# Faster algorithms for growing prioritized disks and rectangles

@article{Ahn2019FasterAF, title={Faster algorithms for growing prioritized disks and rectangles}, author={Hee-Kap Ahn and S. Bae and J. Choi and Matias Korman and Wolfgang Mulzer and Eunjin Oh and Ji-won Park and Andr{\'e} van Renssen and A. Vigneron}, journal={Comput. Geom.}, year={2019}, volume={80}, pages={23-39} }

Motivated by map labeling, we study the problem in which we are given a collection of $n$ disks $D_1, \dots, D_n$ in the plane that grow at possibly different speeds. Whenever two disks meet, the one with the lower 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. This algorithm also works for other shapes (such as rectangles) and in any fixed… Expand

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#### 2 Citations

Parametrized Runtimes for Label Tournaments

- Mathematics, Computer Science
- COCOA
- 2019

A new parameter C which denotes the number of different disk sizes in the input is introduced which is upper bounded by n and designed an algorithm which runs in time \(\mathcal {O}(n C \log ^{\mathcal{O} (1)} n)\). Expand

Labeling Points of Interest in Dynamic Maps using Disk Labels

- Computer Science
- GIScience
- 2018

A map labeling scheme, which allows to label maps at an interactive speed, and some extensions to the labeling that could be used for more sophisticated labeling features such as area labels turning into point labels at smaller map scales. Expand

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