Using Duplication for the Multiprocessor Scheduling Problem with Hierarchical Communications

Abstract

We propose a two-step algorithm that efficiently constructs a schedule of minimum makespan for the precedence multiprocessor constrained scheduling problem in the presence of hierarchical communications and task duplication. We consider the case where all the tasks of the precedence graph have unit execution times, and the multiprocessor is composed by an unbounded number of clusters with two identical processors each. The communication delay for transferring the data between a predecessor-task and a successor-task executed on processors of different clusters take a unit of time, while this cost becomes null whenever these tasks are executed on the same processor or on different processors of the same cluster. The first step of the algorithm computes for each task an earliest starting time of any of its copies and constructs a critical graph whereas the second step uses the obtained critical graph and task duplication to build up an earliest optimal schedule.