Crushing Disks Efficiently

Conference paper

DOI: 10.1007/978-3-319-44543-4_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9843)
Cite this paper as:
Funke S., Krumpe F., Storandt S. (2016) Crushing Disks Efficiently. In: Mäkinen V., Puglisi S., Salmela L. (eds) Combinatorial Algorithms. IWOCA 2016. Lecture Notes in Computer Science, vol 9843. Springer, Cham

Abstract

Given a set of prioritized disks with fixed centers in \(\mathbb {R}^2\) whose radii grow linearly over time, we are interested in computing an elimination order of these disks assuming that when two disks touch, the one with lower priority is ‘crushed’. A straightforward algorithm has running time \(O(n^2\log n)\) which we improve to expected \(O(n(\log ^6 n+\varDelta ^2 \log ^2 n + \varDelta ^4\log n))\) where \(\varDelta \) is the ratio between largest and smallest radii amongst the disks. For a very natural application of this problem in the map rendering domain, we have \(\varDelta =O(1)\).

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of StuttgartStuttgartGermany
  2. 2.Universität WürzburgWürzburgGermany

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