Incremental Algorithms for Finding the Convex Hulls of Circles and the Lower Envelopes of Parabolas

@inproceedings{Devillers1994IncrementalAF,
  title={Incremental Algorithms for Finding the Convex Hulls of Circles and the Lower Envelopes of Parabolas},
  author={Olivier Devillers and Mordecai J. Golin},
  booktitle={CCCG},
  year={1994}
}
The existing O(n logn) algorithms for nding the convex hulls of circles and the lower envelope of parabolas follow the divide-and-conquer paradigm. The di culty with developing incremental algorithms for these problems is that the introduction of a new circle or parabola can cause (n) structural changes, leading to (n) 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 rst sorted by… CONTINUE READING
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