SMT and MST in Metric Spaces — A Survey

Abstract

Here, we describe several basic facts about the combinatorial and computational structure of SMT’s and MST’s. Since we first consider arbitrary metric spaces we state only some general facts, namely

• (i) An SMT for n given points has at most n — 2 Steiner points.

• (ii) For any finite set N of points in a metric space the length of an MST for N is less than two times of the length of an SMT for N.

• (iii) Isometric spaces are not distinguished in the sense of Steiner’s Problem.