Recently, Antoniadis et al. (ICLR 2025) proposed a framework for incorporating predictions to approximate NP-hard selection problems. Despite its simplicity, this approach tightly matches theoretical lower bounds, making its generalization highly compelling. We address an open question raised in the work of Antoniadis et al., concerning the extension of this approach to other important problems outside the class of selection problems, such as scheduling. We develop a learning-augmented algorithm for the makespan minimization problem on unrelated machines, denoted by $R\|C_{\max}$. By using predictions of heavy job assignments, we achieve a polynomial-time $(1+\varepsilon)$-approximation for accurate predictions that smoothly degrades to a worst-case 2-approximation as the error increases. We conclude our work with an empirical analysis of our method.

翻译：最近，Antoniadis等人（ICLR 2025）提出了一种结合预测来近似NP难选择问题的框架。尽管该框架实现简单，但其结果紧密匹配理论下界，使其推广极具吸引力。我们解决了Antoniadis等人工作中提出的一个开放性问题，涉及将该框架扩展到选择问题类别之外的其他重要问题（如调度）的可行性。针对非关联机器上的最大完工时间最小化问题（记为$R\|C_{\max}$），我们开发了一种学习增强算法。通过利用重作业分配的预测，该算法在预测准确时可实现多项式时间内的$(1+\varepsilon)$-近似，并随着误差增加平滑退化为最坏情况下的2-近似。最后，我们通过实证分析验证了该方法的有效性。