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.
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.
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.
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 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.
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 Natural Computation Fuzzy Systems And Knowledge Discovery
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Author : Yong Liu
language : en
Publisher: Springer Nature
Release Date : 2019-11-06
Advances In Natural Computation Fuzzy Systems And Knowledge Discovery written by Yong Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-06 with Technology & Engineering categories.
This book discusses the recent advances in natural computation, fuzzy systems and knowledge discovery. Presenting selected, peer-reviewed papers from the 15th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019), held in Kunming, China, from 20 to 22 July 2019, it is a useful resource for researchers, including professors and graduate students, as well as R&D staff in industry.
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.
Advanced Routing Of Electronic Modules
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Author : Michael Pecht
language : en
Publisher: CRC Press
Release Date : 2024-11-01
Advanced Routing Of Electronic Modules written by Michael Pecht and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Technology & Engineering categories.
The rapid growth of the electronic products market has created an increasing need for affordable, reliable, high-speed and high-density multi-layer printed circuit boards (PCBs). This book presents the technologies, algorithms, and methodologies for engineers and others developing the next generation of electronic products. A vision of the future in advanced electronics Advanced Routing of Electronic Modules provides both fundamental theory and advanced technologies for improving routing. Beginning chapters discuss approaches to approximate a minimum rectilinear Steiner tree from a minimum spanning tree and introduce ways to avoid obstacles for routing simple multi-terminal nets sequentially in a workspace. Timing delay, clock skew, and noise control requirements in signal integrity are described as well as computer-aided approaches to managing these requirements in high-speed PCB/MCM routing. Later chapters present the two-layer wiring problem, rip-up and reroute approaches, and parallel routing, including global routing, boundary crossing placement, and detailed maze routing in hardware acceleration. Data structures, data management, and algorithms for parallel routing in a multiple-processor hardware systems are also covered.
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.