The projection median of a set of points
type: Item
instance of: scholarly article
title: The projection median of a set of points
zbMATH Open document ID: 1170.65013
author: Stephane Durocher
author: David Kirkpatrick
published in: Computational Geometry
publication date: 2009-06-18T00:00:00Z
review text: Let \(P\) be a multiset of points in the plane. The point for which the function \(x\mapsto\sum_{p\in P}|x-p|\) takes its minimum value is called the \textit{Euclidean median}; it is known to be unstable in the sense that the Euclidean median of a small perturbation of \(P\) may be located at a large distance away from that of \(P\) itself. The authors define the \textit{projection median} to be the average over all one-dimensional medians obtained by orthogonally projecting \(P\) onto a line passing through the origin. They show that the projection median is stable and gives an approximation to the Euclidean median. The projection median is also compared with two common stable approximation schemes, the \textit{center of mass} and the \textit{rectilinear median.} The article is accessible to a general audience, although familiarity with computational geometry is useful.
reviewed by: Jason Hanson
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 5566419
zbMATH Keywords: median
zbMATH Keywords: Weber point
zbMATH Keywords: projection
zbMATH Keywords: approximation
zbMATH Keywords: stability
zbMATH Keywords: continuity
zbMATH Keywords: facility location
zbMATH Keywords: mobile clients
zbMATH Keywords: bounded velocity
zbMATH Keywords: center of mass
zbMATH Keywords: rectilinear median
MaRDI profile type: Publication
full work available at URL: j.comgeo.2008.06.006
OpenAlex ID: W2038474686
cites work: Q4411341
cites work: Maintaining approximate extent measures of moving points
cites work: The algebraic degree of geometric optimization problems
cites work: Generalizing ham sandwich cuts to equitable subdivisions
cites work: Fast approximations for sums of distances, clustering and the Fermat-Weber problem
cites work: Q4449250
cites work: Dynamic planar convex hull operations in near-logarithmic amortized time
cites work: Algebraic optimization: The Fermat-Weber location problem
cites work: Improved bounds for planar \(k\)-sets and related problems
cites work: THE STEINER CENTRE OF A SET OF POINTS: STABILITY, ECCENTRICITY, AND APPLICATIONS TO MOBILE FACILITY LOCATION
cites work: BOUNDED-VELOCITY APPROXIMATION OF MOBILE EUCLIDEAN 2-CENTRES
cites work: Q3147656
cites work: On the Continuous Fermat-Weber Problem
cites work: The Voronoi Partition of a Network and Its Implications in Location Theory
cites work: Smooth kinetic maintenance of clusters
cites work: Q3755206
cites work: Sublinear time algorithms for metric space problems
cites work: Q4219296
cites work: Q4352313
cites work: Q4368539
cites work: Q4203976
cites work: Maintenance of configurations in the plane
cites work: Q5767400
cites work: Q4229604
DOI: 10.1016/J.COMGEO.2008.06.006
description: scientific article; zbMATH DE number 5566419