Incremental algorithms for finding the convex hulls of circles and the lower envelopes of parabolas - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 1994

Incremental algorithms for finding the convex hulls of circles and the lower envelopes of parabolas

Abstract

The existing $O(n \log n)$ algorithms for finding the convex hulls of circles and the lower envelope of parabolas follow the divide-and-conquer paradigm. The difficulty with developing incremental algorithms for these problems is that the introduction of a new circle or parabola can cause $\Theta(n)$ structural changes, leading to $\Theta(n^2)$ total structural changes during the running of the algorithm. In this note we examine the geometry of these problems and show that, if the circles or parabolas are first sorted by appropriate parameters before constructing the convex hull or lower envelope incrementally, then each new addition may cause at most 3 changes in an amortized sense. These observations are then used to develop $O(n \log n)$ incremental algorithms for these problems.
Fichier principal
Vignette du fichier
RR-2280.pdf (248.43 Ko) Télécharger le fichier

Dates and versions

inria-00074391 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00074391 , version 1

Cite

Olivier Devillers, Mordecai Golin. Incremental algorithms for finding the convex hulls of circles and the lower envelopes of parabolas. [Research Report] RR-2280, INRIA. 1994. ⟨inria-00074391⟩
376 View
2954 Download

Share

Gmail Facebook Twitter LinkedIn More