An O(n * log(n)) algorithm for maximum st-flow in a directed planar graph (Borradaile, Klein)

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Could someone explain to me using an example how Borradaile-Klein's algorithm for maximum flow works? http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.83.6392&rep=rep1&type=pdf

There are a lot of Ford-Fulkerson's examples (https://www.youtube.com/watch?v=Tl90tNtKvxs) but I didn't find an example for Borradaile-Klein algorithm.

Thank you.

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