Locating a minisum circle in the plane

Jack Brimberg, Henrik Juel, Anita Schöbel

    Research output: Contribution to journalJournal articleResearchpeer-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 languageEnglish
    JournalDiscrete Applied Mathematics
    Volume157
    Issue number5
    Pages (from-to)901-912
    ISSN0166-218X
    DOIs
    Publication statusPublished - 2009

    Keywords

    • facility location
    • circular facility

    Cite this

    Brimberg, Jack ; Juel, Henrik ; Schöbel, Anita. / Locating a minisum circle in the plane. In: Discrete Applied Mathematics. 2009 ; Vol. 157, No. 5. pp. 901-912.
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    Locating a minisum circle in the plane. / Brimberg, Jack; Juel, Henrik; Schöbel, Anita.

    In: Discrete Applied Mathematics, Vol. 157, No. 5, 2009, p. 901-912.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Locating a minisum circle in the plane

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    AU - Juel, Henrik

    AU - Schöbel, Anita

    PY - 2009

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    N2 - 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.

    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.

    KW - facility location

    KW - circular facility

    U2 - 10.1016/j.dam.2008.03.017

    DO - 10.1016/j.dam.2008.03.017

    M3 - Journal article

    VL - 157

    SP - 901

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    JO - Discrete Applied Mathematics

    JF - Discrete Applied Mathematics

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    ER -