Multi-Resource List Scheduling of Moldable Parallel Jobs under Precedence Constraints

The scheduling literature has traditionally focused on a single type of resource (e.g., computing nodes). However, scientific applications in modern High-Performance Computing (HPC) systems process large amounts of data, hence have diverse requirements on different types of resources (e.g., cores, cache, memory, I/O). All of these resources could potentially be exploited by the runtime scheduler to improve the application performance. In this paper, we study multi-resource scheduling to minimize the makespan of computational workflows comprised of parallel jobs subject to precedence constraints. The jobs are assumed to be moldable, allowing the scheduler to flexibly select a variable set of resources before execution. We propose a multi-resource, list-based scheduling algorithm, and prove that, on a system with $d$ types of schedulable resources, our algorithm achieves an approximation ratio of $1.619d+2.545\sqrt{d}+1$ for any $d$, and a ratio of $d+O(\sqrt[3]{d^2})$ for large $d$. We also present improved results for independent jobs and for jobs with special precedence constraints (e.g., series-parallel graphs and trees). Finally, we prove a lower bound of $d$ on the approximation ratio of any list scheduling scheme with local priority considerations. To the best of our knowledge, these are the first approximation results for moldable workflows with multiple resource requirements.