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 $(1+\delta )optcost+O_{\delta }(n{\log }^{3}n)$ with high probability, where $optcost$ is the value of the optimal solution (for every $\delta >0$). The second algorithm finds the ground truth clustering with an arbitrarily small classification error $\eta$ (under some additional assumptions on the instance).