Blocking flows

It is very hard to find your marriage partner in computer science. In modern society, the marriage means more complicated. Your partner may be animals. You have free choices. I don't care about that.

There is a path between S and T. This is the vector to find your partner. You choose the shortest way.

A blocking flow expand the administrative path with at least the one arc. Moreover, the max flow algorithm is to find the blocking flows.

Life is hard, so you can't go straight always. You need O(m) times to find blocking flows, so the running time of this max flow algorithm is O(mn).

U is the maximum capacity of an edge, and O(mn) is the expanded work. Therefore, the total running time of max flow for scaling blocking flows is O(mn log U).