The future Internet is expected to support applications with quality of service (QoS) requirements. To this end several mechanisms have been suggested in the IETF to support signaling, the most promising among them is DiffServ. An important problem in this framework is how to partition the QoS requirements of an application along a selected path. The problem which is in general NP complete, was solved for continuous convex cost functions by Lorenz and Orda (1999). This work concentrates on discrete cost functions, and presents efficient exact and approximated solutions for various conditions of the problem. We also show that the more complex problem of QoS sensitive routing with discrete cost functions is hard, but has a fully polynomial approximation scheme.
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