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

D. R. Shier
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D. R. Shier: National Bureau of Standards, Washington, D. C.

Transportation Science, 1977, vol. 11, issue 3, 243-252

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.

Date: 1977
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:11:y:1977:i:3:p:243-252

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