Open access
Date
2018Type
- Conference Paper
Abstract
The centerpoint theorem is a well-known and widely used result in discrete geometry. It states that for any point set P of n points in R^d, there is a point c, not necessarily from P, such that each halfspace containing c contains at least n/(d+1) points of P. Such a point c is called a centerpoint, and it can be viewed as a generalization of a median to higher dimensions. In other words, a centerpoint can be interpreted as a good representative for the point set P. But what if we allow more than one representative? For example in one-dimensional data sets, often certain quantiles are chosen as representatives instead of the median. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000314755Publication status
publishedExternal links
Journal / series
Leibniz International Proceedings in Informatics (LIPIcs)Volume
Pages / Article No.
Publisher
Schloss Dagstuhl - Leibniz-Zentrum für InformatikEvent
Subject
centerpoint; point sets; Tukey depthOrganisational unit
03457 - Welzl, Emo (emeritus) / Welzl, Emo (emeritus)
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