Optimum Steiner Ratio for Gradient-Constrained Networks Connecting Three Points in 3-Space, Part II: The Gradient-Constraint m Satisfies 1 <= m <= root 3
The authors have proved in a previous article that the Steiner ratio (the minimum ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree) for a gradient-constrained network on three points is 1/2 + (root 4 + 3m(2) - 1)/(4 root 1 + m(2)) if the maximum gradient m of an edge in the network satisfies m  = root 3. (C) 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(4), 354-361 2011
gradient-constrained networks minimum networks steiner trees locally minimal