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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 4, Pages 379–392
DOI: https://doi.org/10.15372/SJNM20170403 (Mi sjvm658) 		 
This article is cited in 6 scientific papers (total in 6 papers)

An approximation scheme for a problem of finding a subsequence

A. V. Kelmanovab, S. M. Romanchenkoa, S. A. Khamidullina

a Sobolev Institute of Mathematics SB RAS, 4 Acad. Koptyug av., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
Full-text PDF (550 kB) Citations (6)
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DOI: https://doi.org/10.15372/SJNM20170403
Abstract: We consider a strongly NP-hard Euclidean problem of finding a subsequence in a finite sequence. The criterion of the solution is a minimum sum of squared distances from the elements of a sought subsequence to its geometric center (centroid). It is assumed that a sought subsequence contains a given number of elements. In addition, a sought subsequence should satisfy the following condition: the difference between the indices of each previous and subsequent points is bounded with given lower and upper constants. We present an approximation algorithm of solving the problem and prove that it is a fully polynomial-time approximation scheme (FPTAS) when the space dimension is bounded by a constant.
Key words: euclidean space, sequence, minimum sum of squared distances, NP-hardness, FPTAS.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-00462
16-31-00186-мол-а
16-07-00168
Received: 01.09.2016
Revised: 08.01.2017
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 4, Pages 313–323
DOI: https://doi.org/10.1134/S1995423917040036
Bibliographic databases:
Document Type: Article
UDC: 519.2+621.391
Language: Russian
Citation: A. V. Kelmanov, S. M. Romanchenko, S. A. Khamidullin, “An approximation scheme for a problem of finding a subsequence”, Sib. Zh. Vychisl. Mat., 20:4 (2017), 379–392; Num. Anal. Appl., 10:4 (2017), 313–323
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sjvm/v20/i4/p379
    • This publication is cited in the following 6 articles:
    1. Anna Panasenko, Communications in Computer and Information Science, 2239, Mathematical Optimization Theory and Operations Research: Recent Trends, 2024, 349  crossref
    2. A. Kel'manov, S. Khamidullin, V. Khandeev, A. Pyatkin, “Exact algorithms for two integer-valued problems of searching for the largest subset and longest subsequence”, Ann. Math. Artif. Intell., 88:1-3 (2020), 157–168  crossref  mathscinet  zmath  isi  scopus
    3. Sergey Khamidullin, Vladimir Khandeev, Anna Panasenko, Lecture Notes in Computer Science, 12096, Learning and Intelligent Optimization, 2020, 96  crossref
    4. Alexander Kel'manov, Sergey Khamidullin, Vladimir Khandeev, Artem Pyatkin, Lecture Notes in Computer Science, 11353, Learning and Intelligent Optimization, 2019, 326  crossref
    5. A. V. Kel'manov, S. A. Khamidullin, V. I. Khandeev, A. V. Pyatkin, Yu. V. Shamardin, V. V. Shenmaier, “A Polynomial-Time Approximation Algorithm for One Problem Simulating the Search in a Time Series for the Largest Subsequence of Similar Elements”, Pattern Recognit. Image Anal., 28:3 (2018), 363  crossref
    6. Alexander Kel'manov, Artem Pyatkin, Sergey Khamidullin, Vladimir Khandeev, Yury V. Shamardin, Vladimir Shenmaier, Communications in Computer and Information Science, 871, Optimization Problems and Their Applications, 2018, 120  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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