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The following is a simulation of the Dinic's algorithm.
Hence, the running time of Dinic's algorithm is .
The introduction of the concepts of the level graph and blocking flow enable Dinic's algorithm to achieve its performance.
Dinic's algorithm includes additional techniques that reduce the running time to O(V'E).
In fact, a generalization of the technique used in Hopcroft-Karp algorithm to arbitrary flow networks is known as Dinic's algorithm.
Dinic's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim Dinitz.
Using a data structure called dynamic trees, the running time of finding a blocking flow in each phase can be reduced to and therefore the running time of Dinic's algorithm can be improved to .
