Integrality Ratio for Group Steiner Trees and Directed Steiner Trees

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.

Steiner Trees and Steiner Forests

Directed Steiner trees with diffusion costs

Given a directed arc-weighted graph G with n nodes, a root r and k terminals, the Directed Steiner Tree problem (DST) consists in finding a minimum-weight tree rooted at r and spanning all the terminals. If this problem has several applications in multicast routing in packet switching networks, the modeling is not adapted anymore in networks based upon the circuit switching principle in which s...

On Directed Steiner Trees with Multiple Roots

We introduce a new Steiner-type problem for directed graphs named q-Root Steiner Tree. Here one is given a directed graph G = (V,A) and two subsets of its vertices, R of size q and T , and the task is to find a minimum size subgraph of G that contains a path from each vertex of R to each vertex of T . The special case of this problem with q = 1 is the well known Directed Steiner Tree problem, w...

Steiner trees and polyhedra