5 research outputs found
Recursive tilings and space-filling curves with little fragmentation
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.Comment: Manuscript accompanying abstract in EuroCG 2010, including full
proofs, 20 figures, references, discussion et
Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves
Space-filling curves can be used to organise points in the plane into
bounding-box hierarchies (such as R-trees). We develop measures of the
bounding-box quality of space-filling curves that express how effective
different space-filling curves are for this purpose. We give general lower
bounds on the bounding-box quality measures and on locality according to
Gotsman and Lindenbaum for a large class of space-filling curves. We describe a
generic algorithm to approximate these and similar quality measures for any
given curve. Using our algorithm we find good approximations of the locality
and the bounding-box quality of several known and new space-filling curves.
Surprisingly, some curves with relatively bad locality by Gotsman and
Lindenbaum's measure, have good bounding-box quality, while the curve with the
best-known locality has relatively bad bounding-box quality.Comment: 24 pages, full version of paper to appear in ESA. Difference with
first version: minor editing; Fig. 2(m) correcte