## Abstract

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 2^{o(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 language | American English |
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Article number | 107052 |

Journal | Operations Research Letters |

Volume | 52 |

DOIs | |

State | Published - 1 Jan 2024 |

## Keywords

- 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