Correlation clustering with vertex splitting

Bentert, M. and Crane, A. and Drange, P.G. and Reidl, Felix and Sullivan, B.D. (2024) Correlation clustering with vertex splitting. Leibniz International Proceedings in Informatics (LIPIcs) 294 , 8:1-8:17. ISSN 1868-8969.

Abstract

We explore CLUSTER EDITING and its generalization CORRELATION CLUSTERING with a new operation called permissive vertex splitting which addresses finding overlapping clusters in the face of uncertain information. We determine that both problems are NP-hard, yet they exhibit significant differences in terms of parameterized complexity and approximability. For CLUSTER EDITING WITH PERMISSIVE VERTEX SPLITTING, we show a polynomial kernel when parameterized by the solution size and develop a polynomial-time 7-approximation. In the case of CORRELATION CLUSTERING, we establish para-NP-hardness when parameterized by the solution size and demonstrate that computing an n^{1-ε}-approximation is NP-hard for any constant ε > 0. Additionally, we extend an established link between CORRELATION CLUSTERING and MULTICUT to the setting with permissive vertex splits.

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