Further improvements of Steiner tree approximations

The Steiner tree problem requires to find a shortest tree connecting a given set of terminal points in a metric space. We suggest a better and fast heuristic for the Steiner problem in graphs and in rectilinear plane. This heuristic finds a Steiner tree at most 1.757 and 1.267 times longer than the optimal solution in graphs and rectilinear plane, respectively

1.757 and 1.267-Approximation Algorithms for the Network and Rectilinear Steiner Tree Problems

The Steiner tree problem requires to find a shortest tree connecting a given set of terminal points in a metric space. We suggest a better and fast heuristic for the Steiner problem in graphs and in rectilinear plane. This heuristic finds a Steiner tree at most 1.757 and 1.267 times longer than the optimal solution in graphs and rectilinear plane, respectively. Dept. of Computer Science, University of Bonn, 53117 Bonn, and the International Computer Science Institute, Berkeley, California. Research partially supported by the DFG Grant KA 673/4-1, and by the ESPRIT BR Grants 7097 and by ECUS 030. Email: [email protected]. y Institute of Mathematics, Akademiei 5, Kishinev, 277028, Moldova, email: [email protected]. Research partially supported by Volkswagen Stiftung. Parts of this work were done in Max-Planck-Institut fur Informatik, Saarbrucken, Germany 1 Introduction Consider a metric space with a distance function d. For any set of terminal points S one can efficiently..