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Preconditioning 2D integer data for fast convex hull computations

Cadenas, J. O., Megson, G. M. and Luengo Hendriks, C. L. (2016) Preconditioning 2D integer data for fast convex hull computations. PLoS ONE, 11 (3). e0149860. ISSN 1932-6203

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To link to this item DOI: 10.1371/journal.pone.0149860


In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

Item Type:Article
ID Code:62042
Publisher:Public Library of Science


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