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

TL;DR

This paper introduces an efficient algorithm to identify all possible input nodes for controlling complex networks by modifying maximum matching algorithms, significantly improving speed on large networks.

Contribution

The paper presents a novel, rigorously proven algorithm that efficiently finds all input nodes in complex networks, surpassing existing methods in speed.

Findings

Runs several orders of magnitude faster than previous methods on large networks

Successfully applied to synthetic and real-world networks

Provides comprehensive insight into network controllability

Abstract

Understanding structural controllability of a complex network requires to identify a Minimum Input nodes Set (MIS) of the network. It has been suggested that finding an MIS is equivalent to computing a maximum matching of the network, where the unmatched nodes constitute an MIS. However, maximum matching of a network is often not unique, and finding all MISs may provide deep insights to the controllability of the network. Finding all possible input nodes, which form the union of all MISs, is computationally challenging for large networks. Here we present an efficient enumerative algorithm for the problem. The main idea is to modify a maximum matching algorithm to make it efficient for finding all possible input nodes by computing only one MIS. We rigorously proved the correctness of the new algorithm and evaluated its performance on synthetic and large real networks. The experimental results showed that the new algorithm ran several orders of magnitude faster than the existing method on large real networks.