The Steiner Tree Problem

Frank K. Hwang, Dana S. Richards and Pawel Winter (Eds.)978-0-444-89098-6

The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points – locating them has proved problematic and research has diverged along many different avenues. This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarnik and Kossler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging. The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.

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Table of contents :
Content:
General Editor
Page ii

Edited by
Page iii

Copyright page
Page iv

Foreword
Pages v-vi

Chapter 1 Introduction
Pages 3-19

Chapter 2 Exact Algorithms
Pages 21-35

Chapter 3 The Steiner Ratio
Pages 37-49

Chapter 4 Heuristics
Pages 51-61

Chapter 5 Special Terminal-Sets
Pages 63-76

Chapter 6 Generalizations
Pages 77-89

Chapter 1 Introduction
Pages 93-102

Chapter 2 Reductions
Pages 103-124

Chapter 3 Exact Algorithms
Pages 125-149

Chapter 4 Heuristics
Pages 151-176

Chapter 5 Polynomially Solvable Cases
Pages 177-188

Chapter 6 Generalizations
Pages 189-202

Chapter 1 Introduction
Pages 205-219

Chapter 2 Heuristic Algorithms
Pages 221-242

Chapter 3 Polynomially Solvable Cases
Pages 243-255

Chapter 4 Generalizations
Pages 257-266

Chapter 5 Routing
Pages 267-283

Chapter 1 Steiner Trees in Other Metric Spaces
Pages 287-300

Chapter 2 Phylogenetic Trees
Pages 301-321

Subject Index
Pages 323-334

Author Index
Pages 335-339