TY - JOUR

T1 - Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear time

AU - Brönnimann, Hervé

AU - Chan, Timothy M.

N1 - Funding Information:
✩ A preliminary version of this paper appeared under same title and authors in Proc. Latin American Conference on Theoretical Informatics (LATIN), 2004, pp. 162–171. * Corresponding author. E-mail addresses: hbr@poly.edu (H. Brönnimann), tmchan@uwaterloo.ca (T.M. Chan). 1 Research of the first author supported by NSF CAREER Grant CCR-0133599. 2 Research of the second author supported in part by an NSERC Research Grant.

PY - 2006/5

Y1 - 2006/5

N2 - 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(logn) 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.

AB - 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(logn) 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.

KW - Computational geometry

KW - Convex hull

KW - Space-efficient algorithm

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U2 - 10.1016/j.comgeo.2005.11.005

DO - 10.1016/j.comgeo.2005.11.005

M3 - Article

AN - SCOPUS:84867926547

SN - 0925-7721

VL - 34

SP - 75

EP - 82

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

IS - 2

ER -