A polynomial algorithm to optimally schedule tasks on a virtual distributed system under tree-like precedence constraints

In this paper an ideal distributed memory architecture is considered which is called a virtual distributed system. The scheduling problem is formally defined which is associated with the execution in a minimal makespan of a set of dependent tasks over such an architecture. It is shown that if the processing times of the tasks are not less than the data communication times between the tasks, the associated scheduling problem under tree-like precedence constraints is polynomial and an efficient algorithm is provided to solve it.