2016 29th SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI)
Final Published Version
We analyze the correctness of an O(n log n) time divide-and-conquer algorithm for the convex hull problem when each input point is a location determined by a normal distribution. We show that the algorithm finds the convex hull of such probabilistic points to precision within some expected correctness determined by a user-given confidence value phi. In order to precisely explain how correct the resulting structure is, we introduce a new certificate error model for calculating and understanding approximate geometric error based on the fundamental properties of a geometric structure. We show that this new error model implies correctness under a robust statistical error model, in which each point lies within the hull with probability at least φ, for the convex hull problem.
Copyright 2016 Taylor & Francis Group. The published version of this article can be found here: http://doi.org/10.1109/SIBGRAPI.2016.016
F. B. Atalay, S. A. Friedler and D. Xu, "Convex Hull for Probabilistic Points," 2016 29th SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI), Sao Paulo, 2016, pp. 48-55.