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.
Originele taal-2 | Engels |
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Uitgeverij | s.n. |
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Aantal pagina's | 28 |
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Status | Gepubliceerd - 2010 |
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Naam | arXiv.org [cs.CG] |
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Volume | 1002.1843 |
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