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Identification Conditions for the Solvability of NP-complete Problems for the Class of Pre-fractal Graphs

https://doi.org/10.18255/1818-1015-2021-2-126-135

Abstract

Modern network systems (unmanned aerial vehicles groups, social networks, network production chains, transport and logistics networks, communication networks, cryptocurrency networks) are distinguished by their multi-element nature and the dynamics of connections between its elements. A number of discrete problems on the construction of optimal substructures of network systems described in the form of various classes of graphs are NP-complete problems. In this case, the variability and dynamism of the structures of network systems leads to an "additional" complication of the search for solutions to discrete optimization problems. At the same time, for some subclasses of dynamical graphs, which are used to model the structures of network systems, conditions for the solvability of a number of NP-complete problems can be distinguished. This subclass of dynamic graphs includes pre-fractal graphs. The article investigates NP-complete problems on pre-fractal graphs: a Hamiltonian cycle, a skeleton with the maximum number of pendant vertices, a monochromatic triangle, a clique, an independent set. The conditions under which for some problems it is possible to obtain an answer about the existence and to construct polynomial (when fixing the number of seed vertices) algorithms for finding solutions are identified.

About the Authors

Aleksandr Vasil'evich Tymoshenko
National Research University of Electronic Technology (MIET)
Russian Federation


Rasul Ahmatovich Kochkarov
Financial University under the Government of the Russian Federation
Russian Federation


Azret Ahmatovich Kochkarov
Financial University under the Government of the Russian Federation
Russian Federation


References

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For citations:


Tymoshenko A.V., Kochkarov R.A., Kochkarov A.A. Identification Conditions for the Solvability of NP-complete Problems for the Class of Pre-fractal Graphs. Modeling and Analysis of Information Systems. 2021;28(2):126-135. (In Russ.) https://doi.org/10.18255/1818-1015-2021-2-126-135

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ISSN 1818-1015 (Print)
ISSN 2313-5417 (Online)