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• W2764042730 abstract "The emph{vitality} of an arc/node of a graph with respect to the maximum flow between two fixed nodes $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that arc/node. In this paper we address the issue of determining the vitality of arcs and/or nodes for the maximum flow problem. We show how to compute the vitality of all arcs in a general undirected graph by solving only $2(n-1)$ max flow instances and, In $st$-planar graphs (directed or undirected) we show how to compute the vitality of all arcs and all nodes in $O(n)$ worst-case time. Moreover, after determining the vitality of arcs and/or nodes, and given a planar embedding of the graph, we can determine the vitality of a `contiguous' set of arcs/nodes in time proportional to the size of the set." @default.
• W2764042730 created "2017-10-20" @default.
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• W2764042730 date "2017-10-05" @default.
• W2764042730 modified "2023-09-24" @default.
• W2764042730 title "Max flow vitality in general and $st$-planar graphs" @default.
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• W2764042730 hasPublicationYear "2017" @default.
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