Determining the most vital link in a flow network

Abstract : The most vital link in a single commodity flow network is that arc whose removal results in the greatest reduction in the value of the maximal flow in the network between a source node and a sink node. This paper develops an iterative labeling algorithm to determine the most vital link in the network. A necessary condition for an arc to be the most vital link is established and is employed to decrease the number of arcs which must be considered.