Scheduling tasks with communication delays on a two-levels virtual distributed system

A set of tasks has to be scheduled on the parallel identical processors of the clusters of a two-levels distributed memory multiprocessor, subject to precedence constraints and small intra-cluster communication delays. The architecture model includes network of shared memory multiprocessors. In this paper, we present a new critical-path like algorithm that finds an optimal solution to this new problem in polynomial time, if task duplication is allowed and the number of available processors is not limited. The solution found is an earliest schedule that spreads the tasks between the clusters and the processors