# TOPOLOGICAL PROPERTIES OF INTERCONNECTION NETWORKS FOR PARALLEL PROCESSORS - A UNIFIED APPROACH (SIMD)

#### Abstract

Two methods are used to speed up the execution of a computational task. One is new technology development and the other is the exploitation of parallelism in the computation. To take an advantage of the parallelism in a task requires the utilization of parallel computer architectures. At a certain high level of abstraction a parallel computer system is represented as a graph where the nodes represent processors, memories, or other devices, and the edges represent the communication links.^ In this research the following problems of parallel processing are studied. First is a theoretical study of topological properties of interconnection networks. Second is a case study of a network design for a real-time system. Lastly, the use of SIMD networks for performing "shuffles."^ A general model that can be used to describe networks and systems with arbitrary topologies is developed. Based upon the of morphism of groups, the concept of morphism of systems is developed. The morphism of systems is called quasimorphism and allows a method of comparison between topologically arbitrary parallel computer systems. The quasimorphism is used to study the emulation of one system by another.^ The composition, decomposition, and partitionability of single stage networks are studied. Informally, the partitionability property means that the network can be divided into several parts each with a degree of independence. The synthesis of single stage partitionable interconnection networks is examined. The applications of the model to multistage networks is discussed.^ A case study of the design of a network for a real-time signal processing system is performed. A network and network interfaces are designed for a distributed digital signal processing system subject to high throughput, extendibility, fault tolerance, and other constraints.^ The data permuting ability of single stage SIMD networks are studied. Specifically, algorithms for the PM2I and Illiac networks to perform the "shuffle" data permutations are developed. ^

#### Degree

Ph.D.

#### Subject Area

Electrical engineering|Computer science

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