Let $S$ be a set of $n$ sites in the plane, so that every site $s \in S$ has an associated radius $r_s > 0$. Let $\mathcal{D}(S)$ be the disk intersection graph defined by $S$, i.e., the graph with vertex set $S$ and an edge between two distinct sites $s, t \in S$ if and only if the disks with centers $s$, $t$ and radii $r_s$, $r_t$ intersect.Our goal is to design data structures that maintain the connectivity structure of $\mathcal{D}(S)$ as sites are inserted and/or deleted in $S$.

翻译：令 $S$ 为平面上的 $n$ 个站点集合，其中每个站点 $s \in S$ 关联一个半径 $r_s > 0$。设 $\mathcal{D}(S)$ 为由 $S$ 定义的圆盘相交图，即顶点集为 $S$ 的图，且两个不同站点 $s, t \in S$ 之间当且仅当以 $s$、$t$ 为圆心、$r_s$、$r_t$ 为半径的圆盘相交时存在边。我们的目标是设计数据结构，使得当 $S$ 中插入和/或删除站点时，能够维护 $\mathcal{D}(S)$ 的连通性结构。