Convex Hulls under Uncertainty

  • Pankaj K. Agarwal
  • Sariel Har-Peled
  • Subhash Suri
  • Hakan Yıldız
  • Wuzhou Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)


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.


Convex Hull Query Point Membership Probability Membership Query Radial Order 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Pankaj K. Agarwal
    • 1
  • Sariel Har-Peled
    • 2
  • Subhash Suri
    • 3
  • Hakan Yıldız
    • 3
  • Wuzhou Zhang
    • 1
  1. 1.Duke UniversityUSA
  2. 2.University of IllinoisUrbana-ChampaignUSA
  3. 3.University of CaliforniaSanta BarbaraUSA

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