Faster algorithms for growing prioritized disks and rectangles

Hee Kap Ahn, Sang Won Bae, Jongmin Choi, Matias Korman, Wolfgang Mulzer, Eunjin Oh, Ji Won Park, André Van Renssen, Antoine Vigneron

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

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 (n log n) lower bound on the problem, showing that our quadtree algorithms are almost tight.

Original languageEnglish
Title of host publication28th International Symposium on Algorithms and Computation, ISAAC 2017
EditorsTakeshi Tokuyama, Yoshio Okamoto
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770545
DOIs
Publication statusPublished - 2017 Dec 1
Event28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand
Duration: 2017 Dec 92017 Dec 22

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume92
ISSN (Print)1868-8969

Other

Other28th International Symposium on Algorithms and Computation, ISAAC 2017
CountryThailand
CityPhuket
Period17/12/917/12/22

Keywords

  • Elimination order
  • Growing disks
  • Map labeling

ASJC Scopus subject areas

  • Software

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  • Cite this

    Ahn, H. K., Bae, S. W., Choi, J., Korman, M., Mulzer, W., Oh, E., Park, J. W., Van Renssen, A., & Vigneron, A. (2017). Faster algorithms for growing prioritized disks and rectangles. In T. Tokuyama, & Y. Okamoto (Eds.), 28th International Symposium on Algorithms and Computation, ISAAC 2017 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 92). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2017.3