Implications, conflicts, and reductions for Steiner trees

Steiner Trees and Steiner Forests

Steiner trees and polyhedra

Algorithms for Terminal Steiner Trees

The terminal Steiner tree problem (TST) consists of finding a minimum cost Steiner tree where each terminal is a leaf. We describe a factor 2ρ−ρ/(3ρ−2) approximation algorithm for the TST, where ρ is the approximation factor of a given algorithm for the Steiner tree problem. Considering the current best value of ρ, this improves a previous 3.10 factor to 2.52. For the TST restricted to instance...

Cost allocation for steiner trees

A se t of points, called consumers, and another point called central supplier, are located i n a Euclidean plane. The cost of constructing a connection between two points i s proportional t o the distance between them. The minimum cost required for connecting a l l the consumers t o the supplier i s given by a minimal Steiner tree. An example i s given i n which for every allocation of the tota...

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.