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On the algorithmic complexity of a problem in cluster analysis

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Abstract

We prove that the MSSC problem (the problem of clustering the set of the vectors in the Euclidean space which minimizes the sum of squares) is NP-complete in the case when the dimension of the space is an input parameter of the problem, while the number of clusters is not an input parameter.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. V. Dolgushev & A. V. Kel’manov

Authors
  1. A. V. Dolgushev
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  2. A. V. Kel’manov
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Correspondence to A. V. Dolgushev.

Additional information

Original Russian Text © A.V. Dolgushev, A.V. Kel’manov, 2010, published in Diskretnyi Analiz i Issledovanie Operatsii, 2010, Vol. 17, No. 2, pp. 39–45.

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Dolgushev, A.V., Kel’manov, A.V. On the algorithmic complexity of a problem in cluster analysis. J. Appl. Ind. Math. 5, 191–194 (2011). https://doi.org/10.1134/S1990478911020050

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  • DOI: https://doi.org/10.1134/S1990478911020050

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