Target controllability: a feed-forward greedy algorithm in complex networks, meeting Kalman's rank condition

The concept of controllability within complex networks is pivotal in determining the minimal set of driver vertices required for the exertion of external signals, thereby enabling control over the entire network's vertices. Target controllability further refines this concept by focusing on a subset of vertices within the network as the specific targets for control, both of which are known to be NP-hard problems. Crucially, the effectiveness of the driver set in achieving control of the network is contingent upon satisfying a specific rank condition, as introduced by Kalman. On the other hand, structural controllability provides a complementary approach to understanding network control, emphasizing the identification of driver vertices based on the network's structural properties. However, in structural controllability approaches, the Kalman condition may not always be satisfied.

In this study, we address the challenge of target controllability by proposing a feed-forward greedy algorithm designed to efficiently handle large networks while meeting the Kalman controllability rank condition. We further enhance our method's efficacy by integrating it with Barabasi et al.'s structural controllability approach. This integration allows for a more comprehensive control strategy, leveraging both the dynamical requirements specified by Kalman's rank condition and the structural properties of the network. Empirical evaluation across various network topologies demonstrates the superior performance of our algorithms compared to existing methods, consistently requiring fewer driver vertices for effective control. Additionally, our method's application to protein-protein interaction networks associated with breast cancer reveals potential drug repurposing candidates, underscoring its biomedical relevance. This study highlights the importance of addressing both structural and dynamical aspects of network controllability for advancing control strategies in complex systems.

The source code is available for free at:Https://github.com/fatemeKhezry/targetControllability.