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DOI: 10.4230/LIPIcs.ISAAC.2018.44
URN: urn:nbn:de:0030-drops-99925
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9992/
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Gleich, David F. ; Veldt, Nate ; Wirth, Anthony

Correlation Clustering Generalized

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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.

BibTeX - Entry

@InProceedings{gleich_et_al:LIPIcs:2018:9992,
  author =	{David F. Gleich and Nate Veldt and Anthony Wirth},
  title =	{{Correlation Clustering Generalized}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{44:1--44:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9992},
  URN =		{urn:nbn:de:0030-drops-99925},
  doi =		{10.4230/LIPIcs.ISAAC.2018.44},
  annote =	{Keywords: Correlation Clustering, Approximation Algorithms}
}

Keywords: Correlation Clustering, Approximation Algorithms
Seminar: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 27.11.2018


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