  Motivated by map labeling, Funke, Krumpe, and Storandt [IWOCA 2016]
introduced the following problem: we are given a sequence of $n$ disks in the
plane. Initially, all disks have radius $0$, and they grow at constant, but
possibly different, speeds. Whenever two disks touch, the one with the higher
index disappears. The goal is to determine the elimination order, i.e., the
order in which the disks disappear. We provide the first general subquadratic
algorithm for this problem. Our solution extends to other shapes (e.g.,
rectangles), and it works in any fixed dimension.
  We also describe an alternative algorithm that is based on quadtrees. Its
running time is $O\big(n \big(\log n + \min \{ \log \Delta, \log \Phi
\}\big)\big)$, where $\Delta$ is the ratio of the fastest and the slowest
growth rate and $\Phi$ is the ratio of the largest and the smallest distance
between two disk centers. This improves the running times of previous
algorithms by Funke, Krumpe, and Storandt [IWOCA 2016], Bahrdt et al. [ALENEX
2017], and Funke and Storandt [EuroCG 2017].
  Finally, we give an $\Omega(n\log n)$ lower bound, showing that our quadtree
algorithms are almost tight.
