Efficient Algorithms for Listing k Disjoint st-Paths in Graphs.

Given a connected graph G of m edges and n vertices, we consider the basic problem of listing all the choices of k vertex-disjoint st-paths, for any two input vertices s, t of G and a positive integer k. Our algorithm takes O(m) time per solution, using O(m) space and requiring O(F-k(G)) setup time, where F-k(G) = O(mmin{k, n(2/3) log n, root m log n}) is the cost of running a max-flow algorithm on G to compute a flow of size k. The proposed techniques are simple and apply to other related listing problems discussed in the paper.