A correction to the definition of local center

It is known that in order to solve the minimax facility location problem on a graph with a finite set of demand points, only a finite set of possible location points, called ‘local centers’ must be considered.It has been shown that the continuous m-center problem on a graph can be solved by using a series of set covering problems in which each local center covers the demand points at a distance not greater than a corresponding number called ‘the range’ of the local center.However, all points which are at the same distance from more than two demand points, and from which there is no direction where all these distances are decreasing, must also be considered as local centers. This paper proves that, in some special cases, it is not sufficient to consider only the points where this occurs with respect to pairs of demand points. The definition of local center is corrected and the corresponding results and algorithms are revised.