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doi:10.1016/j.dam.2003.10.003 
Copyright © 2003 Elsevier B.V. All rights reserved.
On k nearest points of a finite set in a normed linear space
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Elisabetta Alvoni
Received 31 May 2002;
Revised 22 October 2003;
accepted 29 October 2003.
Available online 5 March 2004.
Abstract
Given a finite set A={a1,a2,…,an} in a normed linear space X; for x
X, let πi(x) be a permutation of {1,2,…,n} such that ||x−aπ1(x)||
||x−aπ2(x)||
||x−aπn(x)||. We consider the following problem: for 1kn, let
be the average distance to the k nearest points from a point x of the space; we are interested in minimizing this average when x describes the space X and in finding optimal solutions. This problem, which has a clear practical meaning, seems to have received little attention. Several properties of the solutions are proved.
Author Keywords: Median; Fermat point; Location
