def test(adj_mat, elapsed_time, i):
G = ntx.Graph(adj_mat)
ntx.draw_networkx(G, pos=ntx.kamada_kawai_layout(G), node_size=50, with_labels=True, font_size=4, width=0.5)
plt.savefig("graph"+i+".png", dpi=1000, quality=95)
plt.show()
t0 = time.perf_counter()
ntx.floyd_warshall(G)
elapsed_time[0].append(time.perf_counter() - t0)
t0 = time.perf_counter()
ntx.johnson(G)
elapsed_time[1].append(time.perf_counter() - t0)
print("finished_test")
return elapsed_time
def test_negative_weights(self):
G = nx.DiGraph()
G.add_weighted_edges_from([('0', '3', 3), ('0', '1', -5),
('0', '2', 2), ('1', '2', 4),
('2', '3', 1)])
paths = nx.johnson(G)
assert_equal(
paths, {
'1': {
'1': ['1'],
'3': ['1', '2', '3'],
'2': ['1', '2']
},
'0': {
'1': ['0', '1'],
'0': ['0'],
'3': ['0', '1', '2', '3'],
'2': ['0', '1', '2']
},
'3': {
'3': ['3']
},
'2': {
'3': ['2', '3'],
'2': ['2']
}
})
paths = nx.johnson(G, new_weight='new_weight')
assert_equal(
paths, {
'1': {
'1': ['1'],
'3': ['1', '2', '3'],
'2': ['1', '2']
},
'0': {
'1': ['0', '1'],
'0': ['0'],
'3': ['0', '1', '2', '3'],
'2': ['0', '1', '2']
},
'3': {
'3': ['3']
},
'2': {
'3': ['2', '3'],
'2': ['2']
}
})
for u, v, w in G.edges(data=True):
assert_true('new_weight' in w)
def test_negative_weights(self):
G = nx.DiGraph()
G.add_weighted_edges_from([("0", "3", 3), ("0", "1", -5),
("0", "2", 2), ("1", "2", 4),
("2", "3", 1)])
paths = nx.johnson(G)
assert paths == {
"1": {
"1": ["1"],
"3": ["1", "2", "3"],
"2": ["1", "2"]
},
"0": {
"1": ["0", "1"],
"0": ["0"],
"3": ["0", "1", "2", "3"],
"2": ["0", "1", "2"],
},
"3": {
"3": ["3"]
},
"2": {
"3": ["2", "3"],
"2": ["2"]
},
}
def shortest_paths(networkx_network):
"""
finds the all pairs shortest paths using Johnson Algo
sets a dictionary, keyed by source and target, of all pairs shortest paths with path_delays in the network as an
attr.
key: (src, dest) , value: ([nodes_on_the_shortest_path], path_delay)
path delays are the sum of individual edge_delays of the edges in the shortest path from source to destination
"""
# in-built implementation of Johnson Algo, just returns a list of shortest paths
# returns a dict with : key: source, value: dict with key: dest and value: shortest path as list of nodes
all_pair_shortest_paths = dict(
nx.johnson(networkx_network, weight='weight'))
# contains shortest paths with path_delays
# key: (src, dest) , value: ([nodes_on_the_shortest_path], path_delay)
shortest_paths_with_delays = {}
for source, v in all_pair_shortest_paths.items():
for destination, shortest_path_list in v.items():
path_delay = 0
# only if the source and destination are different, path_delays need to be calculated, otherwise 0
if source != destination:
# shortest_path_list only contains ordered nodes [node1,node2,node3....] in the shortest path
# here we take ordered pair of nodes (src, dest) to cal. the path_delay of the edge between them
for i in range(len(shortest_path_list) - 1):
path_delay += networkx_network[shortest_path_list[i]][
