Online Interval Scheduling with Predictions.

Joan Boyar, Lene M. Favrholdt, Shahin Kamali, and Kim S. Larsen.
Journal of Computer and System Sciences. Accepted for publication.

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 consisting of pairs of vertices of a known graph, and the goal is to accept a maximum number of requests forming edge-disjoint paths between accepted pairs. We study a setting with a potentially erroneous prediction specifying the set of requests forming the input sequence and provide tight upper and lower bounds on the competitive ratios of online algorithms as a function of the prediction error. 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.

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