Authors R.A. Kochkarov, A.N. Kochkarova
Month, Year 04, 2015 @en
Index UDC 519.1, 519.7
Abstract Modern studies of complex systems such as informational, electrical, Internet, communication systems show that the structure of these systems after the time undergoes certain changes caused by various external circumstances. Structure of the system, an arbitrary (social, socio- economic, technical, chemical, biological, etc.) can be represented as a graph. Graph is an abstract object, as a rule vertexes of graphs correspond to elements of the system, and the edges - relations between the elements of the system. Changes in the structure of the system can be single, and may be permanent. For the second case, we introduce the notion of structural dynamics - changes in the structure of the system over time. Undoubtedly, for the description of structural dynamics is best suited machine prefractal graphs. The growth of structure is one of the most common scripts of structural dynamics is. The growth of structure is a regular appearance of new elements and ties in the structure of the system. The growth of structure can occur on a strictly formulated rules, not excluding the presence of the factor of chance. In this paper, we consider one of the possible rules defining the structural dynamics of complex systems. Formal representation structures change systems according to this rule are self-similar large-scale graphs, called fractal (prefractal). In the formulation of the problems of planning and designing (design constructional) contains requirements and criteria required (optimal) construction or the desired plan. Often these criteria and requirements are contradictory. This leads to staging multicriteria optimization problem. Class of prefractal graphs and multicriteria problem of location center on M-weighted prefractal graph are discussed in the paper. Evaluation radial criterion of prefractal graphs are calculated, algorithm for location center on prefractal graph while preserving contiguity old edgesare proposed. Solution of the problem can be applied by optimizing the placement of air and railway nodes, distributing and routing of streams in the study of infectious diseases of crops in the creation of informational and communicational networks with specified characteristics of reliability and stability.

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Keywords Prefractal graph; multicriteria formulation; M-weighted graph; algorithm for location center.
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