Computing a High Depth Point in the Plane

S. Langerman () and W. Steiger ()
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S. Langerman: Rutgers University, Department of Computer Science
W. Steiger: Rutgers University, Department of Computer Science

A chapter in Developments in Robust Statistics, 2003, pp 228-234 from Springer

Abstract: Summary Given a set S = {P 1,…,P n} of n points in Rd, the depth δ (Q)of n points in Q ∈ R d is the minimum number of points of S that must be in a closed halfspace containing Q. A high depth point is a point whose depth is at least maxi [δ(Pi)] For dimension d = 2 we give a simple, easily implementable O(n(log n)2) deterministic algorithm to compute a high depth point and we give an Ω(n log n) lower bound for this task.

Keywords: Deep Point; Depth Point; Sorting Network; Brute Force Algorithm; Tukey Depth (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57338-5_19

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DOI: 10.1007/978-3-642-57338-5_19

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