Permutation Predictions for Non-Clairvoyant Scheduling

TL;DR

This paper introduces a new prediction model for non-clairvoyant scheduling that predicts job orderings, leading to improved algorithms with strong theoretical guarantees and better empirical performance, especially for weighted jobs and unrelated machines.

Contribution

It proposes a novel prediction model based on job orderings, extending learning-augmented scheduling to weighted jobs and unrelated machines with new algorithms and analysis.

Findings

Algorithms with strong performance guarantees under the new prediction model.

Empirical results show superior performance over previous single-machine algorithms.

The prediction model is learnable and practical in real-world scenarios.

Abstract

In non-clairvoyant scheduling, the task is to find an online strategy for scheduling jobs with a priori unknown processing requirements with the objective to minimize the total (weighted) completion time. We revisit this well-studied problem in a recently popular learning-augmented setting that integrates (untrusted) predictions in online algorithm design. While previous works used predictions on processing requirements, we propose a new prediction model, which 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 predictions have desired properties, admit a natural error measure as well as algorithms with strong performance guarantees and that they are learnable in both, theory and practice. We generalize the algorithmic framework proposed in the seminal paper by Kumar et al. (NeurIPS'18) 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 to the previously suggested single-machine algorithms.