Abstract
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”.
Supported by the DFG Excellence Cluster on Multimodal Computing and Interaction (MMCI) and DFG project DARE (NI 369/11).
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Dörnfelder, M., Guo, J., Komusiewicz, C., Weller, M. (2011). On the Parameterized Complexity of Consensus Clustering. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_64
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DOI: https://doi.org/10.1007/978-3-642-25591-5_64
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