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A Min-Max Theorem for p -Center Problems on a Tree

Author

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  • D. R. Shier

    (National Bureau of Standards, Washington, D. C.)

Abstract

This paper considers the problem of locating p facilities on a tree network in order to minimize the maximum distance from a point on the network to its nearest facility. Such a problem might arise, for example, in optimally locating a fixed number of fire hydrants along a street network. The present, paper identifies an underlying min-max theorem that governs such a p -center problem. More specifically, this p-center problem is shown to be equivalent to the “dual” problem of locating p + 1 points on the network so as to maximize the minimum distance between pairs of points.

Suggested Citation

  • D. R. Shier, 1977. "A Min-Max Theorem for p -Center Problems on a Tree," Transportation Science, INFORMS, vol. 11(3), pages 243-252, August.
    • Handle: RePEc:inm:ortrsc:v:11:y:1977:i:3:p:243-252
    DOI: 10.1287/trsc.11.3.243
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    Cited by:

    1. Lei, Ting L. & Church, Richard L., 2015. "On the unified dispersion problem: Efficient formulations and exact algorithms," European Journal of Operational Research, Elsevier, vol. 241(3), pages 622-630.
    2. Martí, Rafael & Martínez-Gavara, Anna & Pérez-Peló, Sergio & Sánchez-Oro, Jesús, 2022. "A review on discrete diversity and dispersion maximization from an OR perspective," European Journal of Operational Research, Elsevier, vol. 299(3), pages 795-813.

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