Near Optimal LP Rounding Algorithm for CorrelationClustering on Complete and Complete k-partite Graphs

@article{Chawla2015NearOL,
  title={Near Optimal LP Rounding Algorithm for CorrelationClustering on Complete and Complete k-partite Graphs},
  author={Shuchi Chawla and Konstantin Makarychev and Tselil Schramm and Grigory Yaroslavtsev},
  journal={Proceedings of the forty-seventh annual ACM symposium on Theory of Computing},
  year={2015}
}
We give new rounding schemes for the standard linear programming relaxation of the correlation clustering problem, achieving approximation factors almost matching the integrality gaps: For complete graphs our approximation is 2.06 - ε, which almost matches the previously known integrality gap of 2. For complete k-partite graphs our approximation is 3. We also show a matching integrality gap. For complete graphs with edge weights satisfying triangle inequalities and probability constraints, our… 
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