The multi-parameterized cluster editing problem - Abu-Khzam, Faisal N. (2017)
The Cluster Editing problem seeks a transformation of a given undirected graph into a transitive graph via a minimum number of edge-edit operations. Existing algorithms often exhibit slow performance and could deliver clusters of no practical significance, such as singletons. A constrained version of Cluster Editing is introduced, featuring more input parameters that set a lower bound on the size of a clique-cluster as well as upper bounds on the amount of both edge-additions and deletions per vertex. The new formulation allows us to solve Cluster Editing (exactly) in polynomial time when edge-edit operations per vertex is smaller than half the minimum cluster size. Moreover, we address the case where the new edge addition and deletion bounds (per vertex) are small constants. We show that Cluster Editing has a linear-size kernel in this case.