Cluster Editing on Cographs and Related Classes
Manuel Lafond, Alitzel L\'opez S\'anchez, Weidong Luo

TL;DR
This paper investigates the computational complexity of the Cluster Editing problem on cographs and related graph classes, revealing NP-hardness and W[1]-hardness results, and providing algorithms for specific subclasses.
Contribution
It proves NP-hardness and W[1]-hardness of Cluster Editing on cographs and subclasses, and offers algorithms for trivially perfect graphs and bounds based on clique-width.
Findings
NP-hardness of Cluster Editing on cographs
W[1]-hardness parameterized by number of clusters
Cubic-time algorithm for trivially perfect graphs
Abstract
In the Cluster Editing problem, sometimes known as (unweighted) Correlation Clustering, we must insert and delete a minimum number of edges to achieve a graph in which every connected component is a clique. Owing to its applications in computational biology, social network analysis, machine learning, and others, this problem has been widely studied for decades and is still undergoing active research. There exist several parameterized algorithms for general graphs, but little is known about the complexity of the problem on specific classes of graphs. Among the few important results in this direction, if only deletions are allowed, the problem can be solved in polynomial time on cographs, which are the -free graphs. However, the complexity of the broader editing problem on cographs is still open. We show that even on a very restricted subclass of cographs, the problem is NP-hard,…
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