Advances in Steiner Trees

The Volume on Advances in Steiner Trees is divided into two sections. The first section of the book includes papers on the general geometric Steiner tree problem in the plane and higher dimensions. The second section of the book includes papers on the Steiner problem on graphs. The general geometric Steiner tree problem assumes that you have a given set of points in some d-dimensional space and you wish to connect the given points with the shortest network possible. The given set ofpoints are 3 Figure 1: Euclidean Steiner Problem in E usually referred to as terminals and the set ofpoints that may be added to reduce the overall length of the network are referred to as Steiner points. What makes the problem difficult is that we do not know a priori the location and cardinality ofthe number ofSteiner points. Thus)the problem on the Euclidean metric is not known to be in NP and has not been shown to be NP-Complete. It is thus a very difficult NP-Hard problem.

The Steiner Ratio of finite-dimensional ?p-spaces.- Shortest Networks for One line and Two Points in Space..- Rectilinear Steiner Minimal Trees on Parallel Lines.- Computing Shortest Networks with Fixed Topologies.- Steiner Trees, Coordinate Systems, and NP-Hardness.- Exact Algorithms for Plane Steiner Tree Problems: A Computational Study.- On Approximation of the Power-p and Bottleneck Steiner Trees.- Exact Steiner Trees in Graphs and Grid Graphs.- Grade of Service Steiner Trees in Series-Parallel Networks.- Preprocessing the Steiner Problem in Graphs.- A Fully-Polynomial Approximation Scheme for the Euclidean Steiner Augmentation Problem.- Effective Local Search Techniques for the Steiner Tree Problem.- Modern Heuristic Search Methods for the Steiner Problem in Graphs.