Title: Algorithms to determine the edges of a convex hull from its vertices

Authors: Francisco J. López; Art M. Duval

Addresses: Macon State College, 100 College Station Dr, Macon, GA 31206, USA. ' Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA

Abstract: Trying to develop a fast algorithm that finds all the edges of a convex hull produced three different ideas. The analysis of these resulted in geometric and theoretical findings. One of the contributions of this paper is to describe the three algorithms. The dissemination of the geometric insights and the theory developed is also a contribution. Since one of the objectives is execution speed, the paper presents the results of a computational analysis. The article reports on the algorithms' theoretical complexity and computational performance. This includes a comparison among themselves and against the best available algorithm for the same problem. Two of the new algorithms are efficient, especially in the case of large scale problems. The paper also explains that these algorithms can be accelerated by means of well-known speed-up techniques. Implementing an output sensitive algorithm by Dulá and López (2006) into one of the new algorithms produced the fastest approach.

Keywords: adjacency; fast algorithms; convex hulls; hull edges; linear programming; positive hulls; vertices.

DOI: 10.1504/IJMMNO.2012.047704

International Journal of Mathematical Modelling and Numerical Optimisation, 2012 Vol.3 No.3, pp.184 - 209

Received: 20 Jan 2011
Accepted: 14 Sep 2011

Published online: 08 Jul 2012 *

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