Optimal partition of QoS requirements with discrete cost functions

The future Internet is expected to support applications with quality of service (QoS) requirements. To this end, several mechanisms are suggested in the 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 (see IEEE/ACM Trans. Networking. vol.6, p.768-78, 1998 and Proc. IEEE INFOCOM´99, p.246-53, 1999). This paper concentrates on discrete cost functions, which better model the existing and upcoming mechanisms in the Internet. We present efficient exact and approximated solutions for various conditions of the problem. We also show that although the more complex problem of QoS sensitive routing with discrete cost functions is hard, it has a fully polynomial approximation scheme.