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Convex Hulls under Uncertainty $\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\pth}[2][\!]{#1\left({#2}\right)}$


Pankaj K. Agarwal, Sariel Har-Peled, Subhash Suri, Hakan Yildiz, and Wuzhou Zhang.
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 \emphi{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 $\beta$-hull that may be a useful representation of uncertain hulls.
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Last modified: Wed Jun 25 11:01:42 CDT 2014