Abstract
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.
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Mustafa, N.H., Ray, S., Shabbir, M. (2011). Ray-Shooting Depth: Computing Statistical Data Depth of Point Sets in the Plane. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_43
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DOI: https://doi.org/10.1007/978-3-642-23719-5_43
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