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Algorithms
Identification conditions for the solvability of NP-complete problems for the class of pre-fractal graphs
A. V. Tymoshenkoa, R. A. Kochkarovb, A. A. Kochkarovb a National Research University of Electronic Technology (MIET), 1 Shokin Square, Zelenograd 124498, Russia
b Financial University under the Government of the Russian Federation, 49 Leningradsky Prospekt, Moscow 125993, Russia
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.
Keywords:
NP-complete problems, pre-fractal graphs, discrete problems, solvability conditions.
Received: 09.03.2021 Revised: 27.04.2021 Accepted: 12.05.2021
Citation:
A. V. Tymoshenko, R. A. Kochkarov, A. A. Kochkarov, “Identification conditions for the solvability of NP-complete problems for the class of pre-fractal graphs”, Model. Anal. Inform. Sist., 28:2 (2021), 126–135
Linking options:
https://www.mathnet.ru/eng/mais739 https://www.mathnet.ru/eng/mais/v28/i2/p126
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Abstract page: | 116 | Full-text PDF : | 44 | References: | 23 |
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