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Using a directed acyclic graph (DAG) model of algorithms, the paper focuses ontime-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 (3n/sup 2/4/). Asystolic array for the cubical directed mesh is then presented. It completes the mesh using the minimum number of steps and exactly (3n/sup 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.
Index Termshexagon shaped; cylinder connected; processor-time-minimal systolic array; cubical meshalgorithms; directed acyclic graph; time-minimal multiprocessor schedules;processor-time-minimal scheduling; triangular shaped 2-D directed mesh; matrix product;processing elements; topology; 2-D directed mesh; computational complexity; directedgraphs; parallel algorithms; systolic arrays

P. Cappello, "A Processor-Time-Minimal Systolic Array for Cubical Mesh Algorithms," in IEEE Transactions on Parallel & Distributed Systems, vol. 3, no. , pp. 4-13, 1992.
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