An introduction to processor-time-optimal systolic arrays
Highly parallel computaions
Processor Lower Bound Formulas for Array Computations and Parametric Diophantine Systems
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
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The paper, using a directed acyclic graph (dag) model of algorithms, investigates precedence constrained multiprocessor schedules for the n_x \times n_y \times n_z directed rectilinear mesh. Its completion requires at least n_x+n_y+n_z-2 multiprocessor steps. Time-minimal multiprocessor schedules that use as few processors as possible are called processor-time-minimal. Lower bounds are shown for the n_x \times n_y \times n_z directed mesh, and these bounds are shown to be exact by constructing a processor-time-minimal multiprocessor schedule that can be realized on a systolic array whose topology is either a two dimensional mesh or skewed cylinder. The contribution of this paper is two-fold: It generalizes the previous work on cubical mesh algorithms, and it presents a more elegant mathematical method for deriving processor-time lower bounds for such problems.