Dynamic scheduling of parallel computations

Structures of parallel programs are usually represented by task graphs in the scheduling literature. Such graphs are sometimes obtained at compile time. In many other cases, however, they can be determined only at run time. In this paper, we consider the scheduling of parallel computations whose task graphs are generated at run time. We analyze the case where the task graph is a random out-tree. When the number of offspring of a task has a geometric distribution whose parameter is decreasing and convex in the level, then the breadth-first policy stochastically minimizes the makespan. If, however, this parameter is increasing and concave, then the depth-first policy stochastically minimizes the makespan.