The t-median function on graphs

Authors:
F. R. McMorris;Henry Martyn Mulder;Robert C. Powers
Affiliations:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL;Econometrisch Instituut, Erasmus Universiteit, Rotterdam, The Netherlands;Department of Mathematics, University of Louisville, Louisville, KY
Venue:
Discrete Applied Mathematics
Year:
2006

Citing 6
Cited 2

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Abstract

A median of a sequence π= x1, x2,...,xk of elements of a finite metric space (X, d) is an element x for which Σi=1k d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(π) = {x : x is a median of π} is called the median function on X, and is one of the most studied consensus functions. Based on previous characterizations of median sets M(π), a generalization of the median function is introduced and studied on various graphs and ordered sets. In addition, new results are presented for median graphs.