def test_optional_capacity(self):
# Test optional capacity parameter.
G = nx.DiGraph()
G.add_edge('x','a', spam = 3.0)
G.add_edge('x','b', spam = 1.0)
G.add_edge('a','c', spam = 3.0)
G.add_edge('b','c', spam = 5.0)
G.add_edge('b','d', spam = 4.0)
G.add_edge('d','e', spam = 2.0)
G.add_edge('c','y', spam = 2.0)
G.add_edge('e','y', spam = 3.0)
solnFlows = {'x': {'a': 2.0, 'b': 1.0},
'a': {'c': 2.0},
'b': {'c': 0, 'd': 1.0},
'c': {'y': 2.0},
'd': {'e': 1.0},
'e': {'y': 1.0},
'y': {}}
solnValue = 3.0
s = 'x'
t = 'y'
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity = 'spam')
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
assert_equal(nx.min_cut(G, s, t, capacity = 'spam'), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity = 'spam'), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity = 'spam'),
solnFlows)
def compare_flows(G, s, t, solnFlows, solnValue):
flowValue, flowDict = nx.ford_fulkerson(G, s, t)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
assert_equal(nx.min_cut(G, s, t), solnValue)
assert_equal(nx.max_flow(G, s, t), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t), solnFlows)
def get_all_zero_edges(G, s, t, topological_dict):
"""
Get all "zero-edges" from a graph: all the edges that if we remove them,
the graph won't be connected anymore.
"""
if nx.min_cut(G, s, t) != 1:
return []
auxiliary = nx.copy.deepcopy(G)
zero_edges = nx.bidirectional_shortest_path(auxiliary, s, t)
zero_edges = list(zip(zero_edges[:-1], zero_edges[1:]))
kill_list = []
for edge in zero_edges:
auxiliary.remove_edge(edge[0], edge[1])
try:
nx.bidirectional_shortest_path(auxiliary, s, t)
print edge
kill_list.append(edge)
except nx.NetworkXNoPath:
pass
auxiliary.add_edge(edge[0], edge[1])
for edge in kill_list:
zero_edges.remove(edge)
zero_edges.sort(
lambda x, y: cmp(topological_dict[x[0]], topological_dict[y[0]]))
return zero_edges
def compare_flows(G, s, t, solnFlows, solnValue):
flowValue, flowDict = nx.ford_fulkerson(G, s, t)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
assert_equal(nx.min_cut(G, s, t), solnValue)
assert_equal(nx.max_flow(G, s, t), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t), solnFlows)
def get_all_zero_edges(G, s, t, topological_dict):
"""
Get all "zero-edges" from a graph: all the edges that if we remove them,
the graph won't be connected anymore.
"""
if nx.min_cut(G, s, t) != 1:
return []
auxiliary = nx.copy.deepcopy(G)
zero_edges = nx.bidirectional_shortest_path(auxiliary, s, t)
zero_edges = list(zip(zero_edges[:-1], zero_edges[1:]))
kill_list = []
for edge in zero_edges:
auxiliary.remove_edge(edge[0], edge[1])
try:
nx.bidirectional_shortest_path(auxiliary, s, t)
print edge
kill_list.append(edge)
except nx.NetworkXNoPath:
pass
auxiliary.add_edge(edge[0], edge[1])
for edge in kill_list:
zero_edges.remove(edge)
zero_edges.sort(lambda x, y: cmp(topological_dict[x[0]], topological_dict[y[0]]))
return zero_edges
def compare_flows(G, s, t, solnFlows, solnValue, capacity = 'capacity'):
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
flowValue, flowDict = nx.preflow_push(G, s, t, capacity)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity), solnFlows)
def global_mincut(self, G):
"全域最小カット重みを求める"
if isinstance(G, networkx.MultiGraph):
G = self._simplify_multigraph(G)
mincut = None
nodes = G.nodes()
s = nodes.pop()
for t in nodes:
tmp = networkx.min_cut(G, s, t, capacity="weight")
if mincut == None or tmp < mincut:
mincut = tmp
return mincut
def test_optional_capacity(self):
