  In the present paper we show how one can calculate the lengths of edges of a
minimum spanning tree constructed for a finite metric space, in terms of the
Gromov-Hausdorff distances from this space to simplices of sufficiently large
diameter. Here by simplices we mean finite metric spaces all of whose nonzero
distances are the same. As an application, we reduce the problems of finding a
Steiner minimal tree length or a minimal filling length to maximization of the
total distance to some finite number of simplices considered as points of the
Gromov-Hausdorff space.
