Efficient algorithms for listing k disjoint st-paths in graphs

Abstract

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(Fk(G)) setup time, where (Formula presented) 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.