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arXiv · 1002.1843

Recursive tilings and space-filling curves with little fragmentation

Herman Haverkort
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Abstract

This paper defines the Arrwwid number of a recursive tiling (or space-filling curve) as the smallest number w such that any ball Q can be covered by w tiles (or curve sections) with total volume O(vol(Q)). Recursive tilings and space-filling curves with low Arrwwid numbers can be applied to optimise disk, memory or server access patterns when processing sets of points in d-dimensional space. This paper presents recursive tilings and space-filling curves with optimal Arrwwid numbers. For d >= 3, we see that regular cube tilings and space-filling curves cannot have optimal Arrwwid number, and we see how to construct alternatives with better Arrwwid numbers.

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Herman Haverkort. 2010-02-09. Recursive tilings and space-filling curves with little fragmentation. https://arxiv.org/abs/1002.1843

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