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

TL;DR

This paper proposes a new error measure for input predictions based on hypergraph covers, enhancing online graph algorithms by providing error-dependent guarantees and applying to various problems like Steiner tree, facility location, and online routing.

Contribution

It introduces a universal error measure for input predictions, enabling refined online algorithm guarantees and initiating the study of learning-augmented online routing algorithms.

Findings

Refined performance guarantees for Steiner tree and facility location.

Error-dependent bounds for online routing problems like TSP and dial-a-ride.

A general framework for learning-augmented online algorithms.

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.