A unified approach to approximation algorithms for bottleneck problems
Journal of the ACM (JACM)
NP-hard problems in hierarchical-tree clustering
Acta Informatica
A cutting plane algorithm for a clustering problem
Mathematical Programming: Series A and B
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Polynomial time approximation schemes for dense instances of NP -hard problems
Journal of Computer and System Sciences
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Clustering with Qualitative Information
FOCS '03 Proceedings of the 44th Annual IEEE 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
Correlation Clustering: maximizing agreements via semidefinite programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Fixed-Parameter Algorithms for Graph-Modeled Date Clustering
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Correlation Clustering Revisited: The "True" Cost of Error Minimization Problems
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A polynomial time approximation scheme for k-consensus clustering
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Average parameterization and partial kernelization for computing medians
Journal of Computer and System Sciences
Average parameterization and partial kernelization for computing medians
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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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The Correlation Clustering problem has been introduced recently [N. Bansal, A. Blum, S. Chawla, Correlation Clustering, in: Proc. 43rd Symp. Foundations of Computer Science, FOCS, 2002, pp. 238-247] as a model for clustering data when a binary relationship between data points is known. More precisely, for each pair of points we have two scores measuring the similarity and dissimilarity respectively, of the two points, and we would like to compute an optimal partition where the value of a partition is obtained by summing up the similarity scores of pairs involving points from the same cluster and the dissimilarity scores of pairs involving points from different clusters. A closely related problem is Consensus Clustering, where we are given a set of partitions and we would like to obtain a partition that best summarizes the input partitions. The latter problem is a restricted case of Correlation Clustering. In this paper we prove that Minimum Consensus Clustering is APX-hard even for three input partitions, answering an open question in the literature, while Maximum Consensus Clustering admits a PTAS. We exhibit a combinatorial and practical 45-approximation algorithm based on a greedy technique for Maximum Consensus Clustering on three partitions. Moreover, we prove that a PTAS exists for Maximum Correlation Clustering when the maximum ratio between two scores is at most a constant.