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Sufficient control of complex networks

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  • Li, Xiang
  • Li, Guoqi
  • Gao, Leitao
  • Li, Beibei
  • Xiao, Gaoxi

Abstract

In this paper, we propose to study sufficient control of complex networks, which is to control a sufficiently large portion of the network, where only the quantity of controllable nodes matters. To the best of our knowledge, this is the first time that such a problem is investigated. We prove that the sufficient controllability problem can be converted into a minimum-cost flow problem, for which an algorithm with polynomial complexity can be devised. Further, we study the problem of minimum-cost sufficient control, which is to drive a sufficiently large subset of the network nodes to any predefined state with the minimum cost using a given number of controllers. The problem is NP-hard. We propose an “extended L0-norm-constraint-based Projected Gradient Method” (eLPGM) algorithm, which achieves suboptimal solutions for the problems at small or medium sizes. To tackle the large-scale problems, we propose to convert the control problem into a graph problem and devise an efficient low-complexity “Evenly Divided Control Paths” (EDCP) algorithm to tackle the graph problem. Simulation results on both synthetic and real-life networks are provided, demonstrating the satisfactory performance of the proposed methods.

Suggested Citation

  • Li, Xiang & Li, Guoqi & Gao, Leitao & Li, Beibei & Xiao, Gaoxi, 2024. "Sufficient control of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 642(C).
    • Handle: RePEc:eee:phsmap:v:642:y:2024:i:c:s0378437124002607
    DOI: 10.1016/j.physa.2024.129751
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    References listed on IDEAS

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