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Author: Xiuzhen Cheng
Publisher: Springer Science & Business Media
ISBN: 1461302552
Category : Computers
Languages : en
Pages : 508
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Book Description
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.
Author: Xiuzhen Cheng
Publisher: Springer Science & Business Media
ISBN: 1461302552
Category : Computers
Languages : en
Pages : 508
Get Book Here
Book Description
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.
Author: Hans Jürgen Prömel
Publisher: Springer Science & Business Media
ISBN: 3322802914
Category : Mathematics
Languages : en
Pages : 251
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Book Description
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.
Author: F.K. Hwang
Publisher: Elsevier
ISBN: 0080867936
Category : Computers
Languages : en
Pages : 353
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Book Description
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.
Author: Ding-Zhu Du
Publisher: Springer Science & Business Media
ISBN: 147573171X
Category : Mathematics
Languages : en
Pages : 329
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Book Description
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.
Author: Ding-Zhu Du
Publisher: Springer Science & Business Media
ISBN: 0387238301
Category : Business & Economics
Languages : en
Pages : 395
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Book Description
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.
Author: Jürgen Lerner
Publisher: Springer Science & Business Media
ISBN: 3642020933
Category : Computers
Languages : en
Pages : 411
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Book Description
A state-of-the-art survey that reports on the progress made in selected areas of this important and growing field, aiding the analysis of existing networks and the design of new and more efficient algorithms for solving various problems on these networks.
Author: Marcus Brazil
Publisher: Springer
ISBN: 3319139150
Category : Mathematics
Languages : en
Pages : 359
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Book Description
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.
Author: Oscar H. Ibarra
Publisher: Springer
ISBN: 3540456554
Category : Computers
Languages : en
Pages : 619
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Book Description
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.
Author: Tandy Warnow
Publisher: Springer Science & Business Media
ISBN: 3540405348
Category : Computers
Languages : en
Pages : 573
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Book Description
The papers in this volume were presented at the 9th Annual International C- puting and Combinatorics Conference (COCOON 2003), held July 25–28, 2003, in Big Sky, MT, USA. The topics cover most aspects of theoretical computer science and combinatorics related to computing. Submissionstotheconferencethisyearwereconductedelectronically.Atotal of 114 papers were submitted, of which 52 were accepted. The papers were evaluated by an international program committee consisting of Nina Amenta, Tetsuo Asano, Bernard Chazelle, Zhixiang Chen, Francis Chin, Kyung-Yong Chwa, Robert Cimikowski, Anne Condon, Michael Fellows, Anna Gal, Michael Hallett,DanielHuson,NaokiKatoh,D.T.Lee,BernardMoret,BrendanMumey, Gene Myers, Hung Quang Ngo, Takao Nishizeki, Cindy Phillips, David Sanko?, Denbigh Starkey, Jie Wang, Lusheng Wang, Tandy Warnow and Binhai Zhu. It is expected that most of the accepted papers will appear in a more complete form in scienti?c journals. The submitted papers were from Canada (6), China (7), Estonia (1), F- land (1), France (1), Germany (8), Israel (4), Italy (1), Japan (11), Korea (22), Kuwait (1), New Zealand (1), Singapore (2), Spain (1), Sweden (2), Switzerland (3), Taiwan (7), the UK (1) and the USA (34). Each paper was evaluated by at least three Program Committee members, assisted in some cases by subre- rees. In addition to selected papers, the conference also included three invited presentations by Jon Bentley, Dan Gus?eld and Joel Spencer.
Author: Ding-Zhu Du
Publisher: Springer
ISBN: 303026176X
Category : Computers
Languages : en
Pages : 691
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Book Description
This book constitutes the proceedings of the 25th International Conference on Computing and Combinatorics, COCOON 2019, held in Xi’an, China, in July 2019. The 55 papers presented in this volume were carefully reviewed and selected from 124 submissions. The papers cover various topics, including algorithm design, approximation algorithm, graph theory, complexity theory, problem solving, optimization, computational biology, computational learning, communication network, logic, and game theory.
