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

Rubinstein, J. H.; Thomas, D. A.; Weng, J.

Geom. Dedicata 93, 57-70 (2002).

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.

Reviewer: Imre Bárány (Budapest)

MSC:

05C05	Trees
65K10	Numerical optimization and variational techniques

Keywords:

minimum network; Steiner tree

Citations:

Zbl 0947.90094