We consider the problem of constructing a shortest Euclidean 2-connected Steiner network (SMN) for a set of terminals. This problem has natural applications in the design of survivable communication networks. A SMN decomposes into components that are full Steiner trees. Winter and Zachariasen proved that all cycles in SMNs with Steiner points must have two pairs of consecutive terminals of degree 2. We use this result and the notion of reduced block-bridge trees of Luebke to show that no component in a SMN spans more than approximately one-third of the terminals. Furthermore, we show that no component spans more than two terminals on the boundary of the convex hull of the terminals; such two terminals must in addition be consecutive on the boundary of this convex hull. Algorithmic implications of these results are discussed.
我们考虑为一组终端构建最短的欧几里得2连通Steiner网络(SMN)的问题。这个问题在可生存的通信网络的设计中具有自然的应用。 SMN分解为完整的Steiner树的组件。 Winter和Zachariasen证明,带有Steiner点的SMN中的所有循环必须具有两对连续的2度端点。三分之一的码头。此外,我们表明,在端子的凸包的边界上,没有组件跨越两个以上的端子。另外,这两个终端在该凸包的边界上必须是连续的。讨论了这些结果的算法含义。 P>
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