Ray-shooting depth: Computing statistical data depth of point sets in the plane

Nabil H. Mustafa, Saurabh Ray, Mudassir Shabbir

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationAlgorithms, ESA 2011 - 19th Annual European Symposium, Proceedings
Pages506-517
Number of pages12
DOIs
StatePublished - Sep 20 2011
Event19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany
Duration: Sep 5 2011Sep 9 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6942 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other19th Annual European Symposium on Algorithms, ESA 2011
CountryGermany
CitySaarbrucken
Period9/5/119/9/11

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Mustafa, N. H., Ray, S., & Shabbir, M. (2011). Ray-shooting depth: Computing statistical data depth of point sets in the plane. In Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings (pp. 506-517). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6942 LNCS). https://doi.org/10.1007/978-3-642-23719-5_43