Research on the Maximum Network Flow Problem

The maximum flow problem and its dual problem—the minimum cut problem are a pair of classical combinatorial optimization problems, which arise in many engineering and scientific applications They are important parts of computer science and operational research The research on the maximum flow problem has a history of more than 40 years Recently, with the rapid development of various networks, the research on the maximum flow problem has made remarkable achievements Detailed summarization of the research on the problem is made, and the research directions are forecasted