Structural Target Controllability of Linear Networks

Computational analysis of the structure of intra-cellular molecular interaction networks can suggest novel therapeutic approaches for systemic diseases like cancer. Recent research in the area of network science has shown that network control theory can be a powerful tool in the understanding and manipulation of such bio-medical networks. In 2011, Liu et al. developed a polynomial time algorithm computing the size of the minimal set of nodes controlling a linear network. In 2014, Gao et al. generalized the problem for target control, minimizing the set of nodes controlling a target within a linear network. The authors developed a Greedy approximation algorithm while leaving open the complexity of the optimization problem. We prove here that the target controllability problem is NP-hard in all practical setups, i.e., when the control power of any individual input is bounded by some constant. We also show that the algorithm provided by Gao et al. fails to provide a valid solution in some special cases, and an additional validation step is required. We fix and improve their algorithm using several heuristics, obtaining in the end an up to 10-fold decrease in running time and also a decrease in the size of solutions.