A data structure is presented that explicitly maintains the graph of a Voronoi diagram of $N$ point sites in the plane or the dual graph of a convex hull of points in three dimensions while allowing insertions of new sites/points. Our structure supports insertions in $\tilde O (N^{3/4})$ expected amortized time, where $\tilde O$ suppresses polylogarithmic terms. This is the first result to achieve sublinear time insertions; previously it was shown by Allen et al. that $\Theta(\sqrt{N})$ amortized combinatorial changes per insertion could occur in the Voronoi diagram but a sublinear-time algorithm was only presented for the special case of points in convex position.

中文翻译：

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次线性显式增量平面 Voronoi 图

提出了一种数据结构，该结构明确维护平面中 $N$ 点站点的 Voronoi 图或三维点的凸包的对偶图，同时允许插入新站点/点。我们的结构支持在 $\tilde O (N^{3/4})$ 预期摊销时间中插入，其中 $\tilde O$ 抑制多对数项。这是实现次线性时间插入的第一个结果；以前，它是由 Allen 等人展示的。$\Theta(\sqrt{N})$ 每次插入的摊销组合变化可能发生在 Voronoi 图中，但只针对凸位置点的特殊情况提出了亚线性时间算法。