Modern communication networks support local fast rerouting mechanisms to quickly react to link failures: nodes store a set of conditional rerouting rules which define how to forward an incoming packet in case of incident link failures. The rerouting decisions at any node $v$ must rely solely on local information available at $v$: the link from which a packet arrived at $v$, the target of the packet, and the incident link failures at $v$. Ideally, such rerouting mechanisms provide perfect resilience: any packet is routed from its source to its target as long as the two are connected in the underlying graph after the link failures. Already in their seminal paper at ACM PODC '12, Feigenbaum, Godfrey, Panda, Schapira, Shenker, and Singla showed that perfect resilience cannot always be achieved. While the design of local rerouting algorithms has received much attention since then, we still lack a detailed understanding of when perfect resilience is achievable. This paper closes this gap and presents a complete characterization of when perfect resilience can be achieved. This characterization also allows us to design an $O(n)$-time algorithm to decide whether a given instance is perfectly resilient and an $O(nm)$-time algorithm to compute perfectly resilient rerouting rules whenever it is. Our algorithm is also attractive for the simple structure of the rerouting rules it uses, known as skipping in the literature: alternative links are chosen according to an ordered priority list (per in-port), where failed links are simply skipped. Intriguingly, our result also implies that in the context of perfect resilience, skipping rerouting rules are as powerful as more general rerouting rules. This partially answers a long-standing open question by Chiesa, Nikolaevskiy, Mitrovic, Gurtov, Madry, Schapira, and Shenker [IEEE/ACM Transactions on Networking, 2017] in the affirmative.

翻译：现代通信网络支持本地快速重路由机制以快速应对链路故障：节点存储一组条件重路由规则，用于定义在发生入射链路故障时如何转发到达的数据包。任意节点$v$处的重路由决策必须仅依赖于$v$处可用的本地信息：数据包到达$v$的链路、数据包的目标地址以及$v$处的入射链路故障状态。理想情况下，此类重路由机制能提供完美弹性：只要源节点与目标节点在链路故障后的底层图中保持连通，任何数据包都能从源路由至目标。早在ACM PODC '12的开创性论文中，Feigenbaum、Godfrey、Panda、Schapira、Shenker和Singla已证明完美弹性并非总能实现。尽管此后本地重路由算法的设计受到广泛关注，我们仍缺乏对完美弹性可实现条件的深入理解。本文填补了这一空白，提出了完美弹性可实现性的完整刻画。该刻画同时使我们能够设计$O(n)$时间算法判定给定实例是否具有完美弹性，并在可实现时以$O(nm)$时间计算完美弹性重路由规则。我们的算法还因其使用的重路由规则结构简单而具有吸引力——这类规则在文献中称为跳跃式路由：根据有序优先级列表（按入端口）选择替代链路，故障链路被直接跳过。有趣的是，我们的结果还表明在完美弹性背景下，跳跃式重路由规则与更通用的重路由规则具有同等表达能力。这从肯定方向部分回答了Chiesa、Nikolaevskiy、Mitrovic、Gurtov、Madry、Schapira和Shenker在[IEEE/ACM Transactions on Networking, 2017]中提出的长期开放性问题。