Strong fault-tolerance: Parallel routing in networks with faults

A d-regular network G is strongly fault-tolerant if for any copy G(f) of G with at most d-2 faulty nodes, every pair of non-faulty nodes u and nu in G(f) admits min{d(f)(u), d(f)(nu)} node-disjoint paths in Gf from u to v, where df (u) and df (v) are the degrees of the nodes u and nu in G(f). We show that popular network structures, such as hypercube and star networks, are strongly fault-tolerant. We develop efficient algorithms that construct the maximum number of node-disjoint paths of optimal or nearly optimal length in these networks with faulty nodes. Our algorithms are optimal in terms of their running time.