Max Flow Vitality of Edges and Vertices in Undirected Planar Graphs
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We study the problem of computing the vitality with respect to max flow of edges and vertices in undirected planar graphs, where the vitality of an edge/vertex in a graph with respect to max flow between two fixed vertices s,t is defined as the max flow decrease when the edge/vertex is removed from the graph. We show that the vitality of any k selected edges can be computed in O(kn + nloglog n) worst-case time, and that a δ additive approximation of the vitality of all edges with capacity at most c can be computed in O(c/δn +n loglog n) worst-case time, where n is the size of the graph. Similar results are given for the vitality of vertices. All our algorithms work in O(n) space.
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