On the complexity of QoS routing

We present SAMCRA, an exact QoS routing algorithm that guarantees to Þnd a feasible path if such a path exists. Because SAMCRA is an exact algorithm, its complexity also characterizes that of QoS routing in general. The complexity of SAMCRA is simulated in speciÞc classes of graphs. Since the complexity of an algorithm involves a scaling of relevant parameters, the second part of this paper analyzes how routing with multiple independent link weights affects the hopcount distribution. Both the complexity and the hopcount analysis indicate that for a special class of networks, QoS routing exhibits features similar to single-parameter routing. These results suggest that there may exist classes of graphs in which QoS routing is not NP-complete. 1 QoS Routing in Perspective. After almost Þve years since the appearance of our ”Aspects of QoS routing” [21], a brief update seems desirable because more understanding has been gained since then although basically little on the concepts has been changed. Our starting point here is the complementarity between routing algorithm and routing protocol. We quote from [21] Network routing essentially consists of two identities, the routing algorithm and the routing protocol. The routing algorithm assumes a temporarily static or frozen view of the network topology. [...] The routing protocol, on the other hand, provides each node in the network topology with a consistent view of that topology at some moment... If this duality is acceptable, it says that capturing the dynamics of the topology and the link weights is taken care of by the routing protocol. Once the graph where each link is speciÞed by a QoS link weight vector with as components for example delay, cell/packet loss, available bandwidth, monetary cost, etc... is offered by the routing protocol to a node, a local QoS routing algorithm is applied to determine in that graph a path from A to B subject to a QoS constraint vector. If an effective QoS routing protocol exists together with a QoS routing algorithm, we argue intuitively that the load in the network will be distributed automatically by QoS routing (both protocol and algorithm) and will tend closely to an optimally load-balanced network. Thus, under these assumptions, many ∗email: {P.VanMieghem,F.A.Kuipers}@its.tudelft.nl