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Minimal NetworksThe Steiner Problem and Its Generalizations

1994-03-16 Mathematics
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Release : 1994-03-16
Genre : Mathematics
Kind : eBook
Book Rating : 428/5 ( reviews)

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Book Synopsis Minimal NetworksThe Steiner Problem and Its Generalizations by : Alexander O. Ivanov

Download or read book Minimal NetworksThe Steiner Problem and Its Generalizations written by Alexander O. Ivanov. This book was released on 1994-03-16. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the classic Steiner Problem and illustrates how results of the problem's development have generated the Theory of Minimal Networks, that is systems of "rubber" branching threads of minimal length. This theory demonstrates a brilliant interconnection among differential and computational geometry, topology, variational calculus, and graph theory. All necessary preliminary information is included, and the book's simplified format and nearly 150 illustrations and tables will help readers develop a concrete understanding of the material. All nontrivial statements are proved, and plenty of exercises are included.

Steiner Tree Problems in Computer Communication Networks

2008-01-01 Mathematics
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Release : 2008-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 450/5 ( reviews)

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Book Synopsis Steiner Tree Problems in Computer Communication Networks by : Dingzhu Du

Download or read book Steiner Tree Problems in Computer Communication Networks written by Dingzhu Du. This book was released on 2008-01-01. Available in PDF, EPUB and Kindle. Book excerpt: The Steiner tree problem is one of the most important combinatorial optimization problems. It has a long history that can be traced back to the famous mathematician Fermat (1601-1665). This book studies three significant breakthroughs on the Steiner tree problem that were achieved in the 1990s, and some important applications of Steiner tree problems in computer communication networks researched in the past fifteen years. It not only covers some of the most recent developments in Steiner tree problems, but also discusses various combinatorial optimization methods, thus providing a balance between theory and practice. Sample Chapter(s). Chapter 1: Minimax Approach and Steiner Ratio (372 KB). Contents: Minimax Approach and Steiner Ratio; k -Steiner Ratios and Better Approximation Algorithms; Geometric Partitions and Polynomial Time Approximation Schemes; Grade of Service Steiner Tree Problem; Steiner Tree Problem for Minimal Steiner Points; Bottleneck Steiner Tree Problem; Steiner k -Tree and k -Path Routing Problems; Steiner Tree Coloring Problem; Steiner Tree Scheduling Problem; Survivable Steiner Network Problem. Readership: Researchers and graduate students of computer science and engineering as well as operations research.

Steiner Minimal Trees

2013-03-09 Computers
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Release : 2013-03-09
Genre : Computers
Kind : eBook
Book Rating : 851/5 ( reviews)

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Book Synopsis Steiner Minimal Trees by : Dietmar Cieslik

Download or read book Steiner Minimal Trees written by Dietmar Cieslik. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: The problem of "Shortest Connectivity", which is discussed here, has a long and convoluted history. Many scientists from many fields as well as laymen have stepped on its stage. Usually, the problem is known as Steiner's Problem and it can be described more precisely in the following way: Given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. Steiner's Problem seems disarmingly simple, but it is rich with possibilities and difficulties, even in the simplest case, the Euclidean plane. This is one of the reasons that an enormous volume of literature has been published, starting in 1 the seventeenth century and continuing until today. The difficulty is that we look for the shortest network overall. Minimum span ning networks have been well-studied and solved eompletely in the case where only the given points must be connected. The novelty of Steiner's Problem is that new points, the Steiner points, may be introduced so that an intercon necting network of all these points will be shorter. This also shows that it is impossible to solve the problem with combinatorial and geometric methods alone.

Branching Solutions To One-dimensional Variational Problems

2001-01-17 Mathematics
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Release : 2001-01-17
Genre : Mathematics
Kind : eBook
Book Rating : 33X/5 ( reviews)

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Book Synopsis Branching Solutions To One-dimensional Variational Problems by : Alexandr Ivanov

Download or read book Branching Solutions To One-dimensional Variational Problems written by Alexandr Ivanov. This book was released on 2001-01-17. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the new class of one-dimensional variational problems — the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.

Shortest Connectivity

2006-06-02 Business & Economics
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Release : 2006-06-02
Genre : Business & Economics
Kind : eBook
Book Rating : 396/5 ( reviews)

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Book Synopsis Shortest Connectivity by : Dietmar Cieslik

Download or read book Shortest Connectivity written by Dietmar Cieslik. This book was released on 2006-06-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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