A Study on a Method of Determining the Most Vital Arc in the Maximum Flow Problem

최대유통문제에서 MVA를 결정하는 방법에 관한 연구

The most vital arc in the maximum flow problem is that arc whose removal results in the greatest reduction in the value of the maximal flow between a source node and a sink node. This paper develops an algorithm to determine such a most vital arc(MVA) in the maximum flow problem. We first define the transformed network corresponding In a given network in order to compute the minimal capacity for each candidate arc. The set of candidate arcs for a MVA consists of the arcs whose flow is at least as greate as the flow over every arc in a minimal cut As a result, we present a method in which the MVA is determined more easily by computing the minimal capacity in the transformed network. The proposed method is demonstrated by numerical example.