To ensure a high availability, most modern 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 efficiently verify whether a given network reroutes flows along feasible paths, without violating capacity constraints, for up to k link failures? We chart the algorithmic complexity landscape of resilient routing under link failures, considering shortest path routing based on link weights (e.g., the widely deployed ECMP protocol). We study two models: a pessimistic model where flows interfere in a worst-case manner along equal-cost shortest paths, and an optimistic model where flows are routed in a best-case manner and we present a complete picture of the algorithmic complexities for these models. We further propose a strategic search algorithm that checks only the critical failure scenarios while still providing correctness guarantees. Our experimental evaluation on a large benchmark of Internet and datacenter topologies confirms an improved performance of our strategic search algorithm by several orders of magnitude.

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