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arXiv · 1412.1039

Convex Hull for Probabilistic Points

F. Betul Atalay·Sorelle A. Friedler·Dianna Xu
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Abstract

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. 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 that of the user-given confidence value, for the convex hull problem.

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F. Betul Atalay, Sorelle A. Friedler, Dianna Xu. 2016-08-05. Convex Hull for Probabilistic Points. https://arxiv.org/abs/1412.1039

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