Optimum steiner ratio for gradient-constrained networks connecting three points in 3-space, part II: The gradient-constraint m satisfies equation image



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 equation image if the maximum gradient m of an edge in the network satisfies m ≤ 1. In this article, we continue this study and use the same strategy to show that this result still holds when the maximum value of m satisfies equation image. However the ratio becomes equation image if equation image. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(4), 354–361