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Diskretn. Anal. Issled. Oper., 2009, Volume 16, Number 4, Pages 31–46 (Mi da578)  

This article is cited in 4 scientific papers (total in 4 papers)

On one problem of searching for tuples of fragments in a numerical sequence

A. V. Kel'manov, L. V. Mikhaylova, S. A. Khamidullin

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

Abstract: A discrete optimization problem is considered to which the problem of the noise-proof detection of the recurring tuple of fragments in a numerical sequence is reduced. A variant of the problem in which the fragments from the desired tuples coincide (in the noiseless case) with the elements of the given tuple of vectors is analyzed. A new exact polynomial algorithm for solving this special optimization problem is proved. This algorithm provides that the solution is optimal under the minimum sum-of-squared deviations criterion. If noise is additive and it is a Gaussian sequence of independent identically distributed variables, then the solution is optimal under the maximum likelihood criterion as well. The time complexity of our algorithm is proved to be less then the complexity of the previously known algorithm. Bibl. 4.

Keywords: discrete optimization problem, numerical sequence, recurring tuple of fragments, off-line algorithm.

Full text: PDF file (286 kB)
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Bibliographic databases:
UDC: 519.2+621.391
Received: 10.02.2009
Revised: 05.03.2009

Citation: A. V. Kel'manov, L. V. Mikhaylova, S. A. Khamidullin, “On one problem of searching for tuples of fragments in a numerical sequence”, Diskretn. Anal. Issled. Oper., 16:4 (2009), 31–46

Citation in format AMSBIB
\Bibitem{KelMikKha09}
\by A.~V.~Kel'manov, L.~V.~Mikhaylova, S.~A.~Khamidullin
\paper On one problem of searching for tuples of fragments in a~numerical sequence
\jour Diskretn. Anal. Issled. Oper.
\yr 2009
\vol 16
\issue 4
\pages 31--46
\mathnet{http://mi.mathnet.ru/da578}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2589400}
\zmath{https://zbmath.org/?q=an:1249.93162}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kel'manov, S. M. Romanchenko, S. A. Khamidullin, “Approximation algorithms for some NP-hard problems of searching a vectors subsequence”, J. Appl. Industr. Math., 6:4 (2012), 443–450  mathnet  crossref  mathscinet
    2. A. V. Kelmanov, A. V. Pyatkin, “O slozhnosti nekotorykh zadach vybora podposledovatelnosti vektorov”, Zh. vychisl. matem. i matem. fiz., 52:12 (2012), 2284–2291  mathnet
    3. A. V. Kelmanov, S. M. Romanchenko, S. A. Khamidullin, “Tochnye psevdopolinomialnye algoritmy dlya nekotorykh trudnoreshaemykh zadach poiska podposledovatelnosti vektorov”, Zh. vychisl. matem. i matem. fiz., 53:1 (2013), 143–153  mathnet  crossref  elib
    4. A. V. Kel'manov, A. V. Pyatkin, “On the complexity of some vector sequence clustering problems”, J. Appl. Industr. Math., 7:3 (2013), 363–369  mathnet  crossref  mathscinet
  • Дискретный анализ и исследование операций
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