Steiner Trees in Industry

Front Cover
Xiuzhen Cheng, Ding-Zhu Du
Springer Science & Business Media, Dec 1, 2013 - Computers - 507 pages
This book is a collection of articles studying various Steiner tree prob lems with applications in industries, such as the design of electronic cir cuits, computer networking, telecommunication, and perfect phylogeny. The Steiner tree problem was initiated in the Euclidean plane. Given a set of points in the Euclidean plane, the shortest network interconnect ing the points in the set is called the Steiner minimum tree. The Steiner minimum tree may contain some vertices which are not the given points. Those vertices are called Steiner points while the given points are called terminals. The shortest network for three terminals was first studied by Fermat (1601-1665). Fermat proposed the problem of finding a point to minimize the total distance from it to three terminals in the Euclidean plane. The direct generalization is to find a point to minimize the total distance from it to n terminals, which is still called the Fermat problem today. The Steiner minimum tree problem is an indirect generalization. Schreiber in 1986 found that this generalization (i.e., the Steiner mini mum tree) was first proposed by Gauss.
 

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Contents

Genetic Algorithm Approaches to Solve Various
30
Solving MStTG Problem by Genetic Algorithm
39
Solving CMStTG Problem by Genetic Algorithm
49
Solving MEStT Problem by Genetic Algorithm
55
29
66
Neural Network Approaches to Solve Various
71
vi
73
Steiner Tree Problems in VLSI Layout Designs
101
Approximation Algorithms for the Steiner
235
A Proposed Experiment on Soap Film Solutions
280
Steiner Tree Based Distributed Multicast Routing
326
On Cost Allocation in Steiner Tree Networks
353
Steiner Trees and the Dynamic Quadratic
376
Polynomial Time Algorithms for the Rectilinear
405
Minimum Networks for Separating
427
A First Level Scatter Search Implementation for Solving
440

Polyhedral Approaches for the Steiner Tree
174
The Perfect Phylogeny Problem
203
A Tutorial
467
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