Name Independent Fault Tolerant Routing Scheme

We consider the problem of routing in presence of faults in undirected weighted graphs. More specifically, we focus on the design of compact name-independent fault-tolerant routing schemes, where the designer of the scheme is not allowed to assign names to nodes, i.e., the name of a node is just its identifier. Given a set $F$ of faulty (or forbidden) edges, the goal is to route from a source node $s$ to a target $t$ avoiding the forbidden edges in $F$. Given any name-dependent fault-tolerant routing scheme and any name-independent routing scheme, we show how to use them as a black box to construct a name-independent fault-tolerant routing scheme. In particular, we present a name-independent routing scheme able to handle any set $F$ of forbidden edges in $|F|+1$ connected graphs. This has stretch $O(k^{2\,|F|3(|F|+\log2} n)\log D)$, where $D$ is the diameter of the graph. It uses tables of size $ \widetilde{O}(k\, n^{1/k}(k + deg(v)))$ bits at every node $v$, where $deg(v)$ is the degree of node $v$. In the context of networks that suffer only from occasional failures, we present a name-independent routing scheme that handles only $1$ fault at a time, and another routing scheme that handles at most $2$ faults at a time. The former uses $\widetilde{O}(k^2\, n^{1/k} + k\,deg(v))$ bits of memory per node, with stretch $O(k^3\log D)$. The latter consumes in average $ \widetilde{O}(k² \,n^{1/k} + deg(v))$ bits of memory per node, with stretch $O(k^2\log D)$.