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

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(n2 log2 n)-time algorithm for computing a point of high RayShooting depth. We also present a linear time approximation algorithm.

• Type: Journal
• Year: 2011
• Where: ESA
• Authors: Nabil H. Mustafa, Saurabh Ray, Mudassir Shabbir
• Keywords: Algorithms, ESA 2011, Log2, Time Algorithm, Time Approximation Algorithm