On fault tolerant routings in general networks (Q1089309)

We construct fault-tolerant routings for several families of graphs, including all graphs of maximal degree less than \(cn^{1/3}\) for some \(c>0\). With these routings, the diameter of the surviving graph is bounded by a constant (e.g. 4 or 6), so long as the number of faults is less than the connectivity of the graph. This result partially confirms a conjecture of \textit{D. Dolev, J. Halpern, B. Simons} and \textit{R. Strong} [A new look at fault tolerant network routing, in: Proc. 16th ACM Symp. Theory of Computing, 526-535 (1984)].