A correction to the definition of local center
type: Item
instance of: scholarly article
title: A correction to the definition of local center
zbMATH Open document ID: 0564.90014
DOI: 10.1016/0377-2217(85)90011-6
author: José A. Moreno
published in: European Journal of Operational Research
publication date: 1985-01-01T00:00:00Z
review text: It is known that in order to solve the minimax facility location problem on a graph with a finite set of demand points, only a finite set of possible location points, called 'local centers' must be considered. It has been shown that the continuous m-center problem on a graph can be solved by using a series of set covering problems in which each local center covers the demand points at a distance not greater than a corresponding number called 'the range' of the local center. However, all points which are at the same distance from more than two demand points, and from which there is no direction where all these distances are decreasing, must also be considered as local centers. This paper proves that, in some special cases, it is not sufficient to consider only the points where this occurs with respect to pairs of demand points. The definition of local center is corrected and the corresponding results and algorithms are revised.
Mathematics Subject Classification ID: 90B05
zbMATH DE Number: 3900471
zbMATH Keywords: location on networks
zbMATH Keywords: minimax facility location
zbMATH Keywords: graph
zbMATH Keywords: local centers
MaRDI profile type: Publication
full work available at URL: 0377-2217(85)90011-6
OpenAlex ID: W2093066533
cites work: Locational analysis
cites work: Q3316922
cites work: The m-Center Problem
description: scientific article; zbMATH DE number 3900471