Geodesic
On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 1, pp. 170-179 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. S. Val'kov. On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 1, pp. 170-179. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_1_a11/

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