洋葱的联合：快速洋葱分解的预处理不精确点
Unions of Onions: Preprocessing Imprecise Points for Fast Onion Decomposition
摘要：
令$\mathcal{D}$是平面中的一组$n$成对不相交的单位圆盘。我们描述了如何建立一个数据结构的$\mathcal{D}$，使任何点集$P$恰好包含一个点，从每个磁盘，我们可以快速找到洋葱分解（凸层）的$P$。我们的数据结构可以在$O(n \log n)$时间内构建，并且具有线性大小。给定$P$，我们可以在$O(n \log k)$时间内找到它的洋葱分解，其中$k$是层数。我们还提供了一个匹配的下限。我们的解决方案是基于递归空间分解，结合一个快速算法来计算两个不相交洋葱的并集
英文摘要：
Let $\mathcal{D}$ be a set of $n$ pairwise disjoint unit disks in the plane. We describe how to build a data structure for $\mathcal{D}$ so that for any point set $P$ containing exactly one point from each disk, we can quickly find the onion decomposition (convex layers) of $P$. Our data structure can be built in $O(n \log n)$ time and has linear size. Given $P$, we can find its onion decomposition in $O(n \log k)$ time, where $k$ is the number of layers. We also provide a matching lower bound. Our solution is based on a recursive space decomposition, combined with a fast algorithm to compute the union of two disjoint onion
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。
