γ-clustering problems: Classical and parametrized complexity

Abstract

We introduce the γ-clustering problems, which are variants of the well-known Cluster Editing/Deletion/Completion problems, and defined as: given a graph G, how many edges must be edited in G, deleted from G, or added to G in order to have a disjoint union of γ-quasi-cliques. We provide here the complete complexity classification of these problems along with FPT algorithms parameterized by the number of modifications, for the NP-complete problems. We also study here a variant of these problems where the number of final clusters is a fixed constant, obtaining mostly the same results regarding classical and parameterized complexity.