A Note on Clustering Aggregation for Binary Clusterings

Jiehua Chen; Danny Hermelin; Manuel Sorge

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arXiv · 1807.08949

A Note on Clustering Aggregation for Binary Clusterings

Jiehua Chen·Danny Hermelin·Manuel Sorge

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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 $2^{o(n)}\cdot |I'|^{O(1)}$-time algorithm exists that solves any given clustering instance $I'$ with $n$ elements, unless the \ETH{} fails. On the positive side, we show that the problem is fixed-parameter tractable with respect to the number of input clusterings and we give an integer linear programming formulation.

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Jiehua Chen, Danny Hermelin, Manuel Sorge. 2018-07-24. A Note on Clustering Aggregation for Binary Clusterings. https://arxiv.org/abs/1807.08949

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