For a survivable portion of a network, a backup port for a first router of the survivable network, to reach a destination node in the event of a single node failure, may be determined by (a) accepting a routing path graph having the destination node, wherein the routing path graph includes one or more links terminated by one or more primary ports of the first router; and (b) for each router of at least a part of the routing path graph, (1) assuming that the current router is removed, defining (A) a first part of the routing path graph including the destination node, and (B) a second part of the routing path graph separated from the first part wherein the second part defines one or more sub-graphs, and (2) determining the backup port for the first router by examining at least one of the one or more sub-graphs to find a link to the first part of the routing path graph.