On-line construction of the convex hull of a simple polyline
Information Processing Letters
Algorithmic geometry
Asymptotically efficient in-place merging
Theoretical Computer Science
Nordic Journal of Computing
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Space-efficient planar convex hull algorithms
Theoretical Computer Science - Latin American theorotical informatics
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Optimal in-place and cache-oblivious algorithms for 3-d convex hulls and 2-d segment intersection
Computational Geometry: Theory and Applications
In-Place algorithms for computing (layers of) maxima
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
In-place randomized slope selection
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Covering paths for planar point sets
GD'12 Proceedings of the 20th international conference on Graph Drawing
Reprint of: Memory-constrained algorithms for simple polygons
Computational Geometry: Theory and Applications
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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.