Generalised k-Steiner Tree Problems in Normed Planes

The local Steiner problem in normed planes

Minimum Steiner Trees in Normed Planes

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. In this note we investigate various properties of minimum Steiner trees in normed planes, i.e., where the "unit disk" is an arbitrary compact convex centrally symmetric domain D having nonempty interior. We show that if the boundary of D is strictly convex and di...

Steiner Tree Problems

Solving Rectilinear Steiner Tree Problems

The rectilinear Steiner tree problem asks for a shortest tree connecting given points in the plane with rectilinear distance. The best theoretically analyzed algorithm for this problem with a fairly practical behaviour bases on dynamic programming and has a running time of O(n 2 2:62 n) (Ganley/Cohoon). The best implementation can solve random problems of size 35 (Salowe/Warme) within a day. In...

Online Priority Steiner Tree Problems

A central issue in the design of modern communication networks is the provision of Quality-of-Service (QoS) guarantees at the presence of heterogeneous users. For instance, in QoS multicasting, a source needs to efficiently transmit a message to a set of receivers, each requiring support at a different QoS level (e.g., bandwidth). This can be formulated as the Priority Steiner tree problem: Her...