Learning-Augmented Online TRP on a Line

TL;DR

This paper introduces a learning-augmented approach to the online traveling repairperson problem on a line, providing new bounds and algorithms that leverage predictions about request locations to improve performance.

Contribution

The paper establishes a lower bound and designs a deterministic algorithm with competitive ratios that adapt to prediction accuracy, pioneering the application of learning-augmented methods to this problem.

Findings

Established a 3-competitive lower bound for the problem.

Designed a deterministic algorithm with a 3.732-competitive ratio under perfect predictions.

Algorithm's competitive ratio degrades gracefully with prediction error, up to a maximum of 4.

Abstract

We study the online traveling repairperson problem on a line within the recently proposed learning-augmented framework, which provides predictions on the requests to be served via machine learning. In the original model (with no predictions), there is a stream of requests released over time along the line. The goal is to minimize the sum (or average) of the completion times of the requests. In the original model, the state-of-the-art competitive ratio lower bound is $1+\sqrt{2} > 2.414$ for any deterministic algorithm and the state-of-the-art competitive ratio upper bound is 4 for a deterministic algorithm. Our prediction model involves predicted positions, possibly error-prone, of each request in the stream known a priori but the arrival times of requests are not known until their arrival. We first establish a 3-competitive lower bound which extends to the original model. We then design a deterministic algorithm that is $(2+\sqrt{3})\approx 3.732$-competitive when predictions are perfect. With imperfect predictions (maximum error $\delta > 0$), we show that our deterministic algorithm becomes $\min\{3.732+4\delta,4\}$-competitive, knowing $\delta$. To the best of our knowledge, these are the first results for online traveling repairperson problem in the learning-augmented framework.