Алгоритм построения наследственно минимаксной сети с заданным вектором степеней узлов
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 1
57
The minimax values determine the necessary and sufficient
conditions under which the truncated polyhedrons are not
empty sets. Finally, we obtained an algorithm for
constructing a hereditarily-minimax network in network
polyhedrons
REFERENCES
[1]
Cormen T., Leiserson Ch., Rivest R., Stein C. Introduction to algorithms. 3rd Edition.
MIT Press, 2009.
[2]
Zykov A.A. Osnovy teorii grafov [Fundamentals of graph theory]. Moscow, Vuzovskaya
kniga, 2004. 664 p.
[3]
Mironov A.A., Tsurkov V.I. Hereditarily minimax matrices in models of transportation
type.
Journal of Computer and Systems Sciences International
, 1998, vol. 37, no. 6, pp. 927–944.
[4] Mironov A.A., Tsurkov V.I. Open transportation models with a minimax criterion.
Dokl.
Math
., 2001, vol. 64 (3), pp. 374–377.
[5]
Tsurkov V., Mironov A. Minimax under transportation constrains. Dordrecht–Boston–
London, Kluwer Academic Publishers, 1999.
[6]
Lukoyanov
N.Yu. Minimax and viscosity solutions in optimization problems for heredi-
tary systems.
Proc. Steklov Inst. Math
., 2010, vol. 269, pp. 214–225.
DOI: 10.1134/S0081543810060179
[7]
Holstein E.G., Yudin D.B. Zadachi lineynogo programmirovaniya transportnogo tipa
[Linear programming problem of the transport type]. Moscow, Nauka Publ., 1969. 382 p.
[8]
Goldsmith A. Wireless communications. Cambridge University Press, 2005. 571 p.
[9]
Lewis F.L
.
Wireless sensor networks.
Smart Environments: Technologies, Protocols, and
Applications
. N.Y., John Wiley, 2004. 432 p.
[10]
Tishchenko S.A. Separators in planar graphs as a new characterization tool.
Fundam.
Prikl. Mat.
, 2002, vol. 8, no. 4, pp. 1193–1214 (in Russ.).
[11] Voloshin V.I. Introduction to graph and hypergraph theory. N.Y., Nova Science
Publishers, 2009.
[12]
Selin P.S., Tsurkov V.I. Method of characteristic functions for classes of networks with
fixed node degrees.
Journal of Computer and Systems Sciences International
, 2014, vol. 53,
no. 5, pp. 645–655. DOI: 10.1134/S1064230714050128
[13]
Ding J., Tana P., Lu Y.-Z. Optimizing the controllability index of directed networks with
the fixed number of control nodes.
Neurocomputing
, 2016, vol. 171, pp. 1524–1532.
[14]
Fontanari J.F., Rodrigues F.A
.
Influence of network topology on cooperative problem-
solving systems.
Theory in Biosciences
, 2015, pp. 1–10.
[15]
Peng G.-S., Wu J. Optimal network topology for structural robustness based on natural
connectivity.
Physica A: Statistical Mechanics and its Applications
, 2016, vol. 443, pp. 212–220.
Available at:
http://dx.doi.org/10.1016/j.physa.2015.09.023[16]
Abello J., Queyroi F. Network decomposition into fixed points of degree peeling.
Social
Network Analysis and Mining
, 2014, no. 4, pp. 191.
[17]
Horvat E.-A., Zweig K.A. A fixed degree sequence model for the one-mode projection of
multiplex bipartite graphs.
Social Network Analysis and Mining
, 2013, vol. 3, no. 4, pp. 1209–
1224.