A localization property for facility-location problems with arbitrary norms

In an earlier article the authors showed that, for facilities-location problems characterized by generalized distance norms and any even number of existing facilities, the optimal location of the new facility is at the intersection of the lines joining the pairs of facilities if these lines intersect at a single point. In this article they extend this concept to show that, for a more general class of problems, the optimal location is one of a set of points which is specified by the existing facilities.