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Precomputation-based methods have recently been proposed as an instrument to facilitate scalability, improve response time, and reduce computation load on network elements. The key idea is, in effect, to reduce the time needed to handle an event by performing some computation in advance, i.e., prior to the event's arrival. Such computations are performed as background processes, enabling a solution to be provided promptly upon a request, through a simple, fast procedure. We investigate precomputation methods in the context of quality-of-service (QoS) routing. Precomputation is highly desirable for QoS routing schemes due to the high computational complexity of selecting QoS paths, and the need to provide a satisfactory path promptly upon a request. We consider two major settings of QoS routing. The first case is where the QoS constraint is of the "bottleneck" type, e.g., a bandwidth requirement, and network optimization is sought through hop minimization. The second is the more general setting of "additive" QoS constraints (e.g., delay) and general link costs. The paper mainly focuses on the first setting. We show that, by exploiting the typical hierarchical structure of large-scale networks, a substantial improvement can be achieved in terms of computational complexity. We consider networks with topology aggregation. We show that precomputation is a necessary element for any QoS routing scheme and establish a precomputation scheme appropriate for such settings. We consider the case of additive QoS constraints (e.g., delay) and general link costs. As the routing problem becomes NP-hard, we focus on ε-optimal approximations and derive a precomputation scheme that offers a major improvement over the standard approach.