# Steiner Trees in Industry

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Part of the Combinatorial Optimization book series (COOP, volume 11)

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Part of the Combinatorial Optimization book series (COOP, volume 11)

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.

algorithms Approximation communication computer computer network design interconnect layout metrics network neural networks phylogeny Routing telecommunications VLSI

- DOI https://doi.org/10.1007/978-1-4613-0255-1
- Copyright Information Springer-Verlag US 2001
- Publisher Name Springer, Boston, MA
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4613-7963-8
- Online ISBN 978-1-4613-0255-1
- Series Print ISSN 1388-3011
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