Abstract
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 d p , is the maximum ratio of d p (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.
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Dai, H.K., Su, H.C. (2004). On p-Norm Based Locality Measures of Space-Filling Curves. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_33
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DOI: https://doi.org/10.1007/978-3-540-30551-4_33
Publisher Name: Springer, Berlin, Heidelberg
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