Consider a directed communication network G in which a limited number of directed link and/or node faults F might occur. A routing % for the network (a fixed path for each ordered pair of nodes) must be chosen without knowing which components might become faulty. The diameter of the surviving route graph R(G,%g)/F (denoted by D(R(G, %)/F)), where two nonfaulty nodes x and y are connected by a directed edge if there are no faults on the route from x to y, could be one of the fault-tolerant measures for the routing %. In this paper, the authors show sufficient conditions for classes of (k+1)-connected directed graphs to have routings %3 and %2 on G such that (D(R(G,%3)/F and D(R(G,%2)/F for any set of faults . Since the diameter of the surviving route graph is more than 1 provided that faults are assumed to occur in the network, they insist that the routing %2 is optimal. The authors also show that constant diameter routings (with the diameters of the surviving route graph being 5 and 7) can be constructed for any -connected digraph satisfying only a certain size condition.
