Abstract: The Cluster Editing is known to be a very important NP-hard problem. As a special case of Correlation Clustering, it plays a significant role on many fields such as computation biology. After the theory of parameterized complexity was brought up, its parameterized version has drawn much attention. We introduced some approximation and parameterized algorithms for this problem and some variants of it, emphasized on the latest results about its kernelization and FPT algorithms. At the end, we presented some further directions for future research.

Key words: Cluster editing, Clustering, NP-hard, Approximation algorithms, Paramctcrizcd algorithms