The paper, using a directed acyclic graph (dag) model of algorithms, investigates precedence constrained multiprocessor schedules for the nx×ny×nz directed rectilinear mesh. Its completion requires at least nx+ny+nz−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 nx×ny×nz 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.
