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 $δ> 0$), we show that our deterministic algorithm becomes $\min\{3.732+4δ,4\}$-competitive, knowing $δ$. To the best of our knowledge, these are the first results for online traveling repairperson problem in the learning-augmented framework.

翻译：我们在近期提出的学习增强框架下研究线段上的线上旅行维修员问题，该框架通过机器学习提供待服务请求的预测。在原始模型（无预测）中，存在沿线段随时间释放的请求流，目标是最小化请求完成时间的总和（或平均值）。原始模型中，任何确定性算法的最优竞争比下界为$1+\sqrt{2} > 2.414$，而确定性算法的最优竞争比上界为4。我们的预测模型包含对请求流中每个请求位置（可能存在误差）的先验预测，但请求的到达时间仅在到达时可知。我们首先建立了可推广至原始模型的3竞争比下界。随后设计了一个确定性算法，在预测完美时达到$(2+\sqrt{3})\approx 3.732$竞争比。对于存在最大误差$δ> 0$的非完美预测，我们证明该确定性算法在已知$δ$时具有$\min\{3.732+4δ,4\}$竞争比。据我们所知，这是线上旅行维修员问题在学习增强框架下的首批研究成果。