A processor-time-minimal schedule for the standard tensor product algorithm

The paper, using a directed acyclic graph (dag) model of algorithms, investigates precedence constrained multiprocessor schedules for the n/spl times/n/spl times/n/spl times/n directed mesh. Its completion requires at least 4n-3 multiprocessor steps. Time-minimal multiprocessor schedules that use as few processors as possible are called processor-time-minimal. For the 4D mesh, such a schedule requires at least (2/3)n/sup 3/+n/3 processors. This lower bound is shown to be exact by constructing a processor-time-minimal multiprocessor schedule that can be realized on a systolic array whose topology is a 3-dimensional twisted torus.<
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