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 $S$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.14935
- arXiv:
- arXiv:2106.14935
- Bibcode:
- 2021arXiv210614935B
- Keywords:
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- Computer Science - Computational Geometry;
- Computer Science - Data Structures and Algorithms
- E-Print:
- 58 pages, 27 figures