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 dp, is the maximum ratio of dp(v, u)m to dp(ṽ, ũ) over all corresponding point-pairs (v,u) and (ṽ,ũ) 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. © Springer-Verlag 2004.
Cite
CITATION STYLE
Dai, H. K., & Su, H. G. (2004). On p-norm based locality measures of space-filling curves. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3341, 364–376. https://doi.org/10.1007/978-3-540-30551-4_33
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