Correlation Clustering with Noisy Partial Information

In this paper, we propose and study a semi-random model for the Correlation Clustering problem on arbitrary graphs G. We give two approximation algorithms for Correlation Clustering instances from this model. The first algorithm finds a solution of value (1 + δ) opt-cost +Oδ(n log n) with high probability, where opt-cost is the value of the optimal solution (for every δ > 0). The second algorithm finds the ground truth clustering with an arbitrarily small classification error η (under some additional assumptions on the instance).