shortest_path_list[i + 1]]['delay']
shortest_paths_with_delays[(source,
destination)] = (shortest_path_list,
path_delay)
networkx_network.graph['shortest_paths'] = shortest_paths_with_delays
def test_negative_weights(self):
G = nx.DiGraph()
G.add_weighted_edges_from([('0', '3', 3), ('0', '1', -5),
('0', '2', 2), ('1', '2', 4),
('2', '3', 1)])
paths = nx.johnson(G)
assert_equal(
paths, {
'1': {
'1': ['1'],
'3': ['1', '2', '3'],
'2': ['1', '2']
},
'0': {
'1': ['0', '1'],
'0': ['0'],
'3': ['0', '1', '2', '3'],
'2': ['0', '1', '2']
},
'3': {
'3': ['3']
},
'2': {
'3': ['2', '3'],
'2': ['2']
}
})
def constraint_correct(G, C, P, w0):
path = nx.johnson(
G, weight='weight') # or nx.all_pairs_dijkstra_path_length(G)
C_max_dist = 0
for i in range(1, len(P) + 1):
if (i in C): continue
else:
min_dist = 1000 * 1000
min_idx = 0
for j in C:
cur_dist = 0
for k in range(len(path[i][j]) - 1):
cur_dist += G[path[i][j][k]][path[i][j][k + 1]]['weight']
if (cur_dist < min_dist):
min_dist = cur_dist
min_idx = j
if (C_max_dist < min_dist):
C_max_dist = min_dist
C_max_v = (i, min_idx)
max_path = path[C_max_v[0]][C_max_v[1]]
max_edges = []
for i in range(len(max_path) - 1):
max_edges.append([max_path[i], max_path[i + 1]])
if C_max_dist > w0:
return False, max_edges
else:
return True, max_edges
def get_makespan(self):
import networkx as nx
G = nx.DiGraph()
edg = tuple(set(unfold(self.A)) | set(unfold(self.E)))
edg_weighted = [(x[0], x[1], -self.getD(x[0])) for x in edg]
G.add_weighted_edges_from(edg_weighted)
s = nx.johnson(G, weight='weight')[-1][self.N - 2]
return sum([self.getD(x) for x in s])
def test_negative_weights(self):
G = nx.DiGraph()
G.add_weighted_edges_from([('0', '3', 3), ('0', '1', -5),
('0', '2', 2), ('1', '2', 4),
('2', '3', 1)])
paths = nx.johnson(G)
assert_equal(paths, {'1': {'1': ['1'], '3': ['1', '2', '3'],
'2': ['1', '2']}, '0': {'1': ['0', '1'],
'0': ['0'], '3': ['0', '1', '2', '3'],
'2': ['0', '1', '2']}, '3': {'3': ['3']},
'2': {'3': ['2', '3'], '2': ['2']}})
paths = nx.johnson(G, new_weight='new_weight')
assert_equal(paths, {'1': {'1': ['1'], '3': ['1', '2', '3'],
'2': ['1', '2']}, '0': {'1': ['0', '1'],
'0': ['0'], '3': ['0', '1', '2', '3'],
'2': ['0', '1', '2']}, '3': {'3': ['3']},
'2': {'3': ['2', '3'], '2': ['2']}})
for u, v, w in G.edges(data=True):
assert_true('new_weight' in w)
def test_negative_weights(self):
G = nx.DiGraph()
G.add_weighted_edges_from([('0', '3', 3), ('0', '1', -5),
('0', '2', 2), ('1', '2', 4),
('2', '3', 1)])
paths = nx.johnson(G)
assert_equal(paths, {'1': {'1': ['1'], '3': ['1', '2', '3'],
'2': ['1', '2']}, '0': {'1': ['0', '1'],
'0': ['0'], '3': ['0', '1', '2', '3'],
'2': ['0', '1', '2']}, '3': {'3': ['3']},
'2': {'3': ['2', '3'], '2': ['2']}})
def test_graphs(self):
validate_path(self.XG, 's', 'v', 9, nx.johnson(self.XG)['s']['v'])
validate_path(self.MXG, 's', 'v', 9, nx.johnson(self.MXG)['s']['v'])
validate_path(self.XG2, 1, 3, 4, nx.johnson(self.XG2)[1][3])
