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On Steiner minimal trees withLpdistance

โœ Scribed by Zi -Cheng Liu; Ding -Zhu Du

Publisher
Springer
Year
1992
Tongue
English
Weight
453 KB
Volume
7
Category
Article
ISSN
0178-4617

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Given a finite set of points P in the Euclidean plane, the Steiner problem asks us to constuct a shortest possible network interconnecting P. Such a network is known as a minimal Steiner tree. The Steiner problem is an intrinsically difficult one, having been shown to be NP-hard [7]; however, it oft

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Let P,,n~>3, be the set of vertices of a regular n-gon and o be the centre of P,. Let P+ = P, u [o}. In this paper we determine the Steiner minimal trees on P+. By this example we will see how complicated the Steiner problem may become if even one regular point not lying on the Steiner polygon is ad

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For a finite set of points in a metric space a Steiner Minimal Tree (SMT) is a shortest tree which interconnects these points. We also consider a relative of this problem allowing at most k additional points in the tree (k-SMT), where k is a given number. We intend to discuss these problems for all