Compatible Weights and Valid Cycles in Non-spanning OSPF Routing Patterns

Many IP (Internet Protocol) networks use OSPF (Open Shortest Path First) for determining the routing of traffic. OSPF routers compute routing paths using link weights set by the network administrator, and the routers send traffic on all shortest paths to the destination. An interesting question is whether or not a set of prespecified routing patterns can be realized in an OSPF network. If not, we seek structural properties that explain why no such weights exist. Mathematical models for finding weights and for combining routing patterns are presented. We show that two possibly non-spanning routing patterns forming a ``valid cycle'' cannot simultaneously be obtained in an OSPF network. Two new methods for finding valid cycles are presented, illustrated by numerical examples, and shown to be faster that those previously known

On the Extremal Structure of an OSPF Related Cone

Abstract. In a telecommunication network using the OSPF protocol, the routing patterns used are the shortest paths with respect to the link weights. By choosing the link weights, a set of desired shortest paths can often be obtained, but in some cases there are no weights giving the desired shortest paths. We study a polyhedral cone associated with the latter situation, and give a characterization of an important class of extreme rays of the cone. The characterization is based on feasible and valid cycles, which can be found efficiently in practice