numberings of an N N array
SIAM Journal on Algebraic and Discrete Methods
Space-filling curves and their use in the design of geometric data structures
Theoretical Computer Science - Special issue: Latin American theoretical informatics
Analysis of the Clustering Properties of the Hilbert Space-Filling Curve
IEEE Transactions on Knowledge and Data Engineering
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
Locality of Corner Transformation for Multidimensional Spatial Access Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
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A discrete space-filling curve provides a linear indexing or traversal of a multi-dimensional grid space We present an analytical study on the locality properties of the 2-dimensional Hilbert curve family The underlying locality measure, based on the p-normed metric dp , is the maximum ratio of dp(v, u)m to $d_{p}(\tilde{v},\tilde{u})$ over all corresponding point-pairs (v, u) and $(\tilde{v},\tilde{u})$ in the m-dimensional grid space and (1-dimensional) index space, respectively Our analytical results close the gaps between the current best lower and upper bounds with exact formulas for p ∈ {1, 2}, and extend to all reals p ≥ 2.