We introduce a novel measure for quantifying the error in input predictions. The error is based on a minimum-cost hyperedge cover in a suitably defined hypergraph and provides a general template which we apply to online graph problems. The measure captures errors due to absent predicted requests as well as unpredicted actual requests; hence, predicted and actual inputs can be of arbitrary size. We achieve refined performance guarantees for previously studied network design problems in the online-list model, such as Steiner tree and facility location. Further, we initiate the study of learning-augmented algorithms for online routing problems, such as the online traveling salesperson problem and the online dial-a-ride problem, where (transportation) requests arrive over time (online-time model). We provide a general algorithmic framework and we give error-dependent performance bounds that improve upon known worst-case barriers, when given accurate predictions, at the cost of slightly increased worst-case bounds when given predictions of arbitrary quality.

Networks , Optimization for and with Machine Learning
36th conference on Neural Information Processing Systems, NeurIPS 2022
Evolutionary Intelligence

Bernardini, G., Lindermayr, A., Marchetti Spaccamela, A., Megow, N., Stougie, L., & Sweering, M. (2022). A universal error measure for input predictions applied to online graph problems. In Proceedings NeurIPS (Annual Conference on Neural Information Processing Systems).