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Chain development

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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.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Yu. V. Malykhin & E. V. Shchepin

Authors
  1. Yu. V. Malykhin
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  2. E. V. Shchepin
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Corresponding author

Correspondence to Yu. V. Malykhin.

Additional information

Original Russian Text © Yu.V. Malykhin, E.V. Shchepin, 2015, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Vol. 290, pp. 317–322.

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Malykhin, Y.V., Shchepin, E.V. Chain development. Proc. Steklov Inst. Math. 290, 300–305 (2015). https://doi.org/10.1134/S0081543815060267

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  • DOI: https://doi.org/10.1134/S0081543815060267

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