Recursive tilings and space-filling curves with little fragmentation

Details Recursive tilings and space-filling curves with little fragmentation Recursive tilings and space-filling curves with little fragmentation

2010-02-09

arxiv.org/abs/1002.1843v1

Computer Science

Computational Geometry

Manuscript accompanying abstract in EuroCG 2010, including full proofs, 20 figures, references, discussion etc

Scientific paper

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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