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Polynomial-Time Approximation Algorithm for the Problem of Cardinality-Weighted Variance-Based 2-Clustering with a Given Center

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Abstract

A strongly NP-hard problem of partitioning a finite set of points of Euclidean space into two clusters is considered. The solution criterion is the minimum of the sum (over both clusters) of weighted sums of squared distances from the elements of each cluster to its geometric center. The weights of the sums are equal to the cardinalities of the desired clusters. The center of one cluster is given as input, while the center of the other is unknown and is determined as the point of space equal to the mean of the cluster elements. A version of the problem is analyzed in which the cardinalities of the clusters are given as input. A polynomial-time 2-approximation algorithm for solving the problem is constructed.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. V. Kel’manov & A. V. Motkova

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    A. V. Kel’manov & A. V. Motkova

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

Additional information

Original Russian Text © A.V. Kel’manov, A.V. Motkova, 2018, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2018, Vol. 58, No. 1, pp. 136–142.

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Kel’manov, A.V., Motkova, A.V. Polynomial-Time Approximation Algorithm for the Problem of Cardinality-Weighted Variance-Based 2-Clustering with a Given Center. Comput. Math. and Math. Phys. 58, 130–136 (2018). https://doi.org/10.1134/S0965542518010074

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