A note on clustering aggregation for binary clusterings

Jiehua Chen, Danny Hermelin, Manuel Sorge

Research output: Contribution to journalArticlepeer-review


We consider the clustering aggregation problem in which we are given a set of clusterings and want to find an aggregated clustering which minimizes the sum of mismatches to the input clusterings. In the binary case (each clustering is a bipartition) this problem was known to be NP-hard under Turing reductions. We strengthen this result by providing a polynomial-time many-one reduction. Our result also implies that no 2o(n)⋅|I|O(1)-time algorithm exists that solves any given clustering instance I with n elements, unless the Exponential Time Hypothesis fails. On the positive side, we show that the problem is fixed-parameter tractable with respect to the number of input clusterings.

Original languageAmerican English
Article number107052
JournalOperations Research Letters
StatePublished - 1 Jan 2024


  • Aggregation of binary strings
  • Median procedure
  • Mirkin distance minimization
  • Parameterized algorithms

All Science Journal Classification (ASJC) codes

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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