Advances In Steiner Trees
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Advances In Steiner Trees
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Advances In Steiner Trees written by Ding-Zhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Steiner Tree Problems In Computer Communication Networks
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Author : Dingzhu Du
language : en
Publisher: World Scientific
Release Date : 2008
Steiner Tree Problems In Computer Communication Networks written by Dingzhu Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.
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.
Advances In Steiner Trees
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-01-31
Advances In Steiner Trees written by Ding-Zhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-31 with Computers categories.
This book presents an up-to-date set of contributions by the most influential authors on the Steiner Tree problem. The authors address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications. Audience: The book is intended for advanced undergraduates, graduates and research scientists in Combinational Optimization and Computer Science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.
The Steiner Tree Problem
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Author : F.K. Hwang
language : en
Publisher: Elsevier
Release Date : 1992-10-20
The Steiner Tree Problem written by F.K. Hwang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-20 with Computers categories.
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.
The Steiner Tree Problem
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Author : Hans Jürgen Prömel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Steiner Tree Problem written by Hans Jürgen Prömel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Steiner Trees In Industry
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Author : Xiuzhen Cheng
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Steiner Trees In Industry written by Xiuzhen Cheng and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Computers categories.
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.
Steiner Trees In Industry
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Author : Xiuzhen Cheng
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-10-31
Steiner Trees In Industry written by Xiuzhen Cheng and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-31 with Computers categories.
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.
Spanning Trees And Optimization Problems
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Author : Bang Ye Wu
language : en
Publisher: CRC Press
Release Date : 2004-01-27
Spanning Trees And Optimization Problems written by Bang Ye Wu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-27 with Computers categories.
The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under
The Steiner Ratio
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Author : Dietmar Cieslik
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Steiner Ratio written by Dietmar Cieslik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Computers categories.
Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms.
Optimal Interconnection Trees In The Plane
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Author : Marcus Brazil
language : en
Publisher: Springer
Release Date : 2015-04-13
Optimal Interconnection Trees In The Plane written by Marcus Brazil and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-13 with Mathematics categories.
This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions. Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane. They show readers how an understanding of this structure can lead to practical exact algorithms for constructing such trees. The book also details numerous breakthroughs in this area over the past 20 years, features clearly written proofs, and is supported by 135 colour and 15 black and white figures. It will help graduate students, working mathematicians, engineers and computer scientists to understand the principles required for designing interconnection networks in the plane that are as cost efficient as possible.