# A Note on Clustering Aggregation

Jiehua Chen, Danny Hermelin, Manuel Sorge

Research output: Working paper/PreprintPreprint

## 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 reduction. We strengthen this result by providing a polynomial-time many-one reduction. Our result also implies that no $2^{o(n)} \cdot |I|^{O(1)}$-time algorithm exists for any 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 English Published - 2018

### Publication series

Name arXiv PrePrint,

## Fingerprint

Dive into the research topics of 'A Note on Clustering Aggregation'. Together they form a unique fingerprint.