Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves

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dc.creatorHaverkort, Herman
dc.creatorvan Walderveen, Freek
dc.date2008-06-29
dc.date2008-07-12
dc.date.accessioned2026-07-07T09:49:41Z
dc.date.available2026-07-07T09:49:41Z
dc.descriptionSpace-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.
dc.description24 pages, full version of paper to appear in ESA. Difference with first version: minor editing; Fig. 2(m) corrected
dc.identifierhttps://arxiv.org/abs/0806.4787
dc.identifierhttp://arxiv.org/abs/0806.4787
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164680
dc.subjectComputational Geometry
dc.subjectDatabases
dc.titleLocality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves
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