Improving the Controllability of Complex Networks by Temporal Segmentation

Controllability is a fundamental issue in complex networks. Though previous studies showed that the network structure has a great impact on the least number of driver nodes to control the whole network, it is still an open issue to optimize the controllability of complex networks based solely on the network structure for a given number of driver nodes. In this paper, we try to address this problem from the perspective of temporal segmentation, i.e., transform a static complex network into a temporal network consisting of a collection of networks with time stamps. With the advantage of temporal network, the controllability of the original network will be improved without adding more driver nodes. The challenge lies in how to decide a segmentation scheme and guarantee its optimality. To address this, we proposed a cactus-based segmentation scheme, which transforms the original network into a cactus-shaped networks at different snapshots. As the last snapshot elapses, the controllability of the original network will be achieved. We also proved that the segmentation approach is the best option, i.e., the least number of obtained snapshots is no larger than any other segmentation approaches. When the network contains no loops, we reduce the problem to the minimum path covering problem and devise an optimal segmentation scheme. For an arbitrary directed graph, the lower bound of the smallest segmentation can also be theoretically obtained. Finally, the performance of proposed algorithms is discussed and a simple illustration is provided to validate our results.