Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, October 08, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Daniel Bertschinger

Tukey Depth Histograms

The Tukey depth (or halfspace depth) is a widely studied measure describing how deep a query point lies within a given set of data points. We study the notion of the depth histogram of a data point set. It describes the distribution of respective depths of all data points. We give a complete characterization of depth histograms of point sets in general position in R^d, that is, we show a necessary and sufficient condition for a vector to be a depth histogram of some point set. This is joint work with J. Passweg and P. Schnider.

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