In online interval scheduling, the input is an online sequence of intervals, and the goal is to accept a maximum number of non-overlapping intervals. In the more general disjoint path allocation problem, the input is a sequence of requests, each involving a pair of vertices of a known graph, and the goal is to accept a maximum number of requests forming edge-disjoint paths between accepted pairs. These problems have been studied under extreme settings without information about the input or with error-free advice. We study an intermediate setting with a potentially erroneous prediction that specifies the set of intervals/requests forming the input sequence. For both problems, we provide tight upper and lower bounds on the competitive ratios of online algorithms as a function of the prediction error. For disjoint path allocation, our results rule out the possibility of obtaining a better competitive ratio than that of a simple algorithm that fully trusts predictions, whereas, for interval scheduling, we develop a superior algorithm. We also present asymptotically tight trade-offs between consistency (competitive ratio with error-free predictions) and robustness (competitive ratio with adversarial predictions) of interval scheduling algorithms. Finally, we provide experimental results on real-world scheduling workloads that confirm our theoretical analysis.

翻译：在在线区间调度问题中，输入是一个由区间构成的在线序列，目标则是接受最大数量的不重叠区间。在更具一般性的不相交路径分配问题中，输入是一个请求序列，每个请求涉及一个已知图中的一对顶点，目标则是接受最大数量的请求，使得被接受的请求对之间形成边不相交路径。这些问题的研究曾在两种极端设定下展开：要么完全没有输入信息，要么依赖于无误差的辅助信息。我们研究了一种中间设定，即存在一个可能带有误差的预测，该预测指明了构成输入序列的区间/请求集合。针对这两个问题，我们给出了在线算法竞争比关于预测误差的紧致上界和下界。对于不相交路径分配，我们的结果排除了获得比完全信任预测的简单算法更优竞争比的可能性；而对于区间调度，我们则设计了一个更优的算法。此外，我们还给出了区间调度算法在一致性（无误差预测下的竞争比）与鲁棒性（对抗性预测下的竞争比）之间渐近紧致的权衡关系。最后，我们提供了基于真实调度工作负载的实验结果，验证了我们的理论分析。