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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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