A Universal Error Measure for Input Predictions Applied to Online Graph Problems

Giulia Bernardini, Alexander Lindermayr, Alberto Marchetti-Spaccamela, Nicole Megow, Leen Stougie, Michelle Sweering

Keywords: learning-augmented algorithms, untrusted predictions, prediction error, online algorithms, network design, routing, TSP

Abstract: 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.

TL;DR: We introduce a universal error measure for input predictions and apply it to both online-list network design problems and online-time routing problems, where for the latter we give the first learning-augmented algorithms.