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Correlation Clustering Generalized

Authors David F. Gleich, Nate Veldt, Anthony Wirth

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LIPIcs.ISAAC.2018.44.pdf
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Author Details

David F. Gleich
  • Department of Computer Science, Purdue University, West Lafayette, Indiana, USA
Nate Veldt
  • Department of Mathematics, Purdue University, West Lafayette, Indiana, USA
Anthony Wirth
  • School of Computing and Information Systems, The University of Melbourne, Parkville, Victoria, Australia

Funding

  • Gleich, David F.: D.F.G. is supported by the DARPA Simplex program, the Sloan Foundation, and NSF awards IIS-154648, CCF-1149756 and CCF-093937.
  • Veldt, Nate: N.V. supported by NSF award CCF-1149756.
  • Wirth, Anthony: A.W. is supported by the Melbourne School of Engineering.

Cite AsGet BibTex

David F. Gleich, Nate Veldt, and Anthony Wirth. Correlation Clustering Generalized. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 44:1-44:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ISAAC.2018.44

Abstract

We present new results for LambdaCC and MotifCC, two recently introduced variants of the well-studied correlation clustering problem. Both variants are motivated by applications to network analysis and community detection, and have non-trivial approximation algorithms. We first show that the standard linear programming relaxation of LambdaCC has a Theta(log n) integrality gap for a certain choice of the parameter lambda. This sheds light on previous challenges encountered in obtaining parameter-independent approximation results for LambdaCC. We generalize a previous constant-factor algorithm to provide the best results, from the LP-rounding approach, for an extended range of lambda. MotifCC generalizes correlation clustering to the hypergraph setting. In the case of hyperedges of degree 3 with weights satisfying probability constraints, we improve the best approximation factor from 9 to 8. We show that in general our algorithm gives a 4(k-1) approximation when hyperedges have maximum degree k and probability weights. We additionally present approximation results for LambdaCC and MotifCC where we restrict to forming only two clusters.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Approximation algorithms
Keywords
  • Correlation Clustering
  • Approximation Algorithms

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