Graph Theory and Interconnection Networks

Graph theory provides a fundamental tool for designing and analyzing such networks. Graph Theory and Interconnection Networks provides a thorough understanding of these interrelated topics. After a brief introduction to gra

Author: Lih-Hsing Hsu

Publisher: CRC Press

ISBN: 1420044826

Category: Computers

Page: 720

View: 582

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The advancement of large scale integrated circuit technology has enabled the construction of complex interconnection networks. Graph theory provides a fundamental tool for designing and analyzing such networks. Graph Theory and Interconnection Networks provides a thorough understanding of these interrelated topics. After a brief introduction to graph terminology, the book presents well-known interconnection networks as examples of graphs, followed by in-depth coverage of Hamiltonian graphs. Different types of problems illustrate the wide range of available methods for solving such problems. The text also explores recent progress on the diagnosability of graphs under various models.
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Topological Structure and Analysis of Interconnection Networks

This book provides the most basic problems, concepts and well-established results on the topological structure and analysis of interconnection networks in the language of graph theory.

Author: Junming Xu

Publisher: Springer Science & Business Media

ISBN: 9781475733877

Category: Computers

Page: 342

View: 930

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The advent of very large scale integrated circuit technology has enabled the construction of very complex and large interconnection networks. By most accounts, the next generation of supercomputers will achieve its gains by increasing the number of processing elements, rather than by using faster processors. The most difficult technical problem in constructing a supercom puter will be the design of the interconnection network through which the processors communicate. Selecting an appropriate and adequate topological structure of interconnection networks will become a critical issue, on which many research efforts have been made over the past decade. The book is aimed to attract the readers' attention to such an important research area. Graph theory is a fundamental and powerful mathematical tool for de signing and analyzing interconnection networks, since the topological struc ture of an interconnection network is a graph. This fact has been univer sally accepted by computer scientists and engineers. This book provides the most basic problems, concepts and well-established results on the topological structure and analysis of interconnection networks in the language of graph theory. The material originates from a vast amount of literature, but the theory presented is developed carefully and skillfully. The treatment is gen erally self-contained, and most stated results are proved. No exercises are explicitly exhibited, but there are some stated results whose proofs are left to the reader to consolidate his understanding of the material.
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Interconnection Networks

Most of the articles in this book deal with static or point-to-point Interconnection Networks. In particular, new constructions are proposed based on different tools from discrete mathematics.

Author: J.-C. Bermond

Publisher: Elsevier

ISBN: 9781483295275

Category: Mathematics

Page:

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Most of the articles in this book deal with static or point-to-point Interconnection Networks. In particular, new constructions are proposed based on different tools from discrete mathematics. Many new records have been established in the table of the maximum number of vertices of graphs with maximum degree &Dgr; and diameter D. Properties of these networks (and of more classical ones) are analyzed in many of the other papers. About 40% of the articles deal with fault tolerance or vulnerability properties using either combinatorial tools or probabilistic ones.
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Combinatorial Network Theory

For example, to minimize delay and to maximize reliability, networks are required that have minimum diameter and maximum connectivity under certain conditions. The book provides a recent solution to this problem.

Author: Ding-Zhu Du

Publisher: Springer Science & Business Media

ISBN: 9781475724912

Category: Mathematics

Page: 214

View: 944

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A basic problem for the interconnection of communications media is to design interconnection networks for specific needs. For example, to minimize delay and to maximize reliability, networks are required that have minimum diameter and maximum connectivity under certain conditions. The book provides a recent solution to this problem. The subject of all five chapters is the interconnection problem. The first two chapters deal with Cayley digraphs which are candidates for networks of maximum connectivity with given degree and number of nodes. Chapter 3 addresses Bruijn digraphs, Kautz digraphs, and their generalizations, which are candidates for networks of minimum diameter and maximum connectivity with given degree and number of nodes. Chapter 4 studies double loop networks, and Chapter 5 considers broadcasting and the Gossiping problem. All the chapters emphasize the combinatorial aspects of network theory. Audience: A vital reference for graduate students and researchers in applied mathematics and theoretical computer science.
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Graph Theory for Operations Research and Management Applications in Industrial Engineering

Graph theory and interconnection networks. Boca Raton, FL: CRC Press. Hsu, L. H., & Lin, C. K. (2009). Graph theory and interconnection networks. New York, NY: CR Press, Taylor & Francis Group. Huang, L. T., & Hsiao, H. C. (1999).

