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Avtomat. i Telemekh., 2017, Issue 1, Pages 80–90 (Mi at14658)  

This article is cited in 3 scientific papers (total in 3 papers)

System Analysis and Operations Research

Exact pseudopolynomial algorithm for one sequence partitioning problem

A. V. Kel'manovab, S. A. Khamidullina, V. I. Khandeevab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

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.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-00462
16-07-00168
16-31-00186-мол-а
This work was supported by the Russian Foundation for Basic Research, projects nos. 15-01-00462, 16-07-00168, and 16-31-00186-mol-a.


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English version:
Automation and Remote Control, 2017, 78:1, 67–74

Bibliographic databases:

Presented by the member of Editorial Board: А. А. Лазарев

Received: 12.01.2015

Citation: A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “Exact pseudopolynomial algorithm for one sequence partitioning problem”, Avtomat. i Telemekh., 2017, no. 1, 80–90; Autom. Remote Control, 78:1 (2017), 67–74

Citation in format AMSBIB
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\paper Exact pseudopolynomial algorithm for one sequence partitioning problem
\jour Avtomat. i Telemekh.
\yr 2017
\issue 1
\pages 80--90
\mathnet{http://mi.mathnet.ru/at14658}
\elib{http://elibrary.ru/item.asp?id=28317448}
\transl
\jour Autom. Remote Control
\yr 2017
\vol 78
\issue 1
\pages 67--74
\crossref{https://doi.org/10.1134/S0005117917010052}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kel'manov A., “Efficient Approximation Algorithms For Some NP-Hard Problems of Partitioning a Set and a Sequence”, 2017 International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON), IEEE, 2017, 87–90  crossref  isi
    2. A. Kel'manov, S. Khamidullin, V. Khandeev, “A randomized algorithm for 2-partition of a sequence”, Analysis of Images, Social Networks and Texts, AIST 2017, Lecture Notes in Computer Science, 10716, eds. W. van der Aalst, D. Ignatov, M. Khachay, S. Kuznetsov, V. Lempitsky, I. Lomazova, N. Loukachevitch, Springer, 2018, 313–322  crossref  isi  scopus
    3. A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, “A randomized algorithm for a sequence 2-clustering problem”, Comput. Math. Math. Phys., 58:12 (2018), 2078–2085  mathnet  crossref  crossref  isi  elib
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