This paper studies several new multiple routing path computation problems in failure-interdependent complex networks such as smart grid communication network, each of which exhibits unique failure interdependency. Despite the difference of the formulation of the problems, we show that each of the problems can be reduced to another within polynomial time, and therefore they are equivalent in terms of hardness. Then, we show that they are not only \(\mathcal {NP}\)-hard, but also cannot be approximated within a certain bound unless \({\mathcal {P}}=\mathcal {NP}\). Besides, we show that their decision versions to determine if there exist two failure independent paths between two given end nodes are still \(\mathcal {NP}\)-complete. Finally, a series of heuristic algorithms are proposed to deal with the daunting hardness of the problems. Most importantly, this paper opens a new series of research problems with daunting complexity based on important real world applications.

本文研究了故障相关的复杂网络（如智能电网通信网络）中的几个新的多路由路径计算问题，每个问题都表现出独特的故障相关性。尽管问题的表述方式不同，但我们表明，每个问题都可以在多项式时间内简化为另一个问题，因此在硬度方面等效。然后，我们证明它们不仅是\（\ mathcal {NP} \）- hard，而且在除非\（{\ mathcal {P}} = \ mathcal {NP} \）的情况下也无法在一定范围内近似。此外，我们证明了用于确定两个给定终端节点之间是否存在两条故障独立路径的决策版本仍然是\（\ mathcal {NP} \）-完成。最后，提出了一系列启发式算法来解决问题的艰巨性。最重要的是，本文基于重要的现实应用，提出了一系列新的研究问题，这些研究问题具有令人生畏的复杂性。