The algorithm developed by Kuhn was largely based on the earlier works of two other [[Hungarian]] mathematicians: [[Denes Kőnig]] and [[Jenő Egerváry]]. The great advantage of Kuhn’s method is that it is strongly polynomial. The main idea of the algorithm is that it combines two separate parts in Egervery’s proof (computing a deficientdeficient set and revising the current π) into one. The procedure of covering the prime zeros can be implemented in a [[flow network]], and automated by means of the [[Ford-Fulkerson algorithm]]. The ''n''×''m'' matrix is transformed in a <math>G=(U,V)</math> bipartite graph, with I/O capacity equal to 1. Each arc joining the nodes of the flow network represents a zero in the cost matrix. After the maximum flow is obtained, the affected arcs represent the prime zeros. The [[minimum cut]] obtained by Ford-Fulkerson automates the process of covering the independent zeros. Each node that gets "cut" on the max-flow graph represents a covered row or line on the cost matrix. However, in the Hungarian method, the assignment can be easily found on the cost matrix, yet the expansion into a max-flow sub-problem is a useful method in more complex scenarios.
