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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.
List of contents
Steiner Minimum Trees in Uniform Orientation Metrics.- Genetic Algorithm Approaches to Solve Various Steiner Tree Problems.- Neural Network Approaches to Solve Various Steiner Tree Problems.- Steiner Tree Problems in VLSI Layout Designs.- Polyhedral Approaches for the Steiner Tree Problem on Graphs.- The Perfect Phylogeny Problem.- Approximation Algorithms for the Steiner Tree Problem in Graphs.- A Proposed Experiment on Soap Film Solutions of Planar Euclidean Steiner Trees.- SteinLib: An Updated Library on Steiner Tree Problems in Graphs.- Steiner Tree Based Distributed Multicast Routing in Networks.- On Cost Allocation in Steiner Tree Networks.- Steiner Trees and the Dynamic Quadratic Assignment Problem.- Polynomial Time Algorithms for the Rectilinear Steiner Tree Problem.- Minimum Networks for Separating and Surrounding Objects.- A First Level Scatter Search Implementation for Solving the Steiner Ring Problem in Telecommunications Network Design.- The Rectilinear Steiner Tree Problem: A Tutorial.
