Incorporating predictions in online graph coloring algorithms

Abstract

We focus on learning augmented algorithms for the online graph coloring problem. We consider incorporating predictions in such algorithms to improve their performance. We apply this strategy in particular to the well-known greedy online graph coloring algorithm FirstFit. Although FirstFit is known to perform poorly in the worst case, we are able to establish a relationship between the structure of the 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 consistent and 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 FirstFitPredictions by combining it with any classical online coloring algorithm (that disregards the predictions).