Abstract
In the train traffic organization, large amount of information should be processed in real time. Thereby in complicated dispatching systems, rational use of resources is needed. To perform this work a model of a management system is constructed and it is represented as a sparse graph. Further optimization of the model requires solving the Maximum Clique Problem (MCP) for the less time than the exponential time. This article contains two procedures for solving the task for subexponential time. Procedure B accurately estimates the size of the maximum clique in the graph and performs the sorting of the vertices, in such a way that the vertices that are not exactly in the maximum clique can be rejected. Procedure A, in fact, finds cliques of the maximum size in a given graph, using the procedure B. The main advantage of this method is that using it is expedient in real time for sufficiently large graphs, which in turn is important for the construction of control systems.
Highlights
The use of ceramic cutting tools from nano-structured refractory compounds [1] partially improves the performance of railway transport
The use of video analysis methods with increasing accuracy leads to a significant increase in information flows and the construction of distributed computer networks
The model of control systems under consideration is equivalent to formal definitions of sparse graphs
Summary
The use of ceramic cutting tools from nano-structured refractory compounds [1] partially improves the performance of railway transport. The use of video analysis methods with increasing accuracy leads to a significant increase in information flows and the construction of distributed computer networks This prompted specialists to search for opportunities to optimize resources, both in the technical and in the information management subsystem. Simulation of the work of a local scheduler on the basis of solving problems of nonlinear Boolean programming has already been considered by the authors in [7] This will optimize computing resources and prevent premature investments in hardware infrastructure. The model of control systems under consideration is equivalent to formal definitions of sparse graphs It can be replaced by the Maximum Clique Problem (MCP), which is one of the known hard-tosolve problems in graph theory. There was a need for the following: - enter procedure B, which allows determining the estimates on top of the sizes of cliques in the graphs; - enter procedure A, which allows using procedure B to generate cliques on the basis of each vertex of the graph and select the largest clique in the graph
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