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 Tr. Mat. Inst. Steklova, 2015, Volume 290, Pages 317–322 (Mi tm3636)

Chain development

Yu. V. Malykhin, E. V. Shchepin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: In a finite set $X$ with distance, we introduce a so-called chain distance. This distance generates a partition of $X$ into clusters such that any point inside each cluster can be connected with any other point of the same cluster by a chain whose every link does not exceed a given threshold value. We construct a chain development, by which we mean a mapping of $X$ into a straight line that preserves the chain distance and allows one to rapidly perform clustering. We also present an efficient algorithm for constructing a chain development.

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 This work is supported by the Russian Science Foundation under grant 14-50-00005.

DOI: https://doi.org/10.1134/S0371968515030267

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 300–305

Bibliographic databases:

UDC: 519.1+519.25

Citation: Yu. V. Malykhin, E. V. Shchepin, “Chain development”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Tr. Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 317–322; Proc. Steklov Inst. Math., 290:1 (2015), 300–305

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3636
• https://doi.org/10.1134/S0371968515030267
• http://mi.mathnet.ru/eng/tm/v290/p317

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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. Yu. V. Malykhin, E. V. Shchepin, “Chain development of metric compacts”, Topology Appl., 221 (2017), 624–629
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