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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

  1. Faisal N. Abu-Khzam, Emmanuel Arrighi, Matthias Bentert, Pål Grønås Drange, Judith Egan, Serge Gaspers, Alexis Shaw, Peter Shaw, Blair D. Sullivan, and Petra Wolf. Cluster editing with vertex splitting. arXiv preprint, 2023. URL: https://arxiv.org/abs/1901.00156.
  2. Faisal N. Abu-Khzam, Joseph R. Barr, Amin Fakhereldine, and Peter Shaw. A greedy heuristic for cluster editing with vertex splitting. In Proceedings of the 4th International Conference on Artificial Intelligence for Industries (AI4I), pages 38-41. IEEE, 2021. Google Scholar
  3. Faisal N. Abu-Khzam, Judith Egan, Serge Gaspers, Alexis Shaw, and Peter Shaw. Cluster editing with vertex splitting. In Proceedings of the 5th International Symposium on Combinatorial Optimization (ISCO), pages 1-13. Springer, 2018. Google Scholar
  4. Sanjeev Arora, Rong Ge, Sushant Sachdeva, and Grant Schoenebeck. Finding overlapping communities in social networks: Toward a rigorous approach. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC), pages 37-54. Association for Computing Machinery, 2012. Google Scholar
  5. Emmanuel Arrighi, Matthias Bentert, Pål Grønås Drange, Blair D. Sullivan, and Petra Wolf. Cluster editing with overlapping communities. In Proceedings of the 18th International Symposium on Parameterized and Exact Computation (IPEC), pages 2:1-2:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. Google Scholar
  6. Gard Askeland. Overlapping community detection using cluster editing with vertex splitting. Master’s thesis, University of Bergen, Bergen, Norway, 2022. Google Scholar
  7. Sanghamitra Bandyopadhyay, Garisha Chowdhary, and Debarka Sengupta. FOCS: Fast overlapped community search. IEEE Transactions on Knowledge and Data Engineering, 27(11):2974-2985, 2015. Google Scholar
  8. Nikhil Bansal, Avrim Blum, and Shuchi Chawla. Correlation clustering. Machine Learning, 56(1-3):89-113, 2004. Google Scholar
  9. Jeffrey Baumes, Mark Goldberg, and Malik Magdon-Ismail. Efficient identification of overlapping communities. In Proceedings of the 2005 IEEE International Conference on Intelligednce and Security Informatics (ISI), pages 27-36. Springer, 2005. Google Scholar
  10. Francesco Bonchi, Aristides Gionis, and Antti Ukkonen. Overlapping correlation clustering. Knowledge and Information Systems, 35(1):1-32, 2013. Google Scholar
  11. Sebastian Böcker. A golden ratio parameterized algorithm for cluster editing. Journal of Discrete Algorithms, 16:79-89, 2012. Google Scholar
  12. Leizhen Cai. Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters, 58(4):171-176, 1996. Google Scholar
  13. Moses Charikar, Venkatesan Guruswami, and Anthony Wirth. Clustering with qualitative information. Journal of Computer and System Sciences, 71(3):360-383, 2005. Google Scholar
  14. Moses Charikar and Anthony Wirth. Maximizing quadratic programs: Extending Grothendieck’s inequality. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 54-60. IEEE, 2004. Google Scholar
  15. Shuchi Chawla, Robert Krauthgamer, Ravi Kumar, Yuval Rabani, and D. Sivakumar. On the hardness of approximating multicut and sparsest-cut. Computational Complexity, 15(2):94-114, 2006. Google Scholar
  16. Jianer Chen and Jie Meng. A 2k kernel for the cluster editing problem. Journal of Computer and System Sciences, 78(1):211-220, 2012. Google Scholar
  17. Vincent Cohen-Addad, Euiwoong Lee, Shi Li, and Alantha Newman. Handling correlated rounding error via preclustering: A 1.73-approximation for correlation clustering. In 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), pages 1082-1104. IEEE, 2023. Google Scholar
  18. Alex Crane, Brian Lavallee, Blair D. Sullivan, and Nate Veldt. Overlapping and robust edge-colored clustering in hypergraphs. In Proceedings of the 17th ACM International Conference on Web Search and Data Mining, pages 143-151, 2024. Google Scholar
  19. George B. Davis and Kathleen M. Carley. Clearing the FOG: Fuzzy, overlapping groups for social networks. Social Networks, 30(3):201-212, 2008. Google Scholar
  20. Erik D. Demaine, Dotan Emanuel, Amos Fiat, and Nicole Immorlica. Correlation clustering in general weighted graphs. Theoretical Computer Science, 361(2-3):172-187, 2006. Google Scholar
  21. Reinhard Diestel. Graph Theory. Springer, 2012. Google Scholar
  22. Nan Du, Bai Wang, Bin Wu, and Yi Wang. Overlapping community detection in bipartite networks. In Proceedings of the 2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology (WI-IAT), pages 176-179, 2008. Google Scholar
  23. Esther Galbrun, Aristides Gionis, and Nikolaj Tatti. Overlapping community detection in labeled graphs. Data Mining and Knowledge Discovery, 28(5-6):1586-1610, 2014. Google Scholar
  24. Reynaldo Gil-García and Aurora Pons-Porrata. Dynamic hierarchical algorithms for document clustering. Pattern Recognition Letters, 31(6):469-477, 2010. Google Scholar
  25. Mark Goldberg, Stephen Kelley, Malik Magdon-Ismail, Konstantin Mertsalov, and Al Wallace. Finding overlapping communities in social networks. In Proceedings of the 2nd IEEE International Conference on Social Computing (SC), pages 104-113, 2010. Google Scholar
  26. Steve Gregory. An algorithm to find overlapping community structure in networks. In Proceedings of the 11th European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD), pages 91-102. Springer, 2007. Google Scholar
  27. Qinna Wang and Eric Fleury. Uncovering overlapping community structure. In Proceedings of the 2nd International Workshop on Complex Networks (COMPLEX NETWORKS), pages 176-186. Springer, 2010. Google Scholar
  28. Xufei Wang, Lei Tang, Huiji Gao, and Huan Liu. Discovering overlapping groups in social media. In Proceedings of the 2010 IEEE International Conference on Data Mining (ICDM), pages 569-578, 2010. Google Scholar
  29. David Zuckerman. Linear degree extractors and the inapproximability of max clique and chromatic number. Theory of Computing, 3(1):103-128, 2007. Google Scholar
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