Geodesic
Probabilistic properties of topologies of finite metric spaces' minimal fillings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 181-196.

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

In this work, we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, got from the analytical solution, coincide with the computer simulation for the computed cases. Also the built technique makes possible to find the asymptotic of the ratio for families of graph structures. 
@article{FPM_2013_18_2_a14,
     author = {V. N. Salnikov},
     title = {Probabilistic properties of topologies of finite metric spaces' minimal fillings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {181--196},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a14/}
}
TY  - JOUR
AU  - V. N. Salnikov
TI  - Probabilistic properties of topologies of finite metric spaces' minimal fillings
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2013
SP  - 181
EP  - 196
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a14/
LA  - ru
ID  - FPM_2013_18_2_a14
ER  - 
%0 Journal Article
%A V. N. Salnikov
%T Probabilistic properties of topologies of finite metric spaces' minimal fillings
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2013
%P 181-196
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a14/
%G ru
%F FPM_2013_18_2_a14
V. N. Salnikov. Probabilistic properties of topologies of finite metric spaces' minimal fillings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 181-196. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a14/

[1] Erëmin A. Yu., “Formula vesa minimalnogo zapolneniya konechnogo metricheskogo prostranstva”, Mat. sb., 204:9 (2013), 51–72 | DOI | Zbl

[2] Zaretskii K. A., “Postroenie dereva po naboru rasstoyanii mezhdu visyachimi vershinami”, Uspekhi mat. nauk, 20:6 (1965), 90–92 | MR | Zbl

[3] Ivanov A. O., Tuzhilin A. A., Teoriya ekstremalnykh setei, In-t kompyut. issled., M.–Izhevsk, 2003

[4] Ivanov A. O., Tuzhilin A. A., “Odnomernaya problema Gromova o minimalnom zapolnenii”, Mat. sb., 203:5 (2012), 65–118 | DOI | MR | Zbl

[5] Ovsyannikov Z. N., Obobschënno additivnye prostranstva, (gotovitsya k pechati)

[6] Garey M. R., Graham R. L., Johnson D. S., “The complexity of computing Steiner minimal trees”, SIAM J. Appl. Math., 32 (1977), 835–859 | DOI | MR | Zbl

[7] Gromov M., “Filling Riemannian manifolds”, J. Differential Geom., 18 (1983), 1–147 | MR | Zbl

[8] Karp R. M., “Reducibility among combinatorial problems”, Complexity of Computer Computations, Proc. of a Symp. on the Complexity of Computer Computations, IBM Res. Symp. Ser., eds. R. E. Miller, J. W. Thatcher, Plenum, New York, 1972, 85–103 | MR