Recursive tilings and space-filling curves with little fragmentation

H.J. Haverkort

Research output: Book/ReportReportAcademic

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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.
Original languageEnglish
Publishers.n.
Number of pages28
Publication statusPublished - 2010

Publication series

NamearXiv.org [cs.CG]
Volume1002.1843

Fingerprint

Space-filling Curves
Tiling
Fragmentation
Tile
Set of points
Regular hexahedron
Ball
Server
Optimise
Curve
Alternatives

Cite this

Haverkort, H. J. (2010). Recursive tilings and space-filling curves with little fragmentation. (arXiv.org [cs.CG]; Vol. 1002.1843). s.n.
Haverkort, H.J. / Recursive tilings and space-filling curves with little fragmentation. s.n., 2010. 28 p. (arXiv.org [cs.CG]).
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Haverkort, HJ 2010, Recursive tilings and space-filling curves with little fragmentation. arXiv.org [cs.CG], vol. 1002.1843, s.n.

Recursive tilings and space-filling curves with little fragmentation. / Haverkort, H.J.

s.n., 2010. 28 p. (arXiv.org [cs.CG]; Vol. 1002.1843).

Research output: Book/ReportReportAcademic

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Haverkort HJ. Recursive tilings and space-filling curves with little fragmentation. s.n., 2010. 28 p. (arXiv.org [cs.CG]).