# Test optional capacity parameter.
G = nx.DiGraph()
G.add_edge('x', 'a', spam=3.0)
G.add_edge('x', 'b', spam=1.0)
G.add_edge('a', 'c', spam=3.0)
G.add_edge('b', 'c', spam=5.0)
G.add_edge('b', 'd', spam=4.0)
G.add_edge('d', 'e', spam=2.0)
G.add_edge('c', 'y', spam=2.0)
G.add_edge('e', 'y', spam=3.0)
solnFlows = {
'x': {
'a': 2.0,
'b': 1.0
},
'a': {
'c': 2.0
},
'b': {
'c': 0,
'd': 1.0
},
'c': {
'y': 2.0
},
'd': {
'e': 1.0
},
'e': {
'y': 1.0
},
'y': {}
}
solnValue = 3.0
s = 'x'
t = 'y'
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity='spam')
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
assert_equal(nx.min_cut(G, s, t, capacity='spam'), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity='spam'), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity='spam'),
solnFlows)
def compare_flows(G, s, t, solnFlows, solnValue, capacity = 'capacity'):
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
flowValue, flowDict = nx.preflow_push(G, s, t, capacity)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
flowValue, flowDict = nx.shortest_augmenting_path(G, s, t, capacity,
two_phase=False)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
flowValue, flowDict = nx.shortest_augmenting_path(G, s, t, capacity,
two_phase=True)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity), solnFlows)
def min_cut(grid):
G = nx.DiGraph()
#node name:
# x-y-(in|out)
for x in range(w):
for y in range(h):
if not grid[x][y]:
continue
ad = adj(grid, x, y)
for a in ad:
G.add_edge(name(*a)+"-out", name(x,y)+"-in", capacity=1)
G.add_edge(name(x,y)+"-in", name(x,y)+"-out", capacity=1)
G.add_edge(name(x,y)+"-out", name(*a)+"-in", capacity=1)
# supernodes
for x in range(w):
if grid[x][0]:
G.add_edge("start", name(x,0)+"-in", capacity=1)
if grid[x][h-1]:
G.add_edge(name(x,h-1)+"-out", "end", capacity=1)
if "start" not in G or "end" not in G:
return 0
return nx.min_cut(G, 'start', 'end')
def compare_flows(G, s, t, solnFlows, solnValue, capacity='capacity'):
flowValue, flowDict = nx.ford_fulkerson(G, s, t, capacity)
assert_equal(flowValue, solnValue)
assert_equal(flowDict, solnFlows)
flowValue, flowDict = nx.preflow_push(G, s, t, capacity)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
flowValue, flowDict = nx.shortest_augmenting_path(G,
s,
t,
capacity,
two_phase=False)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
flowValue, flowDict = nx.shortest_augmenting_path(G,
s,
t,
capacity,
two_phase=True)
assert_equal(flowValue, solnValue)
validate_flows(G, s, t, flowDict, solnValue, capacity)
assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
assert_equal(nx.ford_fulkerson_flow(G, s, t, capacity), solnFlows)
def compare_value_flows_highest_label(G, s, t, solnValue, capacity='capacity'):
flowValue, flowDict = nx.highest_label_maxflow(G, s, t, capacity)
nst.assert_equal(flowValue, solnValue)
nst.assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
nst.assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
def compare_value_flows_relabel_to_front(G, s, t, solnValue, capacity='capacity'):
flowValue, flowDict = nx.relabel_to_front_maxflow(G, s, t, capacity)
nst.assert_equal(flowValue, solnValue)
nst.assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
nst.assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
def compare_value_flows_vanilla_push_relabel(G, s, t, solnValue, capacity='capacity'):
flowValue, flowDict = nx.vanilla_push_relabel_maxflow(G, s, t, capacity)
nst.assert_equal(flowValue, solnValue)
nst.assert_equal(nx.min_cut(G, s, t, capacity), solnValue)
nst.assert_equal(nx.max_flow(G, s, t, capacity), solnValue)
# neighbours[2].remove(3)
# neighbours[3].remove(2)
# neighbours[4].remove(5)
# neighbours[5].remove(4)
# neighbours[3].remove(1)
# neighbours[1].remove(3)
#neighbours[0].remove(2)
#neighbours[2].remove(0)
#neighbours[0].remove(3)
#neighbours[3].remove(0)
clique = eval(sys.argv[2]) #[(0, 3), (0, 4), (0, 5), (1, 2), (1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)]
G = nx.Graph()
G.add_nodes_from(xrange(0, size))
G.add_edges_from(clique, capacity = 1.0)
mincut = min(map(lambda x: nx.min_cut(G, x[0], x[1]), itertools.combinations(xrange(0, size), 2)))
print mincut
