Given a collection 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 C, where t is a nonnegative integer. We present a parameterized algorithm for Consensus Clustering with running time O(4.24 k · k 3 + |C| · |S| 2, where k := t/|C| is the average Mirkin distance of the solution partition to the partitions of 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". © 2011 Springer-Verlag.
CITATION STYLE
Dörnfelder, M., Guo, J., Komusiewicz, C., & Weller, M. (2011). On the parameterized complexity of consensus clustering. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7074 LNCS, pp. 624–633). https://doi.org/10.1007/978-3-642-25591-5_64
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