Automation and Remote Control

, Volume 78, Issue 1, pp 67–74 | Cite as

Exact pseudopolynomial algorithm for one sequence partitioning problem

  • A. V. Kel’manovEmail author
  • S. A. Khamidullin
  • V. I. Khandeev
System Analysis and Operations Research


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.

Key words

partition sequence of vectors Euclidean space minimal sum of squared distances NP-hardness exact pseudopolynomial algorithm 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • A. V. Kel’manov
    • 1
    • 2
    Email author
  • S. A. Khamidullin
    • 1
  • V. I. Khandeev
    • 1
    • 2
  1. 1.Sobolev Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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