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We study the minimum number of driver nodes control of which leads a Boolean network (BN) from an initial state to a target state in a specified number of time steps. We show that the problem is NP-hard and present an integer linear programming-based method that solves the problem exactly. We mathematically analyze the average size of the minimum set of driver nodes for random Boolean networks with bounded in-degree and with a small number of time steps. The results of computational experiments using randomly generated BNs show good agreements with theoretical analyses. A further examination in realistic BNs demonstrates the efficiency and generality of our theoretical analyses.

FINDING AND ANALYZING THE MINIMUM SET OF DRIVER NODES IN CONTROL OF BOOLEAN NETWORKS