Minimax Location of a Facility in a Network

The problem is that of locating a facility in a network N so as to minimize the largest of its distances from the vertices of N. A method is given that either solves the problem, or else reduces it to an analogous problem for a single “cyclic component” of N. When N is acyclic (a tree), a very efficient solution algorithm results. Partial analogs of these results are given for a “weighted-distance” extension of the problem.