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arXiv · 2106.14935

Dynamic Connectivity in Disk Graphs

Alexander Baumann·Haim Kaplan·Katharina Klost·Kristin Knorr·Wolfgang Mulzer·Liam Roditty·Paul Seiferth
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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 $S$.

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Alexander Baumann, Haim Kaplan, Katharina Klost, Kristin Knorr, Wolfgang Mulzer, Liam Roditty, Paul Seiferth. 2021-06-28. Dynamic Connectivity in Disk Graphs. https://doi.org/10.1007/s00454-023-00621-x

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