Steiner Trees in Industry
Steiner Trees in Industry

Author: Xiuzhen Cheng

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 508

ISBN-13: 1461302552

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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.

The Steiner Tree Problem
The Steiner Tree Problem

Author: Hans Jürgen Prömel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 251

ISBN-13: 3322802914

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In recent years, algorithmic graph theory has become increasingly important as a link between discrete mathematics and theoretical computer science. This textbook introduces students of mathematics and computer science to the interrelated fields of graphs theory, algorithms and complexity.

The Steiner Tree Problem
The Steiner Tree Problem

Author: F.K. Hwang

Publisher: Elsevier

Published: 1992-10-20

Total Pages: 353

ISBN-13: 0080867936

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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 Jarník and Kössler 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.

Advances in Steiner Trees
Advances in Steiner Trees

Author: Ding-Zhu Du

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 329

ISBN-13: 147573171X

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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.

Handbook of Combinatorial Optimization
Handbook of Combinatorial Optimization

Author: Ding-Zhu Du

Publisher: Springer Science & Business Media

Published: 2006-08-18

Total Pages: 395

ISBN-13: 0387238301

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This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.

Automata, Languages, and Programming
Automata, Languages, and Programming

Author: Fedor V. Fomin

Publisher: Springer

Published: 2013-07-03

Total Pages: 879

ISBN-13: 3642392067

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This two-volume set of LNCS 7965 and LNCS 7966 constitutes the refereed proceedings of the 40th International Colloquium on Automata, Languages and Programming, ICALP 2013, held in Riga, Latvia, in July 2013. The total of 124 revised full papers presented were carefully reviewed and selected from 422 submissions. They are organized in three tracks focussing on algorithms, complexity and games; logic, semantics, automata and theory of programming; and foundations of networked computation.

Shortest Connectivity
Shortest Connectivity

Author: Dietmar Cieslik

Publisher: Springer Science & Business Media

Published: 2006-06-02

Total Pages: 277

ISBN-13: 0387235396

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The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology.

Combinatorial Optimization
Combinatorial Optimization

Author: Bernhard Korte

Publisher: Springer Science & Business Media

Published: 2006-01-27

Total Pages: 596

ISBN-13: 3540292977

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This well-written textbook on combinatorial optimization puts special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. The book contains complete (but concise) proofs, as well as many deep results, some of which have not appeared in any previous books.

Frontiers in Nature-Inspired Industrial Optimization
Frontiers in Nature-Inspired Industrial Optimization

Author: Mahdi Khosravy

Publisher: Springer Nature

Published: 2021-08-06

Total Pages: 245

ISBN-13: 981163128X

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The book provides a collection of recent applications of nature inspired optimization in industrial fields. Different optimization techniques have been deployed, and different problems have been effectively analyzed. The valuable contributions from researchers focus on three ultimate goals (i) improving the accuracy of these techniques, (ii) achieving higher speed and lower computational complexity, and (iii) working on their proposed applications. The book is helpful for active researchers and practitioners in the field.

Computing and Combinatorics
Computing and Combinatorics

Author: Oscar H. Ibarra

Publisher: Springer

Published: 2003-08-02

Total Pages: 619

ISBN-13: 3540456554

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This book constitutes the refereed proceedings of the 8th Annual International Computing and Combinatorics Conference, COCOON 2002, held in Singapore in August 2002. The 60 revised full papers presented together with three invited contributions were carefully reviewed and selected from 106 submissions. The papers are organized in topical sections on complexity theory, discrete algorithms, computational biology and learning theory, radio networks, automata and formal languages, Internet networks, computational geometry, combinatorial optimization, and quantum computing.