Ford-Fulkerson implementation java

Question

I'm trying to learn to implement the Ford-Fulkersons algorithm in java and found some help on the internet but I got stuck at this snippet of code

        // update residual capacities of the edges and
        // reverse edges along the path
        for (v=t; v != s; v=parent[v])
        {
            u = parent[v];
            rGraph[u][v] -= path_flow;
            rGraph[v][u] += path_flow;
        }

I sort of understand how it works thanks to the comment, but not completely sure why it's required. Why do you need to subtract?

Source: http://www.geeksforgeeks.org/ford-fulkerson-algorithm-for-maximum-flow-problem/

score 2 · Accepted Answer · answered Apr 14 '16 at 08:22

If you can push a flow in either direction along an edge, then the net flow from A to B has to be equal in magnitude and opposite in sign to the net flow from B to A.

It's just like in circuit analysis: if 5 amps of current flow from A to B, then -5A of current flow from B to A.

A     Resistor      B
O-----[======]------O
  5A ->

A     Resistor      B
O-----[======]------O
             <- -5A

Hence, by pushing "more" from A to B, you have to reduce the amount being pushing from B to A by a corresponding amount.

score 0 · Answer 2 · answered Apr 14 '16 at 07:34

0

You can refer to https://github.com/mission-peace/interview/blob/master/src/com/interview/graph/FordFulkerson.java

and for video https://www.youtube.com/watch?v=GiN3jRdgxU4

answered Apr 14 '16 at 07:34

js_248

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How do you get the final flow value on each edge from that algorithm? For example when searching for the initial feasible flow. Is that the original graph value minus the residual graph values on each edge? Does the orientation change it? Thank you. – Kit Ostrihon Apr 15 '17 at 06:56

Ford-Fulkerson implementation java

2 Answers2