Geodesic
Chain development
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 317-322
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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. 
@article{TM_2015_290_a25,
     author = {Yu. V. Malykhin and E. V. Shchepin},
     title = {Chain development},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     year = {2015},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_290_a25/}
}
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Yu. V. Malykhin; E. V. Shchepin. Chain development. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 317-322. http://geodesic.mathdoc.fr/item/TM_2015_290_a25/

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