递归平铺和空间填充曲线，几乎没有碎片
Recursive tilings and space-filling curves with little fragmentation
摘要：
本文定义了一个递归平铺（或空间填充曲线）的Arrwwid数为使得任意球Q可以被总体积为O（vol（Q））的w个平铺（或曲线段）覆盖的最小数w。当处理d维空间中的点集时，可以应用具有低Arrwwid数的递归平铺和空间填充曲线来优化磁盘、内存或服务器访问模式。本文提出了具有最优Arrwwid数的递归平铺和空间填充曲线。对于d >= 3，我们看到规则的立方体镶嵌和空间填充曲线不可能有最优的Arrwwid数，我们看到如何构造具有更好的Arrwwid数的替代方案。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
