def edmonds_karp(n,s,t,Capacity,Flow): maxFlow=0 #parent = [-1 for x in range(n)] iter_no=0 #print "Capacity matrix: ", Capacity #Make edge matrix: Edge = [[0 for x in range(n)] for x in range(n)] for i in range(0,n): for j in range(0,n): if Capacity[i][j] < 0: Edge[i][j] = 1 Res_graph = deepcopy (Capacity) while 1 : #while x < 10: print "iteration number: ", iter_no iter_no +=1 parent = [-1 for x in range(n)] augmented_flow = max_aug_flow(n,s,t,Res_graph, Flow,parent) print "parent here1: ", parent if augmented_flow == 0: break maxFlow += augmented_flow v = t #print "parent again: ", parent #for check, can be removed while v!=s : u = parent[v] Flow[u][v] += augmented_flow #flow is positive matrix Flow[v][u] -= Flow[u][v] #Flow[v][u] -= augmented_flow #Capacity[u][v] += augmented_flow #positive addition because negative capacity taken due to fib heap structure and postive augmented flow v= u #Make residual graph and send residual graph in the max_aug_flow function for i in range(0,n): for j in range(0,n): if Edge[i][j] == 1: Res_graph[i][j] = -(-Capacity[i][j]-Flow[i][j]) #capacity is negative matrix, hence - sign required and because we need res_graph to have negative values #othewise, Cf = c(u,v) - f(u,v) Res_graph[j][i] = -(-Flow[i][j]) #Cf(v,u) = -f(u,v) , here as positive, because negative capacities for fib heap to work print "Capacity matrix is " print Capacity print "Flow matrix is: " print Flow print "Res_graph is " print Res_graph print "" return maxFlow
def edmonds_karp(n, s, t, Capacity, Flow):
maxFlow = 0
#parent = [-1 for x in range(n)]
iter_no = 0
#print "Capacity matrix: ", Capacity
#Make edge matrix:
Edge = [[0 for x in range(n)] for x in range(n)]
for i in range(0, n):
for j in range(0, n):
if Capacity[i][j] < 0:
Edge[i][j] = 1
Res_graph = deepcopy(Capacity)
while 1:
#while x < 10:
print "iteration number: ", iter_no
iter_no += 1
parent = [-1 for x in range(n)]
augmented_flow = max_aug_flow(n, s, t, Res_graph, Flow, parent)
print "parent here1: ", parent
if augmented_flow == 0:
break
maxFlow += augmented_flow
v = t
#print "parent again: ", parent #for check, can be removed
while v != s:
u = parent[v]
Flow[u][v] += augmented_flow #flow is positive matrix
Flow[v][u] -= Flow[u][v]
#Flow[v][u] -= augmented_flow
#Capacity[u][v] += augmented_flow #positive addition because negative capacity taken due to fib heap structure and postive augmented flow
v = u
#Make residual graph and send residual graph in the max_aug_flow function
for i in range(0, n):
for j in range(0, n):
if Edge[i][j] == 1:
Res_graph[i][j] = -(
-Capacity[i][j] - Flow[i][j]
) #capacity is negative matrix, hence - sign required and because we need res_graph to have negative values
#othewise, Cf = c(u,v) - f(u,v)
Res_graph[j][i] = -(
-Flow[i][j]
) #Cf(v,u) = -f(u,v) , here as positive, because negative capacities for fib heap to work
print "Capacity matrix is "
print Capacity
print "Flow matrix is: "
print Flow
print "Res_graph is "
print Res_graph
print ""
return maxFlow
def edmonds_karp(n, s, t, Capacity, Flow):
maxFlow = 0
parent = [-1 for x in range(n)]
x = 0
while 1:
print "iteration number: ", x
x += 1
augmented_flow = max_aug_flow(n, s, t, Capacity, Flow, parent)
if augmented_flow == 0:
break
maxFlow += augmented_flow
v = t
while v != s:
u = parent[v]
Flow[u][v] += augmented_flow
#Flow[v][u] -= augmented_flow
Capacity[u][
v] += augmented_flow # += because negative capacities and positive flow taken
v = u
return maxFlow
def max_min_bottleneck(n,s,t,Capacity,Flow): maxFlow=0 #parent = [-1 for x in range(n)] iter_no=0 #Number of times every edge gets saturated = no. of times it is selected while finding maximum augmenting path No_Edge_Sat_Max_Flow = [[0 for x in range(n)] for x in range(n)] #Number of times an edge reverses its direction No_Edge_Flip = [[0 for x in range(n)] for x in range(n)] Edge_Direction = [[0 for x in range(n)] for x in range(n)] #print "Capacity matrix: ", Capacity #Make edge matrix: Edge = [[0 for x in range(n)] for x in range(n)] for i in range(0,n): for j in range(0,n): if Capacity[i][j] < 0: Edge[i][j] = 1 Res_graph = deepcopy (Capacity) while 1 : #while x < 10: print "iteration number: ", iter_no iter_no +=1 parent = [-1 for x in range(n)] augmented_flow = max_aug_flow(n,s,t,Res_graph, Flow,parent, No_Edge_Sat_Max_Flow) #augmented_flow, sat_u, sat_v = max_aug_flow(n,s,t,Res_graph, Flow,parent) #No_Edge_Sat_Max_Flow[sat_u][sat_v] += 1 print "parent here1: ", parent if augmented_flow == 0: break maxFlow += augmented_flow v = t #print "parent again: ", parent #for check, can be removed while v!