Ray-Shooting Depth: Computing Statistical Data Depth of Point Sets in the Plane

  • Nabil H. Mustafa
  • Saurabh Ray
  • Mudassir Shabbir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)


Over the past several decades, many combinatorial measures have been devised for capturing the statistical data depth of a set of n points in ℝ2. These include Tukey depth [15], Oja depth [12], Simplicial depth [10] and several others. Recently Fox et al. [7] have defined the Ray-Shooting depth of a point set, and given a topological proof for the existence of points with high Ray-Shooting depth in ℝ2. In this paper, we present an O(n 2 log 2 n)-time algorithm for computing a point of high Ray-Shooting depth. We also present a linear time approximation algorithm.


Input Point Range Space Good Cone Simplicial Depth Statistical Computing Software 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nabil H. Mustafa
    • 1
  • Saurabh Ray
    • 2
  • Mudassir Shabbir
    • 3
  1. 1.Dept. of Computer ScienceLUMSPakistan
  2. 2.Max-Plank-Institut für InformatikSaarbrückenGermany
  3. 3.Dept. of Computer ScienceRutgersUSA

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