The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

Koorde is a new distributed hash table (DHT) based on Chord 15 and the de Bruijn graphs 2. While inheriting the simplicity of Chord, Koorde meets various lower bounds, such as O(log n) hops per lookup request with only 2 neighbors per node (where n is the number of nodes in the DHT), and O(log n/log log n) hops per lookup request with O(log n) neighbors per node.

Koorde: A Simple Degree-Optimal Distributed Hash Table.

The performance of most digital systems today is limited by their communication or interconnection, not by their logic or memory. As designers strive to make more efficient use of scarce interconnection bandwidth, interconnection networks are emerging as a nearly universal solution to the system-level communication problems for modern digital systems. 


Interconnection networks have become pervasive in their traditional application as processor-memory and processor-processor interconnect. Point-to-point interconnection networks have replaced buses in an ever widening range of applications that include on-chip interconnect, switches and routers, and I/O systems. 


In this book, the authors present in a structured way the basic underlying concepts of most interconnection networks and provide representative solutions that have been implemented in the industry or proposed in the research literature.

* Gives a coherent, comprehensive treatment of the entire field
* Presents a formal statement of the basic concepts, alternative design choices, and design trade-offs
* Provides thorough classifications, clear descriptions, accurate definitions, and unified views to structure the knowledge on interconnection networks
* Focuses on issues critical to designers

Table of Contents

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

Interconnection Networks

This survey provides a comprehensive and unified analysis of symmetry in a wide variety of Cayley graphs of permutation groups. These include the star graph, bubble-sort graph, modified bubble-sort graph, complete-transposition graph, prefix-reversal graph, alternating-group graph, binary and base-b (b ≥ 3) hypercube, cube connected cycles, bisectional graph, folded hypercube and binary orthogonal graph. In addition, we also define a variety of generalizations of the hypercube and orthogonal graphs. The types of symmetry analyzed include vertex and edge transitivity, distance regularity and distance transitivity. Since these notions of symmetry depend on the shortest paths, as a by product we also describe the shortest path routing algorithms for these graphs. We present a number of open problems related to the networks described in this paper.

Symmetry in interconnection networks based on Cayley graphs of permutation groups: a survey

Considerable attention in recent theoretical computer science is devoted to parallel computing. Here, we would like to present a special part of this large topic, namely, the part devoted to an abstract study of the dissemination of information in interconnection networks. The importance of this research area lies in the fact that the ability of a network to effectively disseminate information is an important qualitative measure for the suitabilty of the network for parallel computing. This follows simply from the observation that the communication among processes working in parallel is one of the main parts of the whole parallel computation. So, the effectivity of information exchange among processors essentially influences the effectivity of the whole computation process.

Dissemination of Information in Interconnection Networks (Broadcasting & Gossiping)

It is shown that the binary de Bruijn multiprocessor network (BDM) can solve a wide variety of classes of problems. The BDM admits an N-node linear array, an N-node ring, (N-1)-node complete binary trees, ((3N/4)-2)-node tree machines, and an N-node one-step shuffle-exchange network, where N (=2/sup k/, k an integer) is the total number of nodes. The de Bruijn multiprocessor networks are proved to be fault-tolerant as well as extensible. A tight lower bound of the VLSI layout area of the BDM is derived; a procedure for an area-optimal VLSI layout is also described. It is demonstrated that the BDM is more versatile than the shuffle-exchange and the cube-connected cycles. Recent work has classified sorting architectures into (1) sequential input/sequential output, (2) parallel input/sequential output, (3) parallel input/parallel output, (4) sequential input/parallel output, and (5) hybrid input/hybrid output. It is demonstrated that the de Bruijn multiprocessor networks can sort data items in all of the abovementioned categories. No other network which can sort data items in all the categories is known. >

Maheswara R. Samatham

Papers

The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI

The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI