  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.
