Polynomial time approximation schemes for dense instances of NP -hard problems
Journal of Computer and System Sciences
A randomized approximation scheme for metric MAX-CUT
Journal of Computer and System Sciences
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Sublinear Time Approximation Scheme for Clustering in Metric Spaces
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Integrating Microarray Data by Consensus Clustering
ICTAI '03 Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence
Approximation schemes for Metric Bisection and partitioning
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Correlation Clustering: maximizing agreements via semidefinite programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Machine Learning
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Clustering with qualitative information
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Correlation clustering in general weighted graphs
Theoretical Computer Science - Approximation and online algorithms
The Minimum Feedback Arc Set Problem is NP-Hard for Tournaments
Combinatorics, Probability and Computing
ACM Transactions on Knowledge Discovery from Data (TKDD)
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the Approximation of Correlation Clustering and Consensus Clustering
Journal of Computer and System Sciences
Aggregating inconsistent information: Ranking and clustering
Journal of the ACM (JACM)
A Local-Search 2-Approximation for 2-Correlation-Clustering
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Linear time approximation schemes for the Gale-Berlekamp game and related minimization problems
Proceedings of the forty-first annual ACM symposium on Theory of computing
A randomized PTAS for the minimum Consensus Clustering with a fixed number of clusters
Theoretical Computer Science
On the parameterized complexity of consensus clustering
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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This paper introduces a polynomial time approximation scheme for the metric Correlation Clustering problem, when the number of clusters returned is bounded (by k). Consensus Clustering is a fundamental aggregation problem, with considerable application, and it is analysed here as a metric variant of the Correlation Clustering problem. The PTAS exploits a connection between Correlation Clustering and the k-cut problems. This requires the introduction of a new rebalancing technique, based on minimum cost perfect matchings, to provide clusters of the required sizes. Both Consensus Clustering and Correlation Clustering have been the focus of considerable recent study. There is an existing dichotomy between the k-restricted Correlation Clustering problems and the unrestricted versions. The former, in general, admit a PTAS, whereas the latter are, in general, APX-hard. This paper extends the dichotomy to the metric case, responding to the result that Consensus Clustering is APX-hard to approximate.