A processor-time-minimal systolic array for cubical mesh algorithms |
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Authors: | Cappello P |
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Affiliation: | Dept. of Comput. Sci., California Univ., Santa Barbara, CA; |
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Abstract: | Using a directed acyclic graph (DAG) model of algorithms, the paper focuses on time-minimal multiprocessor schedules that use as few processors as possible. Such a processor-time-minimal scheduling of an algorithm's DAG first is illustrated using a triangular shaped 2-D directed mesh (representing, for example, an algorithm for solving a triangular system of linear equations). Then, algorithms represented by an n×n×n directed mesh are investigated. This cubical directed mesh is fundamental; it represents the standard algorithm for computing matrix product as well as many other algorithms. Completion of the cubical mesh required 3n-2 steps. It is shown that the number of processing elements needed to achieve this time bound is at least 3n2/4]. A systolic array for the cubical directed mesh is then presented. It completes the mesh using the minimum number of steps and exactly 3n 2/4] processing elements it is processor-time-minimal. The systolic array's topology is that of a hexagonally shaped, cylindrically connected, 2-D directed mesh |
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