Locating a minisum circle in the plane

Jack Brimberg; Henrik Juel; Anita Schöbel

doi:10.1016/j.dam.2008.03.017

Locating a minisum circle in the plane

Jack Brimberg, Henrik Juel, Anita Schöbel

Georg-August-Universität Göttingen

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We consider the problem of locating a circle with respect to existing facilities in the plane such that the sum of weighted distances between the circle and the facilities is minimized, i.e., we approximate a set of given points by a circle regarding the sum of weighted distances. If the radius of the circle is a variable we show that there always exists an optimal circle passing through two of the existing facilities. For the case of a fixed radius we provide characterizations of optimal circles in special cases. Solution procedures are suggested.

Original language	English
Journal	Discrete Applied Mathematics
Volume	157
Issue number	5
Pages (from-to)	901-912
ISSN	0166-218X
DOIs	https://doi.org/10.1016/j.dam.2008.03.017
Publication status	Published - 2009

Keywords

facility location
circular facility

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AB - We consider the problem of locating a circle with respect to existing facilities in the plane such that the sum of weighted distances between the circle and the facilities is minimized, i.e., we approximate a set of given points by a circle regarding the sum of weighted distances. If the radius of the circle is a variable we show that there always exists an optimal circle passing through two of the existing facilities. For the case of a fixed radius we provide characterizations of optimal circles in special cases. Solution procedures are suggested.

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DO - 10.1016/j.dam.2008.03.017

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

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Locating a minisum circle in the plane

Abstract

Keywords

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