In this article, to maximize the dimension of controllable subspace, we consider target controllability problem with maximum covered nodes set in multiplex networks. We call such an issue as maximum-cost target controllability problem. Likewise, minimum-cost target controllability problem is also introduced which is to find minimum covered node set and driver node set. To address these two issues, we first transform them into a minimum-cost maximum-flow problem based on graph theory. Then an algorithm named target minimum-cost maximum-flow (TMM) is proposed. It is shown that the proposed TMM ensures the target nodes in multiplex networks to be controlled with the minimum number of inputs as well as the maximum (minimum) number of covered nodes. Simulation results on Erdos-Rényi (ER-ER) networks, scale-free (SF-SF) networks, and real-life networks illustrate satisfactory performance of the TMM.

中文翻译：

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通过最小成本最大流方法实现多层网络中的目标可控性


在本文中，为了最大化可控子空间的维数，我们考虑复用网络中最大覆盖节点集的目标可控性问题。我们将这样的问题称为最大成本目标可控性问题。同样，还引入了最小成本目标可控性问题，即寻找最小覆盖节点集和驱动节点集。为了解决这两个问题，我们首先将它们转化为基于图论的最小成本最大流问题。然后提出了一种名为目标最小成本最大流（TMM）的算法。结果表明，所提出的TMM确保了多路复用网络中的目标节点能够以最小数量的输入以及最大（最小）数量的覆盖节点进行控制。 Erdos-Rényi (ER-ER) 网络、无标度 (SF-SF) 网络和现实网络的仿真结果表明 TMM 具有令人满意的性能。