On the Parameterized Complexity of Consensus Clustering

  • Martin Dörnfelder
  • Jiong Guo
  • Christian Komusiewicz
  • Mathias Weller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

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”.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Martin Dörnfelder
    • 1
  • Jiong Guo
    • 1
  • Christian Komusiewicz
    • 2
  • Mathias Weller
    • 2
  1. 1.Universität des SaarlandesSaarbrückenGermany
  2. 2.Institut für Softwaretechnik und Theoretische InformatikTechnische Universität BerlinBerlinGermany

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