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Vietnam Journal of Mathematics 35:4(2007) 507-522  On the Extremal Structure of an OSPF Related Cone Peter Brostr\''{o}m and Kaj Holmberg 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.     Keywords: OSPF, polyhedral cone, extreme ray, multicommodity, valid cycle.

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