On the rectangular p-center problem.

*(English)*Zbl 0614.90034The p-center problem consists in finding the location of p facilities such that any among n given points is as close as possible to anyone of these facilities. In other words minimize the maximal distance of the given points to their nearest facility.

This paper studies ways to solve the p-center problem in the plane, when distances are rectilinear. After describing the well-known O(n) solution method for the 1-center problem, it is shown how the 2-center problem may be solved in O(n) time, and the 3-center problem in O(n log n) time.

Making use of this last result an \(O(n^{2p-5}\log n)\) algorithm is suggested for cases where \(p>3\), which can further be simplified into an O(n log\({}^{p-2}n)\) heuristic.

This paper studies ways to solve the p-center problem in the plane, when distances are rectilinear. After describing the well-known O(n) solution method for the 1-center problem, it is shown how the 2-center problem may be solved in O(n) time, and the 3-center problem in O(n log n) time.

Making use of this last result an \(O(n^{2p-5}\log n)\) algorithm is suggested for cases where \(p>3\), which can further be simplified into an O(n log\({}^{p-2}n)\) heuristic.

Reviewer: F.Plastria

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\textit{Z. Drezner}, Nav. Res. Logist. 34, No. 1--2, 229--234 (1987; Zbl 0614.90034)

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