The overwhelming majority of survivable (fault-tolerant) network design models assume a uniform fault model. Such a model assumes that every subset of the network resources (edges or vertices) of a given cardinality $k$ may fail. While this approach yields problems with clean combinatorial structure and good algorithms, it often fails to capture the true nature of the scenario set coming from applications. One natural refinement of the uniform model is obtained by partitioning the set of resources into vulnerable and safe resources. The scenario set contains every subset of at most $k$ faulty resources. This work studies the Fault-Tolerant Path (FTP) problem, the counterpart of the Shortest Path problem in this fault model and the Fault-Tolerant Flow problem (FTF), the counterpart of the $\ell$-disjoint Shortest $s$-$t$ Path problem. We present complexity results alongside exact and approximation algorithms for both models. We emphasize the vast increase in the complexity of the problem with respect to the uniform analogue, the Edge-Disjoint Paths problem.

中文翻译：

---

容错边缘不相交路径——超越统一故障

绝大多数可存活（容错）网络设计模型都假定一个统一的故障模型。这样的模型假设给定基数 $k$ 的网络资源（边或顶点）的每个子集都可能失败。虽然这种方法会在干净的组合结构和良好的算法方面产生问题，但它通常无法捕捉来自应用程序的场景集的真实性质。统一模型的一种自然改进是通过将资源集划分为易受攻击和安全的资源来获得。场景集包含至多 $k$ 故障资源的每个子集。这项工作研究容错路径（FTP）问题，该故障模型中最短路径问题的对应问题和容错流问题（FTF），$\ell$-disjoint Shortest $s$-的对应问题$t$ 路径问题。我们展示了两种模型的复杂性结果以及精确和近似算法。我们强调问题的复杂性相对于统一模拟，即边缘不相交路径问题的巨大增加。