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Toward the minimum vertex cover of complex networks using distributed potential games

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Abstract

Vertex cover of complex networks is essentially a major combinatorial optimization problem in network science, which has wide application potentials in engineering. To optimally cover the vertices of complex networks, this paper employs a potential game for the vertex cover problem, designs a novel cost function for network vertices, and proves that the solutions to the minimum value of the potential function are the minimum vertex covering (MVC) states of a general complex network. To achieve the optimal (minimum) covering states, we propose a novel distributed time-variant binary log-linear learning algorithm, and prove that the MVC state of a general complex network is attained under the proposed optimization algorithm. Furthermore, we estimate the upper bound of the convergence rate of the proposed algorithm, and show its effectiveness and superiority using numerical examples with representative complex networks and optimization algorithms.

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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (Grant Nos. 61751303, 71731004) and National Science Fund for Distinguished Young Scholars of China (Grant No. 61425019).

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Authors and Affiliations

  1. Adaptive Networks and Control Lab, Department of Electronic Engineering, Fudan University, Shanghai, 200433, China

    Jie Chen & Xiang Li

  2. Institute of Complex Networks and Intelligent Systems, Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai, 201210, China

    Xiang Li

Authors
  1. Jie Chen
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  2. Xiang Li
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Correspondence to Xiang Li.

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Chen, J., Li, X. Toward the minimum vertex cover of complex networks using distributed potential games. Sci. China Inf. Sci. 66, 112205 (2023). https://doi.org/10.1007/s11432-021-3291-3

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  • DOI: https://doi.org/10.1007/s11432-021-3291-3

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