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A game-theoretic approach for downgrading the 1-median in the plane with Manhattan metric

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  • Elisabeth Gassner

Abstract

This paper deals with downgrading the 1-median, i.e., changing values of parameters within certain bounds such that the optimal objective value of the location problem with respect to the new values is maximized. We suggest a game-theoretic view at this problem which leads to a characterization of an optimal solution. This approach is demonstrated by means of the Downgrading 1-median problem in the plane with Manhattan metric and implies an $\mathcal {O}(n\log^{2}n)$ time algorithm for this problem. Copyright Springer Science+Business Media, LLC 2009

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  • Elisabeth Gassner, 2009. "A game-theoretic approach for downgrading the 1-median in the plane with Manhattan metric," Annals of Operations Research, Springer, vol. 172(1), pages 393-404, November.
    • Handle: RePEc:spr:annopr:v:172:y:2009:i:1:p:393-404:10.1007/s10479-009-0641-1
    DOI: 10.1007/s10479-009-0641-1
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    References listed on IDEAS

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    1. Juel, Henrik & Love, Robert F., 1983. "Hull properties in location problems," European Journal of Operational Research, Elsevier, vol. 12(3), pages 262-265, March.
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    4. Gassner, Elisabeth, 2009. "Up- and downgrading the 1-center in a network," European Journal of Operational Research, Elsevier, vol. 198(2), pages 370-377, October.
    5. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
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    Cited by:

    1. Esmaeil Afrashteh & Behrooz Alizadeh & Fahimeh Baroughi, 2020. "Optimal approaches for upgrading selective obnoxious p-median location problems on tree networks," Annals of Operations Research, Springer, vol. 289(2), pages 153-172, June.
    2. Frank Plastria, 2016. "Up- and downgrading the euclidean 1-median problem and knapsack Voronoi diagrams," Annals of Operations Research, Springer, vol. 246(1), pages 227-251, November.

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