Abstract: The subject of the study is to obtain spanning trees for propagating traffic over broadcast channels using the known network topology and known routes. To solve this problem, a mathematical model is constructed in which the network topology is regarded as an undirected graph, but the described solution is also suitable for an oriented graph, where a separate direction is represented by a separate edge. The proposed solution does not require flexible scalability of the network, therefore, when changing the initial input parameters, it is necessary to repeatedly execute the sequence of algorithms described in the article. The development of the algorithm was carried out by an experimental-theoretical method using the mathematical model of a graph constructed from the known topology of the network and the compilation of spanning trees on its basis. The result of the presented work is in determining the necessary number of spanning trees for the optimal solution of the network routing problem. The novelty of this research is the possibility of applying the developed solution in the link-layer networks according to the OSI reference model, exclusively for broadcasting traffic of a given network topology.

Abstract: The subject of the study is the formation of a radio network topology with placement of mobile radio stations, in which the total radiated signal power for radio stations will be minimized. The radiation power of signals for all radio stations and the coordinates for mobile radios are determined in the article, it is also assumed that the transmitting antennas of all radio stations have a circular pattern. To solve this problem, a mathematical model is constructed that has a number of assumptions that imply ideal conditions for the propagation of radio waves, as well as the location of radio stations in a Cartesian coordinate system. The development of the algorithm was carried out by an experimental-theoretical method, based on known facts of radio transmission and a mathematical solution of the Steiner problem for four and five vertices. The novelty of the study is the developed algorithm for determining the coordinates of mobile radio stations, as well as the radiation power of signals for stationary and mobile radios with a circular pattern of directionality. The result of the algorithm works is to determine the topology of the network and the range of operation of each radio station, which consumes the lowest radiation power of the transmitting antennas of radio stations.