Maximum Flow

Rex Yuan

June 25, 2015

Maximum Flow

This is the standard Ford-Fulkerson Maximum Flow algorithm implementedwith augment path finding method being Breadth-first Search.

Algorithm 1 Ford-Fulkerson Algorithm

procedure Ford-Fulkerson(graph)build a tree using breadth-first searchfind a augment path on that treeupdate residual networkreturn maximumf low

end procedure

Time Complexity

Ford-Fulkerson Maximum Flow algorithm is

O(Ef)

where E is the number of edges and f is the maximum flow.

Run Time Stats

I created the following table using UNIX POSIX time function and round themean time of 10 trials to five digits after decimal point to calculate the timepast. All samples have the ten possible characters to be encoded, that is 0 9.Variable input length implies the length of the sequence to be decoded.

1

Run Time StatsSample Input Size(V,E) Ford-Fulkerson

1 (6,7) 0.00042 (100,790) 0.055963 (200,1194) 0.177153 (1000,9994) 5.47452

2