Ebook: 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.

---

This book presents an up-to-date set of contributions by the most influential authors on the Steiner Tree problem. The authors address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications.
Audience: The book is intended for advanced undergraduates, graduates and research scientists in Combinational Optimization and Computer Science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.

---

This book presents an up-to-date set of contributions by the most influential authors on the Steiner Tree problem. The authors address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications.
Audience: The book is intended for advanced undergraduates, graduates and research scientists in Combinational Optimization and Computer Science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.
Content:
Front Matter....Pages i-xii
The Steiner Ratio of finite-dimensional L p -spaces....Pages 1-13
Shortest Networks for One Line and Two Points in Space....Pages 15-26
Rectilinear Steiner Minimal Trees on Parallel Lines....Pages 27-37
Computing Shortest Networks with Fixed Topologies....Pages 39-62
Steiner Trees, Coordinate Systems and NP-Hardness....Pages 63-80
Exact Algorithms for Plane Steiner Tree Problems: A Computational Study....Pages 81-116
On Approximation of the Power-p and Bottleneck Steiner Trees....Pages 117-135
Exact Steiner Trees in Graphs and Grid Graphs....Pages 137-162
Grade of Service Steiner Trees in Series-Parallel Networks....Pages 163-174
Preprocessing the Steiner Problem in Graphs....Pages 175-233
A Fully Polynomial Approximation Scheme for the Euclidean Steiner Augmentation Problem....Pages 235-253
Effective Local Search Techniques for the Steiner Tree Problem....Pages 255-281
Modern Heuristic Search Methods for the Steiner Tree Problem in Graphs....Pages 283-323

---

This book presents an up-to-date set of contributions by the most influential authors on the Steiner Tree problem. The authors address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications.
Audience: The book is intended for advanced undergraduates, graduates and research scientists in Combinational Optimization and Computer Science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.
Content:
Front Matter....Pages i-xii
The Steiner Ratio of finite-dimensional L p -spaces....Pages 1-13
Shortest Networks for One Line and Two Points in Space....Pages 15-26
Rectilinear Steiner Minimal Trees on Parallel Lines....Pages 27-37
Computing Shortest Networks with Fixed Topologies....Pages 39-62
Steiner Trees, Coordinate Systems and NP-Hardness....Pages 63-80
Exact Algorithms for Plane Steiner Tree Problems: A Computational Study....Pages 81-116
On Approximation of the Power-p and Bottleneck Steiner Trees....Pages 117-135
Exact Steiner Trees in Graphs and Grid Graphs....Pages 137-162
Grade of Service Steiner Trees in Series-Parallel Networks....Pages 163-174
Preprocessing the Steiner Problem in Graphs....Pages 175-233
A Fully Polynomial Approximation Scheme for the Euclidean Steiner Augmentation Problem....Pages 235-253
Effective Local Search Techniques for the Steiner Tree Problem....Pages 255-281
Modern Heuristic Search Methods for the Steiner Tree Problem in Graphs....Pages 283-323
....