Author: Farahani, Reza Zanjirani

Publisher: IGI Global

ISBN: 9781466626928

Category: Technology & Engineering

Page: 367

View: 686

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While typically many approaches have been mainly mathematics focused, graph theory has become a tool used by scientists, researchers, and engineers in using modeling techniques to solve real-world problems. Graph Theory for Operations Research and Management: Applications in Industrial Engineering presents traditional and contemporary applications of graph theory in the areas of industrial engineering, management science, and applied operations research. This comprehensive collection of research introduces the useful basic concepts of graph theory in real world applications.
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On Network Embeddings

In this work the authors discussed the embedding parameters such as dilation, congestion and wirelenth of certain interconnection networks. Further, they studied faulty interconnection networks.

Author: R. Sundara Rajan

Publisher: LAP Lambert Academic Publishing

ISBN: 365935886X

Category:

Page: 160

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Graph theory is becoming increasingly significant as it is applied to areas of mathematics and science & technology. It is being actively used in fields as varied as biochemistry, electrical engineering, computer science and operations research. Graph embedding is an important technique used in the study of computational capabilities of processor interconnection networks and task distribution. Embeddings of graphs from one class of graphs into another class have important applications in the field of computer science. In the design and implementation of parallel and distributed computing systems, one fundamental issue is the design of the interconnection network through which the computing elements can communicate efficiently. A measure of reliability and fault tolerance of the overall interconnection networks is given by the maximum number of nodes which can fail simultaneously without prohibiting other non-faulty nodes from communicating with others. In this work the authors discussed the embedding parameters such as dilation, congestion and wirelenth of certain interconnection networks. Further, they studied faulty interconnection networks.
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Interconnection Network Reliability Evaluation

3.2.4 Graph Models Graph theory [81] has drawn increased interest of scientists and engineers in the last several decades. Since the evolution of graph theory, it has got a wide range of application in network reliability evaluation.

Author: Neeraj Kumar Goyal

Publisher: John Wiley & Sons

ISBN: 9781119620594

Category: Computers

Page: 240

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Keeping in view the growth of the technological frontiers, there is always a need for the development of reliable, fault tolerant and cost- effective interconnection networks (INs) which are the critical metrics to achieve the goal of parallelism. The main objective of this book is to design new fault tolerant interconnection network layouts capable of path redundancy among dynamic failures. New INs designs are proposed and their observed results are found promising when compared with some of the earlier networks. The book also covers the reliability evaluation of various industrial network topologies considering multiple reliability performance parameters (2-TR, broadcast and ATR). Finally, the book also focuses on reliability evaluation and comparison of various topologies considering connectivity among multiple sources and multiple destinations (MSMT) nodes.
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Interconnection Networks

Foreword -- Foreword to the First Printing -- Preface -- Chapter 1 -- Introduction -- Chapter 2 -- Message Switching Layer -- Chapter 3 -- Deadlock, Livelock, and Starvation -- Chapter 4 -- Routing Algorithms -- Chapter 5 -- ...

Author: José Duato

Publisher: Morgan Kaufmann

ISBN: 9781558608528

Category: Computers

Page: 600

View: 415

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Foreword -- Foreword to the First Printing -- Preface -- Chapter 1 -- Introduction -- Chapter 2 -- Message Switching Layer -- Chapter 3 -- Deadlock, Livelock, and Starvation -- Chapter 4 -- Routing Algorithms -- Chapter 5 -- CollectiveCommunicationSupport -- Chapter 6 -- Fault-Tolerant Routing -- Chapter 7 -- Network Architectures -- Chapter 8 -- Messaging Layer Software -- Chapter 9 -- Performance Evaluation -- Appendix A -- Formal Definitions for Deadlock Avoidance -- Appendix B -- Acronyms -- References -- Index.
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