Geodesic
On the properties of optimal point configurations for a family of comparison functionals for metric configurations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1720-1727 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of searching for an optimal point configuration (i.e., a set of points such that the distances between them best fit a given metric configuration) is considered. An upper bound is obtained for the dimension of a space in which any metric configuration can be represented exactly or approximately by an optimal point configuration. It is shown that, if there is no point configuration that exactly represents a given metric configuration, then, for a natural family of comparison functionals for metric configurations, the dimension of a space in which there is an optimal point configuration is lower than the dimension required in the general case for representing a metric configuration of a given cardinality. 
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A. I. Maysuradze. On the properties of optimal point configurations for a family of comparison functionals for metric configurations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1720-1727. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a14/

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