A processor-time-minimal schedule for 3D rectilinear mesh algorithms

Abstract

The paper, using a directed acyclic graph (dag) model of algorithms, investigates precedence constrained multiprocessor schedules for the n/sub x//spl times/n/sub y//spl times/n/sub z/ directed rectilinear mesh. Its completion requires at least n/sub x/+n/sub y/+n/sub 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/sub x//spl times/n/sub y//spl times/n/sub 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.