Optimal Interconnection Trees In The Plane

Author : Marcus Brazil,Martin Zachariasen
Publisher : Springer
Page : 344 pages
File Size : 40,8 Mb
Release : 2015-04-13
Category : Mathematics
ISBN : 9783319139159

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Optimal Interconnection Trees in the Plane by Marcus Brazil,Martin Zachariasen Pdf

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 : Sara Brunetti
Publisher : Springer Nature
Page : 462 pages
File Size : 50,8 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031577932

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Discrete Geometry and Mathematical Morphology by Sara Brunetti Pdf

Author : Andrew V. Goldberg,Alexander S. Kulikov
Publisher : Springer
Page : 400 pages
File Size : 49,5 Mb
Release : 2016-05-31
Category : Computers
ISBN : 9783319388519

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Experimental Algorithms by Andrew V. Goldberg,Alexander S. Kulikov Pdf

This book constitutes the refereed proceedings of the 15th International Symposium on Experimental Algorithms, SEA 2016, held in St. Petersburg, Russia, in June 2016. The 25 revised full papers presented were carefully reviewed and selected from 54 submissions. The main theme of the symposium is the role of experimentation and of algorithm engineering techniques in the design and evaluation of algorithms and data structures. SEA covers a wide range of topics in experimental algorithmics, bringing together researchers from algorithm engineering, mathematical programming, and combinatorial optimization communities.

Author : Donghyun Kim,R. N. Uma,Zhipeng Cai,Dong Hoon Lee
Publisher : Springer Nature
Page : 678 pages
File Size : 41,6 Mb
Release : 2020-08-27
Category : Computers
ISBN : 9783030581503

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Computing and Combinatorics by Donghyun Kim,R. N. Uma,Zhipeng Cai,Dong Hoon Lee Pdf

This book constitutes the proceedings of the 26th International Conference on Computing and Combinatorics, COCOON 2020, held in Atlanta, GA, USA, in August 2020. Due to the COVID-19 pandemic COCOON 2020 was organized as a fully online conference. The 54 papers presented in this volume were carefully reviewed and selected from 126 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.

Author : Gergely Ambrus,Imre Bárány,Károly J. Böröczky,Gábor Fejes Tóth,János Pach
Publisher : Springer
Page : 458 pages
File Size : 54,5 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9783662574133

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New Trends in Intuitive Geometry by Gergely Ambrus,Imre Bárány,Károly J. Böröczky,Gábor Fejes Tóth,János Pach Pdf

This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.

Author : Andrew B. Kahng,Gabriel Robins
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 53,9 Mb
Release : 2013-04-17
Category : Technology & Engineering
ISBN : 9781475723632

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On Optimal Interconnections for VLSI by Andrew B. Kahng,Gabriel Robins Pdf

On Optimal Interconnections for VLSI describes, from a geometric perspective, algorithms for high-performance, high-density interconnections during the global and detailed routing phases of circuit layout. First, the book addresses area minimization, with a focus on near-optimal approximation algorithms for minimum-cost Steiner routing. In addition to practical implementations of recent methods, the implications of recent results on spanning tree degree bounds and the method of Zelikovsky are discussed. Second, the book addresses delay minimization, starting with a discussion of accurate, yet algorithmically tractable, delay models. Recent minimum-delay constructions are highlighted, including provably good cost-radius tradeoffs, critical-sink routing algorithms, Elmore delay-optimal routing, graph Steiner arborescences, non-tree routing, and wiresizing. Third, the book addresses skew minimization for clock routing and prescribed-delay routing formulations. The discussion starts with early matching-based constructions and goes on to treat zero-skew routing with provably minimum wirelength, as well as planar clock routing. Finally, the book concludes with a discussion of multiple (competing) objectives, i.e., how to optimize area, delay, skew, and other objectives simultaneously. These techniques are useful when the routing instance has heterogeneous resources or is highly congested, as in FPGA routing, multi-chip packaging, and very dense layouts. Throughout the book, the emphasis is on practical algorithms and a complete self-contained development. On Optimal Interconnections for VLSI will be of use to both circuit designers (CAD tool users) as well as researchers and developers in the area of performance-driven physical design.

Author : Dingzhu Du,Xiaodong Hu
Publisher : World Scientific
Page : 373 pages
File Size : 55,9 Mb
Release : 2008
Category : Computers
ISBN : 9789812791443

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Steiner Tree Problems in Computer Communication Networks by Dingzhu Du,Xiaodong Hu Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 136 pages
File Size : 51,9 Mb
Release : 1980
Category : Computer networks
ISBN : UOM:39015000508542

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Proceedings of the Workshop on Interconnection Networks for Parallel and Distributed Processing by Anonim Pdf

Author : Howard Jay Siegel
Publisher : Unknown
Page : 136 pages
File Size : 52,6 Mb
Release : 1980
Category : Computer networks
ISBN : UCSD:31822010657450

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Proceedings of the Workshop on Interconnection Networks for Parallel and Distributed Processing, April 21-22, 1980 by Howard Jay Siegel Pdf

Author : F.K. Hwang,D.S. Richards,P. Winter
Publisher : Elsevier
Page : 336 pages
File Size : 44,6 Mb
Release : 1992-10-20
Category : Computers
ISBN : 0080867936

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The Steiner Tree Problem by F.K. Hwang,D.S. Richards,P. Winter Pdf

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 : Bernard M. E. Moret,Henry D. Shapiro
Publisher : Addison-Wesley Professional
Page : 600 pages
File Size : 40,7 Mb
Release : 1991
Category : Computers
ISBN : UOM:39015019629388

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Algorithms from P to NP: Design & efficiency by Bernard M. E. Moret,Henry D. Shapiro Pdf

Author : Xiuzhen Cheng,Ding-Zhu Du
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 40,6 Mb
Release : 2013-12-01
Category : Computers
ISBN : 9781461302551

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Steiner Trees in Industry by Xiuzhen Cheng,Ding-Zhu Du Pdf

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 : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 50,7 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

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Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Author : Ralf Lehnert, Phuoc Tran-Gia, Joachim Charzinsky
Publisher : Elsevier
Page : 616 pages
File Size : 48,5 Mb
Release : 2003
Category : Electronic
ISBN : 9999903215

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Providing Quality of Service in Heterogeneous Environments by Ralf Lehnert, Phuoc Tran-Gia, Joachim Charzinsky Pdf

Author : Robert H. Kuhn
Publisher : Unknown
Page : 276 pages
File Size : 51,6 Mb
Release : 1980
Category : Computer architecture
ISBN : STANFORD:36105032786936

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Optimization and Interconnection Complexity for Parallel Processors, Single-stage Networks, and Decision Trees by Robert H. Kuhn Pdf