Augmenting Path is a path of edges in the 202206091605# with unused capacity more than 0 from source \(s\) to sink \(t\). If Augmenting Path is exhausted, that is there is no Augmenting Path could be found, this means that we have found the #maximum flow for the #202204112045.
Augmenting Path
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Residual Edge
The sole existence of Residual Edge is to undo or revert bad #202206091601 which doesn’t lead to #maximum flow. The Residual Edge is valid to be included into the augmentation in the later iteration (the edge has been taken at least once). When reverting, add the flow value of the residual edge to the flow edge. It is to avoid having a negative remaining capacity# (the difference of the flow edge’s maximum capacity and flow value).
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Ford-Fulkerson Algorithm
Augments (update) the flow means updating the flow values of the edges along the 202206091601#. This can be done by simply increasing the flow to the forward edges and decreasing the flow to the 202206091616# by the bottleneck value (the smallest maximum capacity in the path).
Ford-Fulkerson Algorithm is a 202204151143# aim to solve #202206091105 by repeatedly finds augmenting paths through the 202206091605# and augments (updates) the flow until there is no 202206091601# to be found. It is essentially finding the bottlenecks, that is the smallest maximum capacity in the augmenting path, and sum them all together to get the maximum flow for the #202204112045. *