Zhang Zenghu, Yin Yongfeng, Zhang Xin, Liu Lijun
School of Reliability and System Engineering, Beihang University, Beijing, China.
PLoS One. 2018 Feb 13;13(2):e0192874. doi: 10.1371/journal.pone.0192874. eCollection 2018.
Controllability of complex networks has been a hot topic in recent years. Real networks regarded as interdependent networks are always coupled together by multiple networks. The cascading process of interdependent networks including interdependent failure and overload failure will destroy the robustness of controllability for the whole network. Therefore, the optimization of the robustness of interdependent network controllability is of great importance in the research area of complex networks. In this paper, based on the model of interdependent networks constructed first, we determine the cascading process under different proportions of node attacks. Then, the structural controllability of interdependent networks is measured by the minimum driver nodes. Furthermore, we propose a parameter which can be obtained by the structure and minimum driver set of interdependent networks under different proportions of node attacks and analyze the robustness for interdependent network controllability. Finally, we optimize the robustness of interdependent network controllability by redundant design including node backup and redundancy edge backup and improve the redundant design by proposing different strategies according to their cost. Comparative strategies of redundant design are conducted to find the best strategy. Results shows that node backup and redundancy edge backup can indeed decrease those nodes suffering from failure and improve the robustness of controllability. Considering the cost of redundant design, we should choose BBS (betweenness-based strategy) or DBS (degree based strategy) for node backup and HDF(high degree first) for redundancy edge backup. Above all, our proposed strategies are feasible and effective at improving the robustness of interdependent network controllability.
近年来，复杂网络的可控性一直是一个热门话题。被视为相互依存网络的实际网络总是由多个网络耦合在一起。相互依存网络的级联过程，包括相互依存故障和过载故障，将破坏整个网络可控性的鲁棒性。因此，相互依存网络可控性鲁棒性的优化在复杂网络研究领域具有重要意义。在本文中，基于首先构建的相互依存网络模型，我们确定了不同节点攻击比例下的级联过程。然后，通过最小驱动节点来衡量相互依存网络的结构可控性。此外，我们提出了一个可以通过不同节点攻击比例下相互依存网络的结构和最小驱动集得到的参数，并分析了相互依存网络可控性的鲁棒性。最后，我们通过包括节点备份和冗余边备份在内的冗余设计来优化相互依存网络可控性的鲁棒性，并根据其成本提出不同策略来改进冗余设计。进行冗余设计的比较策略以找到最佳策略。结果表明，节点备份和冗余边备份确实可以减少遭受故障的节点数量，并提高可控性的鲁棒性。考虑到冗余设计的成本，我们应该选择基于介数的策略（BBS）或基于度的策略（DBS）进行节点备份，选择高度优先策略（HDF）进行冗余边备份。最重要的是，我们提出的策略在提高相互依存网络可控性的鲁棒性方面是可行且有效的。
