Abstract
Let G be an Eulerian digraph, and let {x1, x2}, {y1,y2} be two pairs of vertices in G. A directed path from a vertex s to a vertex t is called an st-path. An instance (G;{x1, x2}, {y1,y2}) is called feasible if there is a choice of h,i,j,k with {h,i} = {j,k} = {1,2} such that G has two arc-disjoint xhxi- and yjyk-paths. In this paper, we characterize the structure of minimal infeasible instances, based on which an O(m+nlog n) time algorithm is presented to decide whether a given instance is feasible, where n and m are the number of vertices and arcs in the instance, respectively. If the instance is feasible, the corresponding two arc-disjoint paths can be computed in O(m(m+nlog n)) time.
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