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Correlation Clustering with Vertex Splitting

Authors Matthias Bentert, Alex Crane , Pål Grønås Drange , Felix Reidl , Blair D. Sullivan

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Author Details

Matthias Bentert
  • University of Bergen, Norway
Alex Crane
  • University of Utah, Salt Lake City, UT, USA
Pål Grønås Drange
  • University of Bergen, Norway
Felix Reidl
  • Birkbeck, University of London, UK
Blair D. Sullivan
  • University of Utah, Salt Lake City, UT, USA

Funding

Alex Crane, Felix Reidl, and Blair D. Sullivan: Gordon & Betty Moore Foundation’s Data Driven Discovery Initiative under award GBMF4560 to Blair D. Sullivan.
  • Bentert, Matthias: European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819416).

Cite AsGet BibTex

Matthias Bentert, Alex Crane, Pål Grønås Drange, Felix Reidl, and Blair D. Sullivan. Correlation Clustering with Vertex Splitting. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SWAT.2024.8

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Parameterized complexity and exact algorithms
  • Mathematics of computing → Approximation algorithms
  • Theory of computation → Problems, reductions and completeness
Keywords
  • graph modification
  • cluster editing
  • overlapping clustering
  • approximation
  • parameterized complexity

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References

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