Minimum networks for four points in space. (English) Zbl 1009.05042

The Steiner tree problem in space is much harder then in the plane. It is shown here, for instance, that Steiner trees on 4 points in space in general cannot be solved by radicals (see also St. Mehlhos [Beitr. Algebra Geom. 41, 151-158 (2000; Zbl 0947.90094)]). The optimal Steiner tree ratio for 4 points in space is also determined.


05C05 Trees
65K10 Numerical optimization and variational techniques


Zbl 0947.90094
Full Text: DOI