Convex Hulls Under Uncertainty
© 2016, Springer Science+Business Media New York. 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 point is described by a probability distribution over a finite number of possible locations including a 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 β-hull that may be a useful representation of uncertain hulls.
Agarwal, PK; Har-Peled, S; Suri, S; Yıldız, H; Zhang, W
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