The Steiner Tree Problem
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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.
"A very simple but instructive problem was treated by Jacob Steiner, the famous representative of geometry at the University of Berlin in the early nineteenth century. Three villages A,B ,C are to be joined by a system of roads of minimum length. " Due to this remark of Courant and Robbins (1941), a problem received its name that actually reaches two hundred years further back and should more appropriately be attributed to the French mathematician Pierre Fermat. At the end of his famous treatise "Minima and Maxima" he raised the question to find for three given points in the plane a fourth one in such a way that the sum of its distances to the given points is minimized - that is, to solve the problem mentioned above in its mathematical abstraction. It is known that Evangelista Torricelli had found a geometrical solution for this problem already before 1640. During the last centuries this problem was rediscovered and generalized by many mathematicians, including Jacob Steiner. Nowadays the term "Steiner prob lem" refers to a problem where a set of given points PI, . . . ,Pn have to be connected in such a way that (i) any two of the given points are joined and (ii) the total length (measured with respect to some predefined cost function) is minimized.
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.
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.
Algorithm Theory Swat 2002
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Author : Martti Penttonen
language : en
Publisher: Springer
Release Date : 2003-08-02
Algorithm Theory Swat 2002 written by Martti Penttonen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-02 with Computers categories.
This book constitutes the refereed proceedings of the 8th Scandinavian Workshop on Algorithm Theory, SWAT 2002, held in Turku, Finland, in July 2002. The 43 revised full papers presented together with two invited contributions were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections on scheduling, computational geometry, graph algorithms, robotics, approximation algorithms, data communication, computational biology, and data storage and manipulation.
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
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 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 Minimal Trees
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Author : Dietmar Cieslik
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Steiner Minimal Trees 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 2013-03-09 with Computers categories.
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.
Nature Inspired Cooperative Strategies For Optimization Nicso 2007
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Author : Natalio Krasnogor
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-14
Nature Inspired Cooperative Strategies For Optimization Nicso 2007 written by Natalio Krasnogor 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 2008-05-14 with Computers categories.
Biological and natural processes have been a continuous source of inspiration for the sciences and engineering. For instance, the work of Wiener in cybernetics was influenced by feedback control processes observable in biological systems; McCulloch and Pitts description of the artificial neuron was instigated by biological observations of neural mechanisms; the idea of survival of the fittest inspired the field of evolutionary algorithms and similarly, artificial immune systems, ant colony optimisation, automated self-assembling programming, membrane computing, etc. also have their roots in natural phenomena. The second International Workshop on Nature Inspired Cooperative Strategies for Optimization (NICSO), was held in Acireale, Italy, during November 8-10, 2007. The aim for NICSO 2007 was to provide a forum were the latest ideas and state of the art research related to cooperative strategies for problem solving arising from Nature could be discussed. The contributions collected in this book were strictly peer reviewed by at least three members of the international programme committee, to whom we are indebted for their support and assistance. The topics covered by the contributions include several well established nature inspired techniques like Genetic Algorithms, Ant Colonies, Artificial Immune Systems, Evolutionary Robotics, Evolvable Systems, Membrane Computing, Quantum Computing, Software Self Assembly, Swarm Intelligence, etc.
Handbook Of Optimization In Telecommunications
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Author : Mauricio G.C. Resende
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Handbook Of Optimization In Telecommunications written by Mauricio G.C. Resende 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 2008-12-10 with Mathematics categories.
This comprehensive handbook brings together experts who use optimization to solve problems that arise in telecommunications. It is the first book to cover in detail the field of optimization in telecommunications. Recent optimization developments that are frequently applied to telecommunications are covered. The spectrum of topics covered includes planning and design of telecommunication networks, routing, network protection, grooming, restoration, wireless communications, network location and assignment problems, Internet protocol, World Wide Web, and stochastic issues in telecommunications. The book’s objective is to provide a reference tool for the increasing number of scientists and engineers in telecommunications who depend upon optimization.