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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 1, Pages 170–179 (Mi zvmmf725)  

This article is cited in 2 scientific papers (total in 2 papers)

On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure

A. S. Val'kov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: The concept of a hierarchical $\varepsilon$-cluster structure is defined, and the properties of such structures are studied. The uniqueness of the decomposition of a metric configuration into a hierarchy of $\varepsilon$ clusters is proved for $\varepsilon<1$. The problem of finding a hierarchical $\varepsilon$-cluster structure in a metric configuration is studied. In the general case, the complexity of this problem is $O(N^2)$. An algorithm for solving this problem is proposed that has complexity from $O(N\ln N)$ to $O(N^2)$ on some specific classes of metric configurations.

Key words: hierarchical $\varepsilon$-cluster structure, metric configurations, fast data analysis algorithms.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:1, 163–171

Bibliographic databases:
UDC: 519.714
Received: 06.04.2004

Citation: A. S. Val'kov, “On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure”, Zh. Vychisl. Mat. Mat. Fiz., 45:1 (2005), 170–179; Comput. Math. Math. Phys., 45:1 (2005), 163–171

Citation in format AMSBIB
\Bibitem{Val05}
\by A.~S.~Val'kov
\paper On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 1
\pages 170--179
\mathnet{http://mi.mathnet.ru/zvmmf725}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2151051}
\zmath{https://zbmath.org/?q=an:1072.91034}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 1
\pages 163--171


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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. A. S. Val'kov, “Fast algorithms for synthesizing plane representations of finite metric configurations”, Comput. Math. Math. Phys., 45:2 (2005), 341–351  mathnet  mathscinet  zmath
    2. Jovanovic B.S., Vulkov L.G., “On the convergence of difference scheme for parabolic problems with concentrated data”, International Journal of Numerical Analysis and Modeling, 5:3 (2008), 386–406  mathscinet  zmath  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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