Motivated by map labeling, we study the problem in which we

are given a collection of n disks in the

plane that grow at possibly different speeds. Whenever two

disks meet, the one with the higher index disappears. This

problem was introduced by Funke, Krumpe, and Storandt[IWOCA 2016].

We provide the first general subquadratic algorithm for computing

the times and the order of disappearance.

Our algorithm also works for other shapes (such as rectangles)

and in any fixed dimension.

Using quadtrees, we provide an alternative

algorithm that runs in near linear time, although

this second algorithm has a logarithmic dependence

on either the ratio of the fastest speed to the slowest speed of disks

or the spread of the disk centers

(the ratio of the maximum to the minimum distance between them).

Our result improves the running times of previous algorithms by

Funke, Krumpe, and

Storandt [IWOCA 2016], Bahrdt et al. [ALENEX 2017], and

Funke and Storandt [EWCG 2017].

Finally, we give an \Omega(n\log n) lower bound on the

problem, showing that our quadtree algorithms are almost tight.