Runtime Data Flow Scheduling of Matrix Computations

We investigate the scheduling of matrix computations expressed as directed acyclic graphs for shared-memory parallelism. Because of the data granularity in this problem domain, even slight variations in load balance or data locality can greatly affect performance. Well-known scheduling algorithms such as work stealing have proven time and space bounds, but these bounds do not provide a discernable indicator of performance between different scheduling algorithms and heuristics. We provide a flexible framework for scheduling matrix computations, which we use to empirically quantify different scheduling algorithms. By building software solutions based on hardware techniques through leveraging a cache coherence protocol, we develop a scheduling algorithm that addresses both load balance and data locality simultaneously and show its performance benefits.