Engineering Optimal Parallel Task Scheduling

The NP-hard scheduling problem P||Cmax encompasses a set of tasks with known execution time which must be mapped to a set of identical machines such that the overall completion time is minimized. In this work, we improve existing techniques for optimal P||Cmax scheduling with a combination of new theoretical insights and careful practical engineering. Most importantly, we derive techniques to prune vast portions of the search space of branch-and-bound (BnB) approaches. We also propose improved upper and lower bounding techniques which can be combined with any approach to P||Cmax. Moreover, we present new benchmarks for P||Cmax, based on diverse application data, which can shed light on aspects which prior synthetic instances fail to capture. In an extensive evaluation, we observe that our pruning techniques reduce the number of explored nodes by 90$\times$ and running times by 12$\times$. Compared to a state-of-the-art ILP-based approach, our approach is preferable for short running time limits and for instances with large makespans.