def maximum_flow(dg,a,b):
"""Edmonds-Karp algorithm. Complexity is O(VE^2)
"""
residual_network = dg.copy()
# a flow is represented by a digraph,
# initally empty, representing flow of zero along
# each edge
flow = DiGraph(residual_network.vertices())
new_path = shortest_path(residual_network,a,b)
while new_path:
# iterate through each arrow ..
for i, frm in enumerate(new_path[:-1]):
to = new_path[i+1]
# .. and adjust the flow
if flow.is_parent(to,frm):
flow.discard_arrow(to,frm)
else:
flow.add_arrow(frm,to)
# reverse arrow
residual_network.discard_arrow(frm,to)
residual_network.add_arrow(to,frm)
new_path = shortest_path(residual_network,a,b)
# need to use residual_network to get bottlenecks.
return flow, residual_network
def vertices_to_edges(ug):
"""complexity is O(V+E)
"""
new_dg = DiGraph()
for vertex in ug.vertices():
neg = (vertex,'-')
pos = (vertex,'+')
new_dg.add_vertex(neg)
new_dg.add_vertex(pos)
new_dg.add_arrow(pos,neg)
for v1, v2 in ug.lines():
new_dg.add_arrow((v1,'-'),(v2,'+'))
new_dg.add_arrow((v2,'-'),(v1,'+'))
return new_dg
