Location on Tree Networks: P-Centre and n-Dispersion Problems

We consider two problems of locating facilities on trees. In the first, we wish to determine the location of n points so as to maximize the minimum distance between any pair. In the second we wish to locate p centers of a single type of facility so as to minimize the maximum distance between any point and the center nearest to it. We provide polynomial algorithms for both problems, of O|N|2 log n · log |N| for the first problem and of O|N|2 log p for the second, where |N| is the number of nodes in the tree.

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