validate_path(self.XG3, 0, 3, 15, nx.johnson(self.XG3)[0][3])
validate_path(self.XG4, 0, 2, 4, nx.johnson(self.XG4)[0][2])
validate_path(self.MXG4, 0, 2, 4, nx.johnson(self.MXG4)[0][2])
def test_graphs(self):
validate_path(self.XG, 's', 'v', 9, nx.johnson(self.XG)['s']['v'])
validate_path(self.MXG, 's', 'v', 9, nx.johnson(self.MXG)['s']['v'])
validate_path(self.XG2, 1, 3, 4, nx.johnson(self.XG2)[1][3])
validate_path(self.XG3, 0, 3, 15, nx.johnson(self.XG3)[0][3])
validate_path(self.XG4, 0, 2, 4, nx.johnson(self.XG4)[0][2])
validate_path(self.MXG4, 0, 2, 4, nx.johnson(self.MXG4)[0][2])
def test_graphs(self):
validate_path(self.XG, "s", "v", 9, nx.johnson(self.XG)["s"]["v"])
validate_path(self.MXG, "s", "v", 9, nx.johnson(self.MXG)["s"]["v"])
validate_path(self.XG2, 1, 3, 4, nx.johnson(self.XG2)[1][3])
validate_path(self.XG3, 0, 3, 15, nx.johnson(self.XG3)[0][3])
validate_path(self.XG4, 0, 2, 4, nx.johnson(self.XG4)[0][2])
validate_path(self.MXG4, 0, 2, 4, nx.johnson(self.MXG4)[0][2])
def test_unweighted_graph(self):
with pytest.raises(nx.NetworkXError):
G = nx.path_graph(5)
nx.johnson(G)
def test_single_node_graph(self):
with pytest.raises(nx.NetworkXError):
G = nx.DiGraph()
G.add_node(0)
nx.johnson(G)
def fast_price_function(g, e, proportional, algorithm='johnson'):
"""
Fast function to find the optimal price for a given edge e.
1. Calculate the shortest path from all-to-all vertices without going through $C$ with either Floyd-Warshall or
Johnson. Default is Johnson
2. Calculate shortest path from $C$ source to all explicitly going through $C$ with Dijkstra.
3. Compare difference between all-to-all cost with all-to-$V$-to-all, producing a cumulative summation over the
difference.
4. Maximizing fee * cumulative difference.
Plots the given fee * cumulative difference over fee curve.
"""
e_data = g.get_edge_data(e[0][0], e[0][1])
# Remove edge e
g.remove_edge(e[0][0], e[0][1])
# Floyd or Johnson
if algorithm == 'johnson':
all_pair_shortest_path = nx.floyd_warshall(g, weight="price")
else:
all_pair_shortest_path = nx.johnson(g, weight="price")
# remove all edges from e source, Add edge e
edges = list(g.out_edges(e[0][0])) # get all edges of source
edges_data = []
for rm in edges:
edges_data.append(g.get_edge_data(rm[0], rm[1]))
g.remove_edge(rm[0], rm[1])
temp_price = e_data["price"]
e_data["price"] = proportional
g.add_edge(e[0][0], e[0][1], **e_data)
# Compute single source dijkstras from e source over e.
edge_to_all = nx.single_source_dijkstra_path_length(g,
e[0][0],
weight="price")
path_price_difference = []
for source in all_pair_shortest_path:
for destination in all_pair_shortest_path[source]:
# SOURCE TO V TO DESTINATION
if source != destination != e[0][0]:
#print("-----")
#print(source)
#print(destination)
#print(all_pair_shortest_path[source][destination])
diff = (all_pair_shortest_path[source][e[0][0]] +
edge_to_all[destination]
) - all_pair_shortest_path[source][destination]
if diff < 0: # TODO: WHAT TO DO WITH TIES?
