All pair Maximum Flow

六眼飞鱼酱① 提交于 2019-12-05 03:51:50

Gomory-Hu Tree does not work with directed graphs, putting that aside, Gomory-Hu Tree will form a Graph maximum flow by applying minimum cuts.

The time complexity is:

O(|V|-1 * T(minimum-cut)) = O(|V|-1 * O(2|V|-2)) ~ O(|V|^2)

* using an optimal minimum-cut algorithm (Max-Flow Min-Cut Reduction)

This example illustrate how Gomory-Hu Tree is constructed from a given Graph

Gomory-Hu tree does not work for directed weighted graph.

It is an open problem whether there exist an algorithm to solve all pair maximum flow faster than running n^2 maximum flows on directed graphs.

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