Pseudo-Gilbert-Steiner trees

✍ Scribed by Trietsch, D.; Weng, J. F.

• Book ID: 101225759
• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 69 KB
• Volume: 33
• Category: Article
• ISSN: 0028-3045
• DOI: 10.1002/(sici)1097-0037(199905)33:3<175::aid-net3>3.0.co;2-l

✦ Synopsis

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.