Greedy and branches-and-boundaries methods for the optimal choice of a subset of vertices in a large communication network

The problems of the proposed paper are generated by the actual tasks of communication networks. The development of communication resources is accompanied by an increase in the dimension of existing communication networks, for which the usual tools for solving network problems are becoming increasingly ineffective.At the same time, the spectrum of communication network problems covers both classical graph theory problems and specialized problems linking them with mathematical models of various fields of mathematics, including optimization theory, dynamic programming, probability theory and the theory of heuristic algorithms. This paper is devoted to the study of the problem of optimal allocation of a certain resource on the objects of the communication network. In this case, a complete set of specialized equipment at the nodes of the communication network is considered as a resource. It is necessary to optimize the number of pieces of equipment with the condition that all fiber-optic communication lines of the network are under the control of installed reflectometers. To solve this problem, variants of two methods were described: the greedy algorithm and the method of branches and boundaries. On the basis of the described algorithms, the computer programs were implemented and computational experiments were carried out; in the latter, the dimension of the communication network was chosen high enough to guarantee the legality of using the selected variants of algorithms for real communication networks. A representative series of experiments has shown that it is more expedient to use variants of the greedy heuristic algorithm for the group of problems under consideration, this paper contains a detailed argumentation of the result obtained. The considered problem can also be transferred to cases of optimal placement of other resources on the objects of the communication network. At the same time, if there is a specific objective function, there will be another formalization of restrictions. But the approaches to choosing the optimum may be identical, which makes the results obtained in the paper more important due to their participation in potential generalizations of the problem.