Convex Hulls Under Uncertainty

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Agarwal P. K., Har-Peled S., Suri S., Yildiz H., Zhang W.

ALGORITHMICA, vol.79, no.2, pp.340-367, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 79 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1007/s00453-016-0195-y
  • Journal Name: ALGORITHMICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.340-367
  • Keywords: Convex hull, Membership probability, Tukey depth, Uncertainty, ALGORITHMS
  • Middle East Technical University Affiliated: No

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 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 beta-hull that may be a useful representation of uncertain hulls.