  Given a set of points, we define a minimum Steiner point tree to be a tree
interconnecting these points and possibly some additional points such that the
length of every edge is at most 1 and the number of additional points is
minimized. We propose using Steiner minimal trees to approximate minimum
Steiner point trees. It is shown that in arbitrary metric spaces this gives a
performance difference of at most $2n-4$, where $n$ is the number of terminals.
We show that this difference is best possible in the Euclidean plane, but not
in Minkowski planes with parallelogram unit balls. We also introduce a new
canonical form for minimum Steiner point trees in the Euclidean plane; this
demonstrates that minimum Steiner point trees are shortest total length trees
with a certain discrete-edge-length condition.
