Finite Dominating Sets for Network Location Problems

A research theme involving location on networks, since its inception, has been the identification of a finite dominating set (FDS), or a finite set of points to which an optimal solution must belong. We attempt to unify and generalize results of this sort. We survey the literature and then prove some theorems that subsume most previous results and that are, at the same time, more general than previous results. The paper is aimed primarily at investigators who wish to know whether an FDS exists for a specific problem.