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Exact pseudopolynomial algorithm for one sequence partitioning problem

  • System Analysis and Operations Research
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Abstract

We consider a strongly NP-hard problem of partitioning a finite sequence of vectors in a Euclidean space into two clusters of given size with the criterion of minimizing the total sum of square distances from cluster elements to their centers. The center of the first cluster is subject to optimization, defined by the mean value of all vectors in this cluster. The center of the second cluster is fixed at the origin. The partition is subject to the following condition: the difference between indices of two subsequent vectors included in the first cluster is bounded from above and below by given constants. We propose an exact pseudopolynomial algorithm for the case of a problem where the dimension of the space is fixed, and components of input vectors are integer-valued.

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Authors and Affiliations

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

    A. V. Kel’manov, S. A. Khamidullin & V. I. Khandeev

  2. Novosibirsk State University, Novosibirsk, Russia

    A. V. Kel’manov & V. I. Khandeev

Authors
  1. A. V. Kel’manov
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  2. S. A. Khamidullin
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  3. V. I. Khandeev
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Correspondence to A. V. Kel’manov.

Additional information

Original Russian Text © A.V. Kel’manov, S.A. Khamidullin, V.I. Khandeev, 2017, published in Avtomatika i Telemekhanika, 2017, No. 1, pp. 80–90.

This paper was recommended for publication by A.A. Lazarev, a member of the Editorial Board

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Kel’manov, A.V., Khamidullin, S.A. & Khandeev, V.I. Exact pseudopolynomial algorithm for one sequence partitioning problem. Autom Remote Control 78, 67–74 (2017). https://doi.org/10.1134/S0005117917010052

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  • DOI: https://doi.org/10.1134/S0005117917010052

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