Abstract
We consider the computational complexity of one extremal problem of choosing a subset of \(p \) points from some given \(2 \)-clustering of a finite set in a metric space. The chosen subset of points has to describe the given clusters in the best way from the viewpoint of some geometric criterion. This is a formalization of an applied problem of data mining which consists in finding a subset of typical representatives of a dataset composed of two classes based on the function of rival similarity. The problem is proved to be NP-hard. To this end, we polynomially reduce to the problem one of the well-known problems NP-hard in the strong sense, the \(p \)-median problem.
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The author was supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314–2019–0015).
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Translated by Ya.A. Kopylov
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Borisova, I.A. Computational Complexity of the Problem of Choosing Typical Representatives in a \(\boldsymbol 2\) -Clustering of a Finite Set of Points in a Metric Space. J. Appl. Ind. Math. 14, 242–248 (2020). https://doi.org/10.1134/S1990478920020039
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DOI: https://doi.org/10.1134/S1990478920020039