AbstractTo ensure a high availability, communication networks provide resilient routing mechanisms that quickly change routes upon failures. However, a fundamental algorithmic question underlying such mechanisms is hardly understood: how to verify whether a given network reroutes flows alongfeasiblepaths, without violating capacity constraints, for up toklink failures? We chart the algorithmic complexity landscape of resilient routing under link failures, considering shortest path routing based on link weights as e.g. deployed in the ECMP protocol. We study two models: apessimisticmodel where flows interfere in a worst-case manner along equal-cost shortest paths, and anoptimisticmodel where flows are routed in a best-case manner, and we present a complete picture of the algorithmic complexities. We further propose a strategic search algorithm that checks only the critical failure scenarios while still providing correctness guarantees. Our experimental evaluation on a benchmark of Internet and datacenter topologies confirms an improved performance of our strategic search by several orders of magnitude.