The master-slave paradigm with heterogeneous processors

We revisit the master-slave tasking paradigm in the context of heterogeneous processors. We assume that communications are handled by a bus and, therefore, at most one communication can take place at a given time step. We present a polynomial algorithm that gives the optimal solution when a single communication is needed before the execution of the tasks on the slave processors. When communications are required both before and after the processing of the tasks, we show that the problem is strongly NP-complete. In this case, we present a guaranteed approximation algorithm. Finally, we present asymptotically optimal algorithms when communications are required before the processing of each task, or both before and after the processing of each task.