Optimal within a constant schedules for forest dags on parallel architectures

Abstract

The authors provide optimal within a constant explicit upper bounds on the makespan of schedules for bounded degree forest structured programs on mesh arrays of processors with links of unit bandwidth and arbitrary positive integer propagation delay, and provide polynomial time algorithms to find schedules with makespan matching these bounds. Thus, The authors provide the first polynomial time approximation algorithm for this NP-hard problem, with performance ratio that is a constant. Programs with forest structure arise often in important classes of algorithms. The mesh array architecture is widely used for actual parallel computers. Further, the authors provide polynomial time computable schedules for forest structured programs on a wide class of parallel architectures. They also show how to schedule, in polynomial time, a complete binary tree structured program on a linear array with optimal within a factor of 1 + o(1) makespan.