Approximation Proofs of a Fast and Efficient List Scheduling Algorithm for Task-Based Runtime Systems on Multicores and GPUs

Abstract

In High Performance Computing, heterogeneity is now the normwith specialized accelerators like GPUs providing efficientcomputational power. The added complexity has led to the developmentof task-based runtime systems, which allow complex computations to beexpressed as task graphs, and rely on scheduling algorithms to performload balancing between all resources of the platforms. Developing goodscheduling algorithms, even on a single node, and analyzing them canthus have a very high impact on the performance of current HPCsystems. The special case of two types of resources (namely CPUs andGPUs) is of practical interest. HeteroPrio is such an algorithm whichhas been proposed in the context of fast multipole computations, andthen extended to general task graphs with very interesting results. Inthis paper, we provide a theoretical insight on the performance ofHeteroPrio, by proving approximation bounds compared to the optimalschedule in the case where all tasks are independent and for differentplatform sizes. Interestingly, this shows that spoliation allows toprove approximation ratios for a list scheduling algorithm on twounrelated resources, which is not possible otherwise. We also establishthat almost all our bounds are tight. Additionally, we provide anexperimental evaluation of HeteroPrio on real task graphs from denselinear algebra computation, which highlights the reasons explainingits good practical performance.