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In this paper we study the Steiner minimal tree T problem for a point set Z with cardinality n and one polygonal obstacle ω in the Euclidean plane. We assume ω touches only one convex path in T that joins two terminals and that the number of extreme points of the obstacle is k . If all degree 2 vertices are omitted, then the topology of T is called the(More)
A Steiner minimal tree for a given set P of points in the Euclidean plane is a shortest network interconnecting P whose vertex set may include some additional points. The construction of Steiner minimal trees has been proved to be an jV/'-complete problem for general P. However, the W-completeness does not exclude the possibility that Steiner trees for sets(More)
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,(More)