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Space-Efficient Algorithms for Computing the Convex Hull of a Simple Polygonal Line in Linear Time

  • Hervé Brönnimann
  • Timothy M. Chan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

Abstract

We present space-efficient algorithms for computing the convex hull of a simple polygonal line in-place, in linear time. It turns out that the problem is as hard as stable partition, i.e., if there were a truly simple solution then stable partition would also have a truly simple solution, and vice versa. Nevertheless, we present a simple self-contained solution that uses O(log n) space, and indicate how to improve it to O(1) space with the same techniques used for stable partition. If the points inside the convex hull can be discarded, then there is a truly simple solution that uses a single call to stable partition, and even that call can be spared if only extreme points are desired (and not their order). If the polygonal line is closed, then the problem admits a very simple solution which does not call for stable partitioning at all.

Keywords

Convex Hull Convex Polygon Simple Polygon Polygonal Line Current Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hervé Brönnimann
    • 1
  • Timothy M. Chan
    • 2
  1. 1.Computer and Information SciencePolytechnic UniversityBrooklynUSA
  2. 2.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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