Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time

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 in-place stable partition, i.e., if there were a truly simple solution then in-place stable partition would also have a truly simple so...

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Veröffentlicht in:Computational geometry : theory and applications Jg. 34; H. 2; S. 75 - 82
Hauptverfasser: Brönnimann, Hervé, Chan, Timothy M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.05.2006
Schlagworte:
Computational geometry
Convex hull
Space-efficient algorithm
Computational geometry
Space-efficient algorithm
Convex hull
ISSN:0925-7721
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Zusammenfassung: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 in-place stable partition, i.e., if there were a truly simple solution then in-place 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, the problem admits a very simple solution which does not call for stable partitioning at all.
ISSN:0925-7721
DOI:10.1016/j.comgeo.2005.11.005