Geodesic
A formula for the weight of a~minimal filling of a~finite metric space
Sbornik. Mathematics, Tome 204 (2013) no. 9, pp. 1285-1306

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

We consider the problem of finding a minimal filling for a finite metric space, that is, a weighted graph of minimal weight joining a given finite metric space. We obtain a minimax formula for the weight of the minimal filling, which we use to prove various properties of minimal fillings. Bibliography: 10 titles.
Keywords: minimal filling, finite metric spaces, graph, Gromov's problem, perimeter of a metric space. 
@article{SM_2013_204_9_a2,
     author = {A. Yu. Eremin},
     title = {A formula for the weight of a~minimal filling of a~finite metric space},
     journal = {Sbornik. Mathematics},
     pages = {1285--1306},
     publisher = {mathdoc},
     volume = {204},
     number = {9},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_9_a2/}
}
TY  - JOUR
AU  - A. Yu. Eremin
TI  - A formula for the weight of a~minimal filling of a~finite metric space
JO  - Sbornik. Mathematics
PY  - 2013
SP  - 1285
EP  - 1306
VL  - 204
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2013_204_9_a2/
LA  - en
ID  - SM_2013_204_9_a2
ER  - 
%0 Journal Article
%A A. Yu. Eremin
%T A formula for the weight of a~minimal filling of a~finite metric space
%J Sbornik. Mathematics
%D 2013
%P 1285-1306
%V 204
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2013_204_9_a2/
%G en
%F SM_2013_204_9_a2
A. Yu. Eremin. A formula for the weight of a~minimal filling of a~finite metric space. Sbornik. Mathematics, Tome 204 (2013) no. 9, pp. 1285-1306. http://geodesic.mathdoc.fr/item/SM_2013_204_9_a2/