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Target Controllability in Multilayer Networks via Minimum-Cost Maximum-Flow Method.

Jie Ding, Changyun Wen, Guoqi Li

    IEEE Transactions on Neural Networks and Learning Systems
    |June 13, 2020
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    Summary

    This study introduces maximum-cost and minimum-cost target controllability problems for multiplex networks. A novel algorithm ensures control of target nodes with minimal inputs and optimal node coverage.

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    Area of Science:

    • Network Science
    • Control Theory
    • Graph Theory

    Background:

    • Multiplex networks exhibit complex structures and dynamics.
    • Controllability of complex networks is crucial for understanding system behavior.
    • Optimizing control strategies in large networks remains a challenge.

    Purpose of the Study:

    • To address the maximum-cost target controllability problem by maximizing covered nodes.
    • To introduce the minimum-cost target controllability problem, minimizing covered and driver nodes.
    • To develop an efficient algorithm for controlling target nodes in multiplex networks.

    Main Methods:

    • Formulating target controllability problems as minimum-cost maximum-flow problems.
    • Utilizing graph theory for network analysis and transformation.
    • Proposing the target minimum-cost maximum-flow (TMM) algorithm.

    Main Results:

    • The TMM algorithm effectively controls target nodes in multiplex networks.
    • The method achieves control with the minimum number of input nodes.
    • Optimal maximum (or minimum) node coverage is ensured by the TMM algorithm.

    Conclusions:

    • The TMM algorithm provides a robust solution for target controllability in multiplex networks.
    • The approach balances control efficiency with network coverage.
    • Simulations demonstrate the algorithm's satisfactory performance on various network types.