Efficient Fault-Tolerant Fixed Routings on (k + 1)-Connected Digraphs

Wada, K. and K. Kawaguchi, Efficient fault-tolerant fixed routings on (k+ 1)connected digraphs, Discrete Applied Mathematics 37/38 (1992) 539-552. Consider a directed communication network G in which a limited number of directed link and/or node faults F might occur. A routing Q 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,&/F (denoted by D(R(G,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 e. In this paper, we show sufficient conditions for classes of (k+ 1)-connected directed graphs to have routings ~3 and ~2 on G such that D(R(G,e3)/F)13 and D(f?(G,&/F)12 for any set of faults F (lb, 5 k). Since the diameter of the surviving route graph is more than 1 provided that faults are asstunled to occur in the network, we insist that the routing e2 is optimal. We also show that constant diameter routings (with the diameters of the surviving route graph being 5 and 7) can be constructed cj~. any (k+ 1)-connected digraph satisfying only a certain size condition.