Cluster Editing with Vertex Splitting

Cluster Editing, also known as Correlation Clustering, is a well-studied graph modification problem. In this problem, one is given a graph and the task is to perform up to k edge additions or deletions to transform it into a cluster graph, i.e., a graph consisting of a disjoint union of cliques. In...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 371; pp. 185 - 195
Main Authors: Abu-Khzam, Faisal N., Arrighi, Emmanuel, Bentert, Matthias, Drange, Pål Grønås, Egan, Judith, Gaspers, Serge, Shaw, Alexis, Shaw, Peter, Sullivan, Blair D., Wolf, Petra
Format: Journal Article
Language:English
Published: Elsevier B.V 15.08.2025
Subjects:
Cluster Editing
Graph modification
Kernelization
NP-hardness
Parameterized algorithms
Vertex Splitting
NP-hardness
Vertex Splitting
Parameterized algorithms
Graph modification
Cluster Editing
Kernelization
ISSN:0166-218X
Online Access:Get full text
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Summary:Cluster Editing, also known as Correlation Clustering, is a well-studied graph modification problem. In this problem, one is given a graph and the task is to perform up to k edge additions or deletions to transform it into a cluster graph, i.e., a graph consisting of a disjoint union of cliques. In this paper, we introduce a variation of Cluster Editing we call Cluster Editing with Vertex Splitting that extends this model to settings where clusters may be overlapping. Specifically, we allow a new edit operation that divides a vertex into two new vertices, each with a subset of the original neighbors. This approach addresses the limitations of assuming disjoint clusters, while still inherently limiting the amount of overlap when the number of edits is small. We show that Cluster Editing with Vertex Splitting is NP-complete and fixed-parameter tractable when parameterized by the number of editing operations k. In particular, we obtain  O(29klogk+n+m)-time algorithm and a 6k-vertex kernel.
ISSN:0166-218X
DOI:10.1016/j.dam.2025.04.013