Steiner forms

Steiner Trees and Steiner Forests

Solving group Steiner problems as Steiner problems

The generalized spanning tree or group Steiner problem (GSP) is a generalization of the Steiner problem in graphs (SPG): one requires a tree spanning (at least) one vertex of each subset, given in a family of vertex subsets, while minimizing the sum of the corresponding edge costs. Specialized solution procedures have been developed for this problem. In this paper we investigate the performance...

The Steiner diameter of a graph

‎The Steiner distance of a graph‎, ‎introduced by Chartrand‎, ‎Oellermann‎, ‎Tian and Zou in 1989‎, ‎is a natural generalization of the‎ ‎concept of classical graph distance‎. ‎For a connected graph $G$ of‎ ‎order at least $2$ and $Ssubseteq V(G)$‎, ‎the Steiner‎ ‎distance $d(S)$ among the vertices of $S$ is the minimum size among‎ ‎all connected subgraphs whose vertex sets contain $S$‎. ‎Let $...

The Steiner Ratio for Obstacle-Avoiding Rectilinear Steiner Trees

We consider the problem of finding a shortest rectilinear Steiner tree for a given set of points in the plane in the presence of rectilinear obstacles that must be avoided. We extend the Steiner ratio to the obstacle-avoiding case and show that it is equal to the Steiner ratio for the obstacle-free case.

Approximations for Steiner Trees with Minimum Number of Steiner Points

Given n terminals in the Euclidean plane and a positive constant, find a Steiner tree interconnecting all terminals with the minimum number of Steiner points such that the Euclidean length of each edge is no more than the given positive constant. This problem is NP-hard with applications in VLSI design, WDM optical networks and wireless communications. In this paper, we show that (a) the Steine...