NP-hard problems in hierarchical-tree clustering
Acta Informatica
A cutting plane algorithm for a clustering problem
Mathematical Programming: Series A and B
Approximate solution of NP optimization problems
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation schemes for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Correlation Clustering: maximizing agreements via semidefinite programming
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Machine Learning
Clustering with qualitative information
Journal of Computer and System Sciences - Special issue: Learning theory 2003
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)
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 polynomial time approximation scheme for k-consensus clustering
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments (Filkov and Skiena (2004a,b) [1,2]. The problem asks for a partition that summarizes a set of input partitions (each corresponding to a different microarray experiment) under a simple and intuitive cost. The problem on instances with two input partitions has a simple polynomial time algorithm, but it becomes APX-hard on instances with three input partitions. The quest for defining the boundary between tractable and intractable instances leads to the investigation of the restriction of Consensus Clustering when the output partition contains a fixed number of sets. In this paper, we give a randomized polynomial time approximation scheme for such problems, while proving its NP-hardness even for 2 output partitions, therefore definitively settling the approximation complexity of the problem.