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 + Ω(ϵ^4)-approximation for the noisy predictions model, where α≈ 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≈ 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.