Ford-Fulkerson algorithm
1. Original procedure of the algorithm
Ford-Fulkerson algorithm is used to find the maximum flow in a flow
network. We work with a network 
,
where 
is a set of nodes
including a source 
and sink 
is a set of
directed edges.
A label of an edge is written as 
where 
indicates its capacity
and 
means a flow (amount of energy) streaming through the edge.
- At the beginning of the algorithm set the flow of all the edges to
. - We repeatedly search for the augmenting path from the source to
the sink
.
As soon as we find such a path we also compute the available capacity
of all its edges, by which we subsequently increase the flow in the network.
When processing the algorithm in the standard way we work with a visual
representation of the network and modify labels of edges. Image 1
illustrates a network 
with seven nodes and the current flow 
(see the path
). The augmenting path 
,
with the available capacity on all its edges is highlighted.
In the next step we can increase the flow and modify labels of
the augmenting path, change to 
for the
paths 
, 
and
to 
for the path 
.
Example 1: network
Image 1: Network
with the flow where the augmenting path
is highlighted
To demonstrate Ford-Fulkerson algorithm we come with an Animation 1 of the computation and use a concrete flow network.
Example 2: network
-
- Start of the algorithm – a flow network with seven nodes ,
, 
, , 
, 
,
- : –– –– –
–: –– ––: ––: –
–: ––: –– –
– –– ––Do not display this label
2. Proposals of adaptation
1. Work with a network on a sheet of a spreadsheet editor:
The network is again converted to a table and organized
in a similar way as in the case of the first method
of Dijsktra's algorithm adaption.
We add labels of the nodes to the first column.
All the other cells on the row for a node 
are reserved
for the edges coming out from and are written as
– where is the
end node of the edge, indicates the current flow through the edge and identifies
its capacity. Let us take the same network illustrated on the Image 1.
The following Table 1 demonstrates the situation after processing the first augmenting
path
Example 3: network
–
–
A blind student finds an augmenting path from the source to the sink .
He/she consecutively goes through the table and holds a sequence of the path's
nodes and actual available capacity of the path's edges in his/her memory.
During the second view he/she modifies
the flow and marks edges with the flow equal
to the capacity, which are directed from the source to the sink.
2. Edges are organized one below each other on lines of a standard text editor:
every edge is written separately on one line
as ––,
where is a starting node and is an ending
node of the edge with a capacity and a current flow .
The edges are ordered alphabetically according to the node
from which they come. We work in a similar way as when using
the previous method. We go through the table twice,
first to find an augmenting path from the source to the sink,
then to increase a flow on the path.
3. Discussion of pros and cons
The first method was evaluated as the better one. It is easy to find the desired information in the table and to search for an augmenting path (Let us mention that it is difficult to find a maximum flow if we need to search for the augmenting path containing edges in the opposite direction.). When going through the graph using the second method a blind student has to observe many lines with data not relevant at the moment. We recommend students to make a note about the processed augmenting path in a temporary text file (it suffices to write down a sequence of nodes from the source to the sink).