A Method for Determining All the k Most Vital Arcs in the Maximum Flow Problem by Ranking of Cardinality Cuts

절단기수의 나열을 통한 최대유통문제에서 모든 k-치명호를 찾는 방법

The k most vital arcs (k-MVA) of a maximum flow problem is defined as those k arcs whose simultaneous removal from the network causes the greatest decrease in the throughput capability of the remaining system between a specified pair of nodes. In this study, we present a method for determining all the k-MVA in maximum flow problem using a minimal cardinality cut algorithm and k-th minimal cut ranking algorithm. For ranking cardinality cuts, we use Hamacher's ranking algorithm for cut capacity and by comparing present residual capacity of cardinality cut with expected residual capacity of next cardinality cut, we also present termination condition for this algorithm. While the previous methods cannot find all the alternatives for this problem, a method presented here has advantage of determining all the k-MVA.