Convex Hulls under Uncertainty

Pankaj K. Agarwal; Sariel Har-Peled; Subhash Suri; Hakan Yildiz; Wuzhou Zhang

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arXiv · 1406.6599

Convex Hulls under Uncertainty

Pankaj K. Agarwal·Sariel Har-Peled·Subhash Suri·Hakan Yildiz·Wuzhou Zhang

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Abstract

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the uncertainty of each input site is described by a probability distribution over a finite number of possible locations including a \emph{null} location to account for non-existence of the point. Our results include both exact and approximation algorithms for computing the probability of a query point lying inside the convex hull of the input, time-space tradeoffs for the membership queries, a connection between Tukey depth and membership queries, as well as a new notion of $\some$-hull that may be a useful representation of uncertain hulls.

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BibTeX RIS

Pankaj K. Agarwal, Sariel Har-Peled, Subhash Suri, Hakan Yildiz, Wuzhou Zhang. 2014-06-25. Convex Hulls under Uncertainty. https://arxiv.org/abs/1406.6599

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