Fast approximation algorithms for task-based runtime systems

In High Performance Computing, heterogeneity is now the norm with specialized accelerators like GPUs providing efficient computational power. Resulting complexity led to the development of task-based runtime systems, where complex computations are described as task graphs, and scheduling decisions are made at runtime to perform load balancing between all the resources of the platforms. Developing good scheduling strategies, even at the scale of a single node, and analyzing them both theoretically and in practice are expected to have a very high impact on the performance of current HPC systems. The special case of 2 kinds of resources, typically CPUs and GPUs, is already of great practical interest. The scheduling policy HeteroPrio has been proposed in the context of fast multipole computations (FMM) and has been extended to general task graphs with very promising results. In this paper, we provide a theoretical study of the performance of HeteroPrio, by proving approximation bounds compared to the optimal schedule, both in the case of independent tasks and in the case of general task graphs. Interestingly, our results establish that spoliation (a technique that enables resources to restart uncompleted tasks on another resource) is enough to prove bounded approximation ratios for a list scheduling algorithm on two unrelated resources, which is known to be impossible otherwise. This result holds true both for the independent and dependent tasks graphs. Additionally, we provide an experimental evaluation of HeteroPrio on real task graphs from dense linear algebra computation, which establishes its strong performance in practice.