We present a novel combinatorial algorithm that achieves a 2 - 2/13 < 1.847-approximation for the Correlation Clustering problem, substantially improving over the classic 3-approximation. Our algorithm uses a local search approach combined with a systematic "flipping" technique to escape bad local minima.
The authors propose the cluster LP as a strong linear program that unifies previous relaxations for the Correlation Clustering problem, and present improved approximation algorithms and hardness results based on this new framework.