A Linear Time Algorithm for the Arc Disjoint Menger Problem in Planar Directed Graphs (Extended Abstract)
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چکیده
Given a graph G V E and two vertices s t V s t the Menger problem is to nd a maximum number of disjoint paths connecting s and t Depending on whether the input graph is directed or not and what kind of disjointness criterion is demanded this general formulation is specialized to the directed or undirected vertex and the edge or arc disjoint Menger problem respectively For planar graphs the edge disjoint Menger problem has been solved to optimality Wei while the fastest algorithm for the arc disjoint version is Weihe s general maximum ow algorithm for planar networks Wei which has running time O jV j log jV j Here we present a linear time i e asymptotically optimal algorithm for the arc disjoint version in planar directed graphs
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