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Abstract This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline onmidentical machines. The main result is anO(1) competitive deterministic algorithm for any number of machines$$m >1$$ $m>1$. 

An important goal of modern scheduling systems is to efficiently manage power usage. In energy-efficient scheduling, the operating system controls the speed at which a machine is processing jobs with the dual objective of minimizing energy consumption and optimizing the quality of service cost of the resulting schedule. Since machine-learned predictions about future requests can often be learned from historical data, a recent line of work on learning-augmented algorithms aims to achieve improved performance guarantees by leveraging predictions. In particular, for energy-efficient scheduling, Bamas et. al. [NeurIPS '20] and Antoniadis et. al. [SWAT '22] designed algorithms with predictions for the energy minimization with deadlines problem and achieved an improved competitive ratio when the prediction error is small while also maintaining worst-case bounds even when the prediction error is arbitrarily large. In this paper, we consider a general setting for energy-efficient scheduling and provide a flexible learning-augmented algorithmic framework that takes as input an offline and an online algorithm for the desired energy-efficient scheduling problem. We show that, when the prediction error is small, this framework gives improved competitive ratios for many different energy-efficient scheduling problems, including energy minimization with deadlines, while also maintaining a bounded competitive ratio regardless of the prediction error. Finally, we empirically demonstrate that this framework achieves an improved performance on real and synthetic datasets. 

Algorithms with predictions is a recent framework that has been used to overcome pessimistic worst-case bounds in incomplete information settings. In the context of scheduling, very recent work has leveraged machine-learned predictions to design algorithms that achieve improved approximation ratios in settings where the processing times of the jobs are initially unknown. In this paper, we study the speed-robust scheduling problem where the speeds of the machines, instead of the processing times of the jobs, are unknown and augment this problem with predictions. Our main result is an algorithm that achieves a $$\min\{\eta^2(1+\alpha), (2 + 2/\alpha)\}$$ approximation, for any $$\alpha \in (0,1)$$, where $$\eta \geq 1$$ is the prediction error. When the predictions are accurate, this approximation outperforms the best known approximation for speed-robust scheduling without predictions of $2-1/m$, where $$m$$ is the number of machines, while simultaneously maintaining a worst-case approximation of $$2 + 2/\alpha$$ even when the predictions are arbitrarily wrong. In addition, we obtain improved approximations for three special cases: equal job sizes, infinitesimal job sizes, and binary machine speeds. We also complement our algorithmic results with lower bounds. Finally, we empirically evaluate our algorithm against existing algorithms for speed-robust scheduling. 

This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline on m identical machines. The main result is an O(1) competitive deterministic algorithm for any number of machines 𝑚>1.