Minimum control latency of dynamic networks

Controlling a dynamic network is interesting and important in practical applications, which is to drive the network from any initial state to any desired state. Much research has been conducted in revealing the controllability and seeking the underlying correlations of the network. However, no existing works have considered the time needed to control the network, which we refer to as control latency. In this paper, we initiate the study of control latency of dynamic networks. First of all, we formulate the minimum control latency (MCL) problem for designing the controlling pattern with minimum number of controllers. We show that the MCL problem is NP-hard by reducing the multiprocessor scheduling problem to it. Then, we propose a greedy algorithm for designing a controlling pattern that can control the network within two times the minimum control latency. Moreover, when the control latency is bounded by a given value, we propose another constant approximation algorithm to design a controlling pattern which uses at most three times the minimum number of controllers. We conduct extensive simulations on both synthetic and real networks to corroborate our theoretic analysis.