Geodesic
Decomposition of finite pseudometric spaces
Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 225-234.

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Here we define decomposable pseudometrics. A pseudometric is decomposable if it can be represented as the sum of two pseudometrics that are obtained in a way other than the multiplication all distances by a positive factor. We consider spaces consisting of $n$ points. We prove that there exist a finite number of indecomposable pseudometrics (that is, a basis) such that any pseudometric is a linear combination of basic pseudometrics with nonnegative coefficients. For $n\le7$, the basic pseudometrics are listed. A decomposability test is derived for finite pseudometric spaces. We also establish some other conditions of decomposability and indecomposability. 
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     author = {M. \'E. Mikhailov},
     title = {Decomposition of finite pseudometric spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {225--234},
     publisher = {mathdoc},
     volume = {63},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a6/}
}
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M. É. Mikhailov. Decomposition of finite pseudometric spaces. Matematičeskie zametki, Tome 63 (1998) no. 2, pp. 225-234. http://geodesic.mathdoc.fr/item/MZM_1998_63_2_a6/

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