Dynamic Connectivity in Disk Graphs

Abstract

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 $S$.

58 pages, 27 figures; a preliminary version appeared at SoCG 2022