Permutation Predictions for Non-Clairvoyant Scheduling

In non-clairvoyant scheduling, the task is to schedule jobs with a priori unknown processing requirements. We revisit this well-studied problem with the objective of minimizing the total (weighted) completion time in a recently popular learning-augmented setting that integrates possibly imperfect predictions into online algorithm design. While previous works used predictions on processing requirements, we propose a new prediction model that provides a relative order of jobs, which could be seen as predicting algorithmic actions rather than parts of the unknown input. We show that these succinct predictions have desired properties, admit a natural error measure, and enable algorithms with strong performance guarantees. Additionally, these predictions are learnable in both theory and practice. We generalize the algorithmic framework proposed in the seminal article by Purohit, Kumar, and Svitkina (NeurIPS 2018) and present the first learning-augmented scheduling results for weighted jobs and unrelated machines. We demonstrate in empirical experiments the practicability and superior performance compared with the previously suggested single-machine algorithms.