二维的空间填充曲线的局部性与限界框性质
Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves
摘要：
空间填充曲线可用于将平面中的点组织成限界框层次（如R树）。我们开发的限界框质量的空间填充曲线，表达如何有效地不同的空间填充曲线是为了这个目的的措施。本文给出了一类空间填充曲线的限界框质量测度和Gotsman和Lindenbaum局部性测度的一般下界。我们描述了一个通用的算法来近似这些和任何给定的曲线类似的质量措施。使用我们的算法，我们发现很好的近似的地方和限界框质量的几个已知的和新的空间填充曲线。令人惊讶的是，Gotsman和Lindenbaum的措施，具有相对较差的局部性的一些曲线具有良好的限界框质量，而具有最知名的局部性的曲线具有相对较差的限界框质量。
英文摘要：
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.
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