Max-Cut with $ε$-Accurate Predictions

We study the approximability of the MaxCut problem in the presence of predictions. Specifically, we consider two models: in the noisy predictions model, for each vertex we are given its correct label in $\{-1,+1\}$ with some unknown probability $1/2 + ε$, and the other (incorrect) label otherwise. In the more-informative partial predictions model, for each vertex we are given its correct label with probability $ε$ and no label otherwise. We assume only pairwise independence between vertices in both models. We show how these predictions can be used to improve on the worst-case approximation ratios for this problem. Specifically, we give an algorithm that achieves an $α+ \widetildeΩ(ε^4)$-approximation for the noisy predictions model, where $α\approx 0.878$ is the MaxCut threshold. While this result also holds for the partial predictions model, we can also give a $β+ Ω(ε)$-approximation, where $β\approx 0.858$ is the approximation ratio for MaxBisection given by Raghavendra and Tan. This answers a question posed by Ola Svensson in his plenary session talk at SODA'23.