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

Due to recent developments of parallel and distributed computing, the design and analysis of various interconnection networks has been a main topic of research for the past few years and is still stimulated by the new technologies of communication networks such as optic fibers. There are many advantages in using Cayley (di)graphs as models for interconnection networks. This work first surveys some classes of Cayley graphs which are well studied as models of interconnection networks. Results and problems related to routings in networks are then presented, with emphasis on loads of nodes and links in routings.

Cayley graphs and interconnection networks

Most MPC networks use wormhole routing to reduce the effect of path length on communication time. Researchers have exploited this by designing ingenious algorithms to speed collective communication. Many projects have addressed the design of efficient collective communication algorithms for wormhole-routed systems. By exploiting the relative distance-insensitivity of wormhole routing, these new algorithms often differ fundamentally from their store-and-forward counterparts. We examine software and hardware approaches to implementing collective communication operations. Although we emphasize methods in which the underlying architecture is a direct network, such as a hypercube or mesh, as opposed to an indirect switch-based network, several approaches apply to systems of either type. We illustrate several issues arising in this research area and describe the major classes of algorithms proposed to solve these problems.

Collective communication in wormhole-routed massively parallel computers

Networks of Workstations (NOW) have become an attractive alternative platform for high performance computing. Due to the commodity nature of workstations and interconnects and due to the multiplicity of vendors and platforms, the NOW environments are being gradually redefined as Heterogeneous Networks of Workstations (HNOW) environments. This paper presents a new framework for implementing collective communication operations (as defined by the Message Passing Interface (MPI) standard) efficiently for the emerging HNOW environments. We first classify different types of heterogeneity in HNOW and then focus on one important characteristic: communication capabilities of workstations. Taking this characteristic into account, we propose two new approaches Speed-Partitioned Ordered Chain (SPOC) and Fastest-Node First (FNF) to implement collective communication operations with reduced latency. We also investigate methods for deriving optimal trees for broadcast and multicast operations. Generating such trees is shown to be computationally intensive. It is shown that the FNF approach, in spite of its simplicity, can deliver performance within 1% of the performance of the optimal trees. Finally, these new approaches are compared with the approach used in the MPICH implementation on experimental as well as on simulated testbeds. On a 24-node existing HNOW environment with SGI workstations and ATM interconnection our approaches reduce the latency of broadcast and multicast operations by a factor of up to 3.5 compared to the approach used in the existing MPICH implementation. On a 64-node simulated testbed, our approaches can reduce the latency of broadcast and multicast operations by a factor of up to 4.5. Thus, these results demonstrate that there is significant potential for our approaches to be applied towards designing scalable collective communication libraries for current and future generation HNOW environments.

Efficient collective communication on heterogeneous networks of workstations

Packet Routing in Fixed-Connection Networks

We give an optimal algorithm that broadcasts on an n-dimensional hypercube in O(n/ log/sub 2/ (n+1)) routing steps with wormhole, e-cube routing and all-port communication. Previously, the best algorithm of P.K. McKinley and C. Trefftz (1993) requires [n/2] routing steps. We also give routing algorithms that achieve tight time bounds for n /spl les/7. >

Optimal broadcast in all-port wormhole-routed hypercubes

We give an optimal algorithm that broadcasts on an n-dimensional hypercube in Theta(n/ log_{2}(n+ 1)) routing steps with wormhole, e-cube routing and all-port communication. Previously, the best algorithm of McKinley and Trefftz requires [n/2] routing steps. We also give routing algorithms that achieve tight time bounds for n leqslant 7.

Optimal Broadcast in All-Port Wormhole-Routed Hypercubes

We consider the problem of broadcasting multiple messages from one processor to many processors in the k-port model for message-passing systems. In such systems, processors communicate in rounds, where in every round, each processor can send k messages to k processors and receive k messages from k processors In this paper, we first present a simple and practical algorithm based on variations of k complete k-ary trees. We then present an optimal algorithm up to an additive term of one for this problem for any number of processors, any number of messages, and any value for k.

Broadcasting multiple messages in the multiport model

Considers the problem of broadcasting multiple messages from one processor to many processors in the k-port model for message-passing systems. In such systems, processors communicate in rounds, where in every round, each processor can send k messages to k processors and can receive k messages from k processors. In this paper, we first present a simple and practical algorithm based on variations of k complete k-ary trees. We then present an optimal algorithm up to an additive term of one for this problem, for any number of processors, any number of messages and any value for k.

Ching-Tien Ho

Papers

Optimal broadcast in all-port wormhole-routed hypercubes

Optimal Broadcast in All-Port Wormhole-Routed Hypercubes

Broadcasting multiple messages in the multiport model

Broadcasting multiple messages in the multiport model