Date of Award

1994

Degree Type

Thesis

Degree Name

Doctor of Philosophy in Electrical Engineering

Department

Electrical and Computer Engineering

First Advisor

Qing Yang

Abstract

Data-partition and migration for efficient communication in distributed memory architectures are critical for performance of data parallel algorithms. This research presents a formal methodology for the process of data-distribution and redistribution using tensor products and stride permutations as mathematical tools. The algebraic expressions representing data-partition and migration directly operate on a data vector, and hence can be conveniently embedded into an algorithm. It is also shown that these expressions are useful for a clear understanding and to efficiently interleave problems that involve different data-distributions at different phases. This compatibility made us successfully utilize these expressions in developing and demonstrating matrix transpose and fast Fourier transform algorithms. Usage of these expressions for data interface generated efficient parallel implementation to solve Euler partial differential equation. An endeavor to minimize communication cost using expressions for data-distribution disclosed a routing scheme for Fourier transform evaluation. Results promised that for large parallel machines, this scheme is a solution to today's problems which feature enormous data. Finally, a unique data-distribution technique that effectively uses transpose algorithms for multiplication of two rectangular matrices is derived. Performance of these algorithms are evaluated by carrying out implementations on Intel's i860 based iPSC/860, Touchstone Delta, Gamma, and Paragon supercomputers.

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