Geodesic
Modeling of optimal networks by means of linkages
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 6, pp. 95-122.

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

The main result of this paper is the description of the construction of the linkage that constructs the shortest network for a set of $n$ points on the Euclidean plane. 
@article{FPM_2019_22_6_a3,
     author = {M. Yu. Zhitnaya},
     title = {Modeling of optimal networks by means of linkages},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {95--122},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a3/}
}
TY  - JOUR
AU  - M. Yu. Zhitnaya
TI  - Modeling of optimal networks by means of linkages
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2019
SP  - 95
EP  - 122
VL  - 22
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a3/
LA  - ru
ID  - FPM_2019_22_6_a3
ER  - 
%0 Journal Article
%A M. Yu. Zhitnaya
%T Modeling of optimal networks by means of linkages
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2019
%P 95-122
%V 22
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a3/
%G ru
%F FPM_2019_22_6_a3
M. Yu. Zhitnaya. Modeling of optimal networks by means of linkages. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 6, pp. 95-122. http://geodesic.mathdoc.fr/item/FPM_2019_22_6_a3/

[1] Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I., Lektsii po teorii grafov, Nauka, M., 1990 | MR

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

[3] Ilyutko D. P., “Lokalno minimalnye seti v $N$-normirovannykh prostranstvakh”, Matem. zametki, 74:5 (2003), 656–668 | DOI | MR | Zbl

[4] Ilyutko D. P., “Geometriya ekstremalnykh setei na $\lambda$-normirovannykh ploskostyakh”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2005, no. 4, 52–54 | MR | Zbl

[5] Ilyutko D. P., “Razvetvlennye ekstremali funktsionala $\lambda$-normirovannoi dliny”, Matem. sb., 197:5 (2006), 75–98 | DOI | MR | Zbl

[6] Ilyutko D. P., Nikonov I. M., “Ekstremalnye seti na $\lambda$-normirovannoi ploskosti, gde $\lambda=3,4,6$”, Matem. sb., 208:4 (2017), 17–50 | DOI | MR | Zbl

[7] Matematicheskie etyudy, http://www.etudes.ru/ru/mov/

[8] Mekhanizmy P. L. Chebysheva, http://tcheb.ru/ru

[9] Oshemkov A. A., Popelenskii F. Yu., Tuzhilin A. A., Fomenko A. T., Shafarevich A. I., Kurs naglyadnoi geometrii i topologii, URSS; Lenand, M., 2014

[10] Sosinskii A. B., Dvumernye poverkhnosti i konfiguratsionnye prostranstva sharnirnykh mekhanizmov. Lektsiya pervaya http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=130

[11] Sosinskii A. B., Dvumernye poverkhnosti i konfiguratsionnye prostranstva sharnirnykh mekhanizmov. Lektsiya vtoraya http://www.mathnet.ru/php/presentation.phtml?presentid=131&option_lang=rus

[12] Fomenko A. T., Naglyadnaya geometriya i topologiya. Matematicheskie obrazy v realnom mire, Izd-vo Mosk. un-ta, M., 1998

[13] Cauchy A. L., “Recherche sur les polyèdres — premier mémoire”, J. l'École Polytech, 9:16 (1813), 66–86

[14] Hwang F. K., “A linear time algorithm for full Steiner trees”, Operations Res. Lett., 4:5 (1986), 235–237 | DOI | MR | Zbl

[15] Ivanov A. O., Tuzhilin A. A., Minimal Networks. Steiner Problem and Its Generalizations, CRC Press, 1994 | MR | Zbl

[16] Kempe A. B., How to Draw a Straight Line: A Lecture on Linkages, Macmillan, 1877

[17] Melzak Z. A. On the problem of Steiner, Can. Math. Bull., 4:2 (1961), 143–148 | DOI | MR | Zbl