Master-slave tasking on heterogeneous processors

In this paper, we consider the problem of scheduling independent identical tasks on heterogeneous processors where communication times and processing times are different. We assume that communication-computation overlap is possible for every processor, but only allow one send and one receive at a time. We propose an algorithm for chains of processors based on an iterative backward construction of the schedule, which is polynomial in the number of processors and in the number of tasks. The complexity is O(np²) where n is the number of tasks and p the number of processors. We prove this algorithm to be optimal with respect to the makespan. We extend this result to a special kind of tree called spider graphs.