=s : u = parent[v] Flow[u][v] += augmented_flow #flow is positive matrix Flow[v][u] -= Flow[u][v] #Flow[v][u] -= augmented_flow #Capacity[u][v] += augmented_flow #positive addition because negative capacity taken due to fib heap structure and postive augmented flow #Record number of edge flips: temp = Edge_Direction[u][v] Edge_Direction[u][v] = 1 #edge direction Edge_Direction[v][u] = -1 if temp != Edge_Direction[u][v]: No_Edge_Flip[u][v] += 1 No_Edge_Flip[v][u] += 1 v= u #Make residual graph and send residual graph in the max_aug_flow function for i in range(0,n): for j in range(0,n): if Edge[i][j] == 1: Res_graph[i][j] = -(-Capacity[i][j]-Flow[i][j]) #capacity is negative matrix, hence - sign required and because we need res_graph to have negative values #othewise, Cf = c(u,v) - f(u,v) Res_graph[j][i] = -(-Flow[i][j]) #Cf(v,u) = -f(u,v) , here as positive, because negative capacities for fib heap to work print "Capacity matrix is " print Capacity print "Flow matrix is: " print Flow print "Res_graph is " print Res_graph print "" print "No_Edge_Sat_Max_Flow is: ", No_Edge_Sat_Max_Flow print "No. of edge flippings is: ", No_Edge_Flip return maxFlow
def max_min_bottleneck(n, s, t, Capacity, Flow, max_possible_flow):
#f = max_possible_flow
maxFlow = 0
#parent = [-1 for x in range(n)]
iter_no = 0
#Number of times every edge gets saturated = no. of times it is selected while finding maximum augmenting path
No_Edge_Sat_Max_Flow = [[0 for x in range(n)] for x in range(n)]
#Number of times an edge reverses its direction
No_Edge_Flip = [[0 for x in range(n)] for x in range(n)]
Edge_Direction = [[0 for x in range(n)] for x in range(n)]
#print "Capacity matrix: ", Capacity
#Make edge matrix:
Edge = [[0 for x in range(n)] for x in range(n)]
for i in range(0, n):
for j in range(0, n):
if Capacity[i][j] < 0:
Edge[i][j] = 1
Res_graph = deepcopy(Capacity)
while 1:
#while x < 10:
print "iteration number: ", iter_no
iter_no += 1
parent = [-1 for x in range(n)]
augmented_flow = max_aug_flow(n, s, t, Res_graph, Flow, parent,
No_Edge_Sat_Max_Flow)
#augmented_flow, sat_u, sat_v = max_aug_flow(n,s,t,Res_graph, Flow,parent)
#No_Edge_Sat_Max_Flow[sat_u][sat_v] += 1
print "parent here1: ", parent
flag = 0
if augmented_flow == 0:
break
#For min, cost, following condition is required to ensure that source only supplies what it has
if augmented_flow > max_possible_flow - maxFlow:
augmented_flow = max_possible_flow - maxFlow
flag = 1
maxFlow += augmented_flow
v = t
#print "parent again: ", parent #for check, can be removed
while v != s:
u = parent[v]
Flow[u][v] += augmented_flow #flow is positive matrix
Flow[v][u] -= Flow[u][v]
#Flow[v][u] -= augmented_flow
#Capacity[u][v] += augmented_flow #positive addition because negative capacity taken due to fib heap structure and postive augmented flow
#Record number of edge flips:
temp = Edge_Direction[u][v]
Edge_Direction[u][v] = 1 #edge direction
Edge_Direction[v][u] = -1
if temp != Edge_Direction[u][v]:
No_Edge_Flip[u][v] += 1
No_Edge_Flip[v][u] += 1
v = u
#Make residual graph and send residual graph in the max_aug_flow function
for i in range(0, n):
for j in range(0, n):
if Edge[i][j] == 1:
Res_graph[i][j] = -(
-Capacity[i][j] - Flow[i][j]
) #capacity is negative matrix, hence - sign required and because we need res_graph to have negative values
#othewise, Cf = c(u,v) - f(u,v)
Res_graph[j][i] = -(
-Flow[i][j]
) #Cf(v,u) = -f(u,v) , here as positive, because negative capacities for fib heap to work
print "Capacity matrix is "
print Capacity
print "Flow matrix is: "
print Flow
print "Res_graph is "
print Res_graph
print ""
if flag == 1:
break
#Can be printed if needed. Work alright.
#print "No_Edge_Sat_Max_Flow is: ", No_Edge_Sat_Max_Flow
#print "No. of edge flippings is: ", No_Edge_Flip
return maxFlow