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A processor-time-minimal systolic array for cubical mesh algorithms

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1 Author(s)
Cappello, P. ; Dept. of Comput. Sci., California Univ., Santa Barbara, CA, USA

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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Parallel and Distributed Systems, IEEE Transactions on  (Volume:3 ,  Issue: 1 )