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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\varepsilon1$. 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. 
@article{ZVMMF_2005_45_1_a11,
     author = {A. S. Val'kov},
     title = {On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {170--179},
     publisher = {mathdoc},
     volume = {45},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_1_a11/}
}
TY  - JOUR
AU  - A. S. Val'kov
TI  - On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 170
EP  - 179
VL  - 45
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_1_a11/
LA  - ru
ID  - ZVMMF_2005_45_1_a11
ER  - 
%0 Journal Article
%A A. S. Val'kov
%T On a fast algorithm for the reconstruction of the hierarchical $\varepsilon$-cluster structure
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 170-179
%V 45
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_1_a11/
%G ru
%F ZVMMF_2005_45_1_a11
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/