Edmonds-Karp Max Flow/Min Cut

[bdeonovic]

An implementation of Max Flow and Min st cut with test/example and documentation. Coincidently someone was requesting this just recently: #202 (I beat you to it @pranavtbhat!)

[mlubin]

Nice! Have you done any benchmarking with existing implementations? Would be nice to know that there are no obvious performance bottlenecks that users will run into

[bdeonovic]

No, someone might want to look over it to see if it can be better written. The code is basically right out of the wikipedia pseudocode.

[bdeonovic]

I did a small test versus Python's networkx package and I seem to get the same results:

Python got 0.0001840381
Julia got 0.00012774970229999962 (after 1 call to get the function compiled)

The example is the example from the networkx package

Python Code

import networkx as nx
import time
from networkx.algorithms.flow import edmonds_karp
G = nx.DiGraph()
G.add_edge('x','a', capacity=3.0)
G.add_edge('x','b', capacity=1.0)
G.add_edge('a','c', capacity=3.0)
G.add_edge('b','c', capacity=5.0)
G.add_edge('b','d', capacity=4.0)
G.add_edge('d','e', capacity=2.0)
G.add_edge('c','y', capacity=2.0)
G.add_edge('e','y', capacity=3.0)

tot_time = 0;
for t in range(0, 10000):
  t0 = time.clock();
  flow_value = nx.maximum_flow_value(G, 'x', 'y');
  t1 = time.clock();
  tot_time = tot_time + (t1 - t0)
print tot_time/10000

Julia Code

using Graphs

g = inclist(["a","b","c","d","e","x","y"], is_directed=true)

c = zeros(8)
add_edge!(g,"x", "a"); c[1] = 3.0
add_edge!(g,"a", "b"); c[2] = 1.0
add_edge!(g,"a", "c"); c[3] = 3.0
add_edge!(g,"b", "c"); c[4] = 5.0
add_edge!(g,"b", "d"); c[5] = 4.0
add_edge!(g,"d", "e"); c[6] = 2.0
add_edge!(g,"c", "y"); c[7] = 2.0
add_edge!(g,"e", "y"); c[8] = 3.0

f = max_flow(g,"x","y",c)
tot_time = 0
for j in 1:10000
  tic()
  f = max_flow(g,"x","y",c)
  tot_time += toq()
end
println(tot_time/10000)

[mlubin]

That's encouraging, though would be good to see the scalability to larger problems. @pranavtbhat, any comments on this implementation?

[bdeonovic]

I agree a large scale example would be beneficial. I'm not an expert in this field and I am not sure where to find such a large example or how to generate one.

[bdeonovic]

Ready to pull?

[mlubin]

Any comments on this implementation, @emreyamangil?

[emreyamangil]

I think adding sister edge information (somewhere) would speed up the code (to get the reverse edge, right now you are doing a linear search in the targets neighborhood?), also if it is a multigraph your code might crash. You can compute the residual flow during the BFS (but not necessary). Other than that it looks good! Though maybe implementing preflow-push with labels might be a good idea for scalability.

[bdeonovic]

Thanks for the comments @emreyamangil. I will probably get around to implementing these changes eventually, but it may be awhile (quite a busy season of life).

[mlubin]

@bdeonovic, I don't think it's necessary to delay merging for these improvements. But I would add to the documentation that the max flow implementation uses a textbook implementation of Edmonds-Karp which is not competitive with state of the art approaches like preflow-push for large scale instances.

[pranavtbhat]

I've found that Bidirectional BFS works much faster with Edmond Karp's algorithm. (especially for large graphs).