Development of Large Communication Networks: Optimization Problems and Heuristics

Abstract

This paper summarizes and continues the previous papers of the authors. We consider some models of optimization problems that arise when building large communication networks. The topology of the communication network is formalized by an undirected graph. The coordinates of the vertices of an undirected graph (nodes of the communication network) are usually set in advance in some way, and a set of edges must be constructed for this set of vertices. The main (and sometimes the only) goal, both of our previous articles and of this article, can be formulated as follows: for some special additional requirements, it is necessary to construct a set of edges of the graph that satisfies these requirements; these edges should have the minimum possible total length. Another important idea is to modify the standard algorithms for working with graphs in order to be able to consider dynamic models (when the input data changes slightly), and it should be possible to use the results of previous calculations when changing the input data. From the point of view of graph theory, all these problems have long been solved, but in practice, the implementation of the corresponding algorithms is fraught with great difficulties: first, in real conditions, we consider graphs consisting of several thousand vertices; second, as we have already noted, the construction of large communication networks usually involves a dynamic change in requirements. The consequence of the two circumstances given is that often even algorithms of quadratic complexity often cannot be applied. For each of our models of optimization problems, we present one or more possible algorithms (primarily heuristic ones) designed to solve it. Our proposed algorithms are usually iterative, and this fact fits well into the capabilities needed to build algorithms that work with dynamically changing data.