A Switching Framework for Online Interval Scheduling with Predictions

TL;DR

This paper introduces a unified framework for online interval scheduling with predictions, balancing performance when predictions are accurate and robustness against errors, with theoretical guarantees and a new interpolating algorithm.

Contribution

The paper presents the SemiTrust-and-Switch framework that combines prediction-based and classical algorithms, providing tight bounds and a smooth interpolation between them.

Findings

Framework achieves a trade-off between consistency and robustness.

Lower bounds demonstrate the tightness of the framework.

New randomized algorithm degrades gracefully with prediction quality.

Abstract

We study online interval scheduling in the irrevocable setting, where each interval must be immediately accepted or rejected upon arrival. The objective is to maximize the total length of accepted intervals while ensuring that no two accepted intervals overlap. We consider this problem in a learning-augmented setting, where the algorithm has access to (machine-learned) predictions. The goal is to design algorithms that leverage these predictions to improve performance while maintaining robust guarantees in the presence of prediction errors. Our main contribution is the SemiTrust-and-Switch framework, which provides a unified approach for combining prediction-based and classical interval scheduling algorithms. This framework applies to both deterministic and randomized algorithms and captures the trade-off between consistency (performance under accurate predictions) and robustness (performance under adversarial inputs). Moreover, we provide lower bounds, proving the tightness of this framework in particular settings. We further design a randomized algorithm that smoothly interpolates between prediction-based and robust algorithms. This algorithm achieves both robustness and smoothness--its performance degrades gracefully with the quality of the prediction.