Pseudo-Gilbert-Steiner trees

The Gilbert network problem is a generalization of the Steiner minimal tree problem derived by adding flow-dependent weights to the edges. In this paper, we define a special class of minimum Gilbert networks, called pseudo-Gilbert–Steiner trees, and we show that it can be constructed by Gilbert’s generalization of Melzak’s method. Besides, a counterexample, a pseudo-Gilbert–Steiner tree, is constructed to show that the condition given by Trietsch was misquoted by Weng. © 1999 John Wiley & Sons, Inc. Networks 33: 175–178, 1999