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An efficient algorithm for finding all possible input nodes for controlling complex networks.

Xizhe Zhang1,2, Jianfei Han3, Weixiong Zhang4,5

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This study introduces an efficient algorithm to find all minimum input node sets (MIS) for complex networks. The method enhances understanding of network controllability by identifying all potential control nodes.

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Area of Science:

  • Network Science
  • Control Theory
  • Computer Science

Background:

  • Structural controllability is key to understanding complex networks.
  • Identifying a Minimum Input Set (MIS) is crucial for this.
  • Existing methods for finding MIS are computationally intensive.

Purpose of the Study:

  • To develop an efficient algorithm for finding all possible Minimum Input Sets (MIS) in a network.
  • To provide insights into network controllability by exploring the union of all MIS.
  • To enable the identification of substituting nodes for each input node.

Main Methods:

  • Modification of a maximum matching algorithm to efficiently enumerate all MIS.
  • Development of an algorithm to compute one MIS and derive all possible input nodes.
  • Rigorous mathematical proof of the algorithm's correctness.

Main Results:

  • An efficient enumerative algorithm for finding all possible input nodes was developed.
  • The algorithm can identify substituting nodes for each input node in an MIS.
  • Experimental results demonstrate significant speedups over existing methods on large networks.

Conclusions:

  • The new algorithm efficiently finds all potential input nodes, enhancing network controllability analysis.
  • The ability to find substituting nodes offers flexibility in network control strategies.
  • The method provides a significant performance improvement for analyzing large-scale complex networks.