We introduce learning augmented algorithms to the online graph coloring problem. Although the simple greedy algorithm FirstFit is known to perform poorly in the worst case, we are able to establish a relationship between the structure of any input graph $G$ that is revealed online and the number of colors that FirstFit uses for $G$. Based on this relationship, we propose an online coloring algorithm FirstFitPredictions that extends FirstFit while making use of machine learned predictions. We show that FirstFitPredictions is both \emph{consistent} and \emph{smooth}. Moreover, we develop a novel framework for combining online algorithms at runtime specifically for the online graph coloring problem. Finally, we show how this framework can be used to robustify by combining it with any classical online coloring algorithm (that disregards the predictions).

翻译：我们为在线图着色问题引入了学习增强算法。尽管简单的贪心算法FirstFit在最坏情况下表现不佳，但我们能够建立在线揭示的任意输入图$G$的结构与FirstFit为$G$使用的颜色数量之间的关系。基于这种关系，我们提出了一种在线着色算法FirstFitPredictions，该算法在利用机器学习预测的同时扩展了FirstFit。我们证明了FirstFitPredictions既具有一致性又具有平滑性。此外，我们开发了一种新颖的框架，专门用于在线图着色问题的运行时组合在线算法。最后，我们展示了如何通过将该框架与任何忽略预测的经典在线着色算法相结合，从而赋予算法鲁棒性。