NP-hard problems in hierarchical-tree clustering
Acta Informatica
Machine Learning
Cluster graph modification problems
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
ACM Transactions on Knowledge Discovery from Data (TKDD)
On the Approximation of Correlation Clustering and Consensus Clustering
Journal of Computer and System Sciences
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
Average parameterization and partial kernelization for computing medians
Journal of Computer and System Sciences
Parameterized Complexity
Hi-index | 0.00 |
Given a collection ${\mathcal{C}}$ of partitions of a base set S, the NP-hard Consensus Clustering problem asks for a partition of S which has a total Mirkin distance of at most t to the partitions in ${\mathcal{C}}$, where t is a nonnegative integer. We present a parameterized algorithm for Consensus Clustering with running time $O(4.24^k\cdot k^3+|{\mathcal C}|\cdot |S|^2)$, where $k:=t/|{\mathcal{C}}|$ is the average Mirkin distance of the solution partition to the partitions of ${\mathcal{C}}$. Furthermore, we strengthen previous hardness results for Consensus Clustering, showing that Consensus Clustering remains NP-hard even when all input partitions contain at most two subsets. Finally, we study a local search variant of Consensus Clustering, showing W[1]-hardness for the parameter "radius of the Mirkin-distance neighborhood". In the process, we also consider a local search variant of the related Cluster Editing problem, showing W[1]-hardness for the parameter "radius of the edge modification neighborhood".