23 pagesThe resilience of a network is the expected number of pairs of nodes
that can communicate. Computing the resilience of a network is a #P-complete
problem even for planar networks with fail-safe nodes. We generalize
an O(n)^2 time algorithm to compute the resilience of n-node k-tree
networks with fail-safe nodes to obtain an O(n) time algorithm that computes
the resilience of n-node partial k-tree networks with edge and node
failures (given a fixed k and an embedding of the partial k-tree in a k-tree)
