The non-clairvoyant scheduling problem has gained new interest within learning-augmented algorithms, where the decision-maker is equipped with predictions without any quality guarantees. In practical settings, access to predictions may be reduced to specific instances, due to cost or data limitations. Our investigation focuses on scenarios where predictions for only $B$ job sizes out of $n$ are available to the algorithm. We first establish near-optimal lower bounds and algorithms in the case of perfect predictions. Subsequently, we present a learning-augmented algorithm satisfying the robustness, consistency, and smoothness criteria, and revealing a novel tradeoff between consistency and smoothness inherent in the scenario with a restricted number of predictions.

翻译：非透明调度问题在学习增强算法中重新引起了关注，其中决策者可以在没有任何质量保证的情况下获得预测。在实际环境中，由于成本或数据限制，对预测的访问可能局限于特定实例。我们的研究聚焦于算法仅能获取$n$个作业大小中$B$个预测的场景。我们首先在完美预测情况下建立了近优下界和算法。随后，我们提出了一种满足鲁棒性、一致性和平滑性标准的学习增强算法，并揭示了在预测数量受限的场景中一致性与平滑性之间固有的新型权衡关系。