global_order = {(x + 1): (((x+1) % (size - 1)) + 1) for x in xrange(0, size - 1)}
routing_table = {x: GenerateTable(x, global_order, size) for x in xrange(1, size)}
tested = 0
passed = 0
for perm in itertools.permutations(xrange(1, size)):
perm_l = list(perm)
xlate = {x: perm[x - 1] for x in xrange(1, size)}
xlate[0] = 0
ret = CheckTables([routing_table], size, clique, G, mincut - 1, len(clique) - 2, xlate)
tested = tested + 1
if ret >= mincut - 1:
passed = passed + 1
print str.format("{0} {1}", ret, [xlate[a] for a in xrange(0, size)])
else:
nx.set_edge_attributes(G, 'capacity', {k : 1.0 for k in G.edges_iter()})
umoded_graph = nx.Graph.copy(G)
try:
source = nx.periphery(G)[0]
except:
continue
diameter = nx.diameter(G)
distances = nx.single_source_dijkstra(G, source)
target = max(distances[1], key=lambda k:distances[0][k])
nbrs = G.neighbors(source)
G.graph['source'] = source
G.graph['dest'] = target
G.node[source]['source'] = True
G.node[target]['target'] = True
paths = []
mincut = min(map(lambda x: nx.min_cut(G, x[0], x[1]), combinations(xrange(0, nodes), 2)))
for ordering in permutations(nbrs):
G = nx.Graph.copy(umoded_graph)
del paths[:]
for order in ordering:
if not nx.has_path(G, order, target):
break
else:
path = nx.dijkstra_path(G, order, target)
paths.append(path)
edges = [(path[i], path[i + 1]) for i in xrange(0, len(path) - 1)]
G.remove_edges_from(edges)
if len(paths) >= mincut:
break
if len(paths) < mincut:
print str.format("Min-cut = {0}", mincut)
import networkx as nx
import sys
def graph_from_dimacs(filename):
f = open(filename)
g = nx.Graph()
for line in f:
if line[0] == 'a':
parsed = line.split()
a = int(parsed[1])
b = int(parsed[2])
c = int(parsed[3])
g.add_edge(a,b,capacity=c)
f.close()
return g
for arg in sys.argv:
if arg[-4:] == ".txt":
g = graph_from_dimacs(arg)
print nx.min_cut(g, 1, len(g.nodes()))
n_trials = int(sys.argv[1])
n = int(sys.argv[2])
m = int(sys.argv[3])
max_cap = float(sys.argv[4])
min_cap = float(sys.argv[5])
epsilon = float(sys.argv[6])
g = networkx.Graph()
all_edges = [(i, j) for i in range(n) for j in range(i+1,n)]
random.shuffle(all_edges)
g.add_edges_from(all_edges[:m])
for e in g.edges():
cap = random.random() * (max_cap - min_cap) + min_cap
graph_util.set_edge_capacity(g, e, cap)
min_cut_actual = networkx.min_cut(g, 0, 1, capacity='capacity')
total_elapsed = 0
for i in range(n_trials):
print 'trial: %d' % i
t_start = time.clock()
if max_cap == min_cap:
sparse_g = sparsification.sparsify(g, epsilon)
else:
sparse_g = sparsification.weighted_sparsify(g, epsilon)
elapsed_time = time.clock() - t_start
total_elapsed += elapsed_time
min_cut_sparsed = networkx.min_cut(sparse_g, 0, 1, capacity='capacity')
error = abs(min_cut_sparsed - min_cut_actual) / abs(min_cut_actual)
print '|E sparse| / |E|: %f' % (sparse_g.number_of_edges() / g.number_of_edges())
print 'relative error: %f' % error
import networkx as nx
import sys
def graph_from_dimacs(filename):
f = open(filename)
g = nx.Graph()
for line in f:
if line[0] == 'a':
parsed = line.split()
a = int(parsed[1])
b = int(parsed[2])
c = int(parsed[3])
g.add_edge(a, b, capacity=c)
f.close()
return g
for arg in sys.argv:
if arg[-4:] == ".txt":
g = graph_from_dimacs(arg)
print nx.min_cut(g, 1, len(g.nodes()))
if cnt == 0:
cnt = 1
else:
DG.add_edge(int(j), int(k), capacity=1.0)
del edges_[:]
#print DG.edges()
#print DG.neighbors(1)
#let's delete all nodes with indegree 1 and outdegree 0 or indegree 0 and outdegree 1
# for n_ in DG.nodes():
# if (DG.in_degree(n_) == 1 and DG.out_degree(n_) == 0) or (DG.in_degree(n_) == 0 and DG.out_degree(n_) == 1):
# DG.remove_node(n_)
success = False
for n_1 in DG.nodes():
for n_2 in DG.nodes():
if n_1 != n_2:
min_c = nx.min_cut(DG, n_1, n_2)
if min_c >= 2:
success = True
break
if success == True:
break
#if i == 5:
#nx.draw_spring(DG,node_color=[float(DG.degree(v)) for v in DG],node_size=10,with_labels=True,cmap=plt.cm.Reds,)
#plt.show()
#success = False
# try:
# top_sort = nx.topological_sort(DG)
# #if i == 5:
# # print top_sort
# for z in top_sort:
# if DG.out_degree(z) == 2:
def st_mincut(self, G, s, t):
"s-t最小カットを求める"
if isinstance(G, networkx.MultiGraph):
G = self._simplify_multigraph(G)
return networkx.min_cut(G, s, t, capacity="weight")
