Exploring Weak Dependencies in DAG Scheduling

Many computational solutions can be expressed as directed acyclic graphs (DAGs) with weighted nodes. In parallel computing, a fundamental challenge is to efficiently map computing resources to the tasks, while preserving the precedence constraints among the tasks. Traditionally, such constraints are preserved by starting a task after all its preceding tasks are completed. However, for a class of DAG structured computations, a task can be partially executed with respect to each preceding task. We define such relationship between the tasks as weak dependency. In this paper, we adapt a traditional DAG scheduling scheme to exploit weak dependencies in a DAG. We perform experiments to study the impact of weak dependency based scheduling method on the execution time using a representative set of task graphs for exact inference in junction trees. For a class of task graphs, on a state-of-the-art general-purpose multicore system, the weak dependency based scheduler runs 4x faster than a baseline scheduler that is based on the traditional scheduling method.