Optimal partition of QoS requirements with discrete cost functions

The future Internet is expected to support applications with quality of ser vice (QoS) requirements. To this end, several mechanisms are suggested in t he IETF; 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, This paper concentrates on discrete cost functions, which better model the existing an d upcoming mechanisms in the Internet, We present efficient exact and appro ximated solutions for various conditions of the problem, We also show that although the more complex problem of QoS sensitive routing with discrete co st functions is hard, it has a fully polynomial approximation scheme.