path_price_difference.append(-diff)
fee_range = range(10, 1350, 10)
plot_list = []
e_data["price"] = temp_price
for i, add in enumerate(edges):
g.add_edge(add[0], add[1], **edges_data[i])
for r in fee_range:
plot_list.append(
len([p for p in path_price_difference if p >= r]) * r *
proportional / 1000)
#plot.plot_fee_curve(fee_range, plot_list)
return plot_list
def test_unweighted_graph(self):
G = nx.path_graph(5)
nx.johnson(G)
def johnson(G, source, destination):
return " -> ".join(nx.johnson(G)[source][destination])
def test_unweighted_graph(self):
G = nx.path_graph(5)
nx.johnson(G)
def optimize(self):
start_time = time.time()
try:
for s_idx, s_session in enumerate(self.sessions):
session_start_time = time.time()
tree = self._solution.get_tree(s_session)
print "curr", s_idx
####################################################################################
#
# Algorithm 1 The construction of multilevel overlay directed network
#
####################################################################################
copy_graph = self.graph.copy()
# Remove edge with insufficient residual capacity
for link_id in set(self.app.links.items()) & set(
copy_graph.edges()):
if self.links[link_id].cap - (
self.links[link_id].used_cap +
self.sessions[s_idx].bw) < 0:
copy_graph.remove_edge(link_id[0], link_id[1])
# Calculate all shortest paths between each pair nodes in G
apsp_length = dict(
nx.all_pairs_dijkstra_path_length(copy_graph,
weight='BandwidthCost'))
apsp_path = nx.johnson(copy_graph, weight='BandwidthCost')
# check if dst is reachable
# Remove session which cannot reach to every destination
try:
if set(self.sessions[s_idx].dsts) - set(
apsp_path[self.sessions[s_idx].src]):
raise ResourceOverloaded
except ResourceOverloaded:
print "ResourceOverloaded!!!!!!!!!!!!!!"
continue
# Replicate all |V|=n nodes k times and place n*k nodes in a n x k grid, Each node can be denoted by v_n_k
# Connect all nodes in i-th column to all nodes in i+1-th column with directed arrows
# Set the edge cost between two nodes as the corresponding shortest path cost in G
multilevel_graph = nx.DiGraph()
for i, service in enumerate(self.service_chains[s_idx][:-1]):
for head in self.service_nodes[service]:
for tail in self.service_nodes[
self.service_chains[s_idx][i + 1]]:
cost = apsp_length[head][tail]
multilevel_graph.add_edge(
str(service) + "_" + str(head),
str(self.service_chains[s_idx][i + 1]) + "_" +
str(tail),
weight=cost)
####################################################################################
#
# Algorithm 2 The Modified Shortest-Path Algorithm (MSA)
#
####################################################################################
if len(self.service_chains[s_idx]) == 0:
st = steiner_tree(copy_graph, [self.sessions[s_idx].src] +
list(self.sessions[s_idx].dsts),
weight='BandwidthCost')
# Convert steiner_tree into directed graph
s_tree = nx.DiGraph()
for dst in self.sessions[s_idx].dsts:
s_tree.add_edge(dst, "sink", weight=0)
for h, t in st:
s_tree.add_edge(
t,
h,
weight=copy_graph[t][h]['BandwidthCost'] *
self.sessions[s_idx].bw)
st_edges = set()
for path in nx.all_simple_paths(
s_tree.to_undirected(),
source=self.sessions[s_idx].src,
target="sink"):
for idx in range(len(path) - 2):
st_edges.add((path[idx], path[idx + 1]))
self._solution.add_path(self.sessions[s_idx],
path[:-1], None)
memo = defaultdict(float)
# Update link usage
try:
for h, t in st_edges:
self.links[(h, t)].used_cap += self.sessions[
s_idx].bw * self.links[(h, t)].bw_cost
memo[(h,
t)] += self.sessions[s_idx].bw * self.links[
(h, t)].bw_cost
self.total_routing_cost += self.sessions[
s_idx].bw * self.links[(h, t)].bw_cost
if self.links[(h, t)].used_cap > self.links[(
h, t)].cap:
raise ResourceOverloaded
except ResourceOverloaded:
print "ResourceOverloaded!!!!!!!!!!!!!!"
for link_id, v in memo.items():
self.links[link_id].used_cap -= v
continue
curr_time = time.time() - session_start_time
self.update_session_cost(solution=self._solution,
session=self.sessions[s_idx],
links=st_edges,
time=curr_time)
self.solution_tree[s_idx] = s_tree
self.session_completed += 1
continue
# Divide each nodes in G' into two parts, and connect theses two parts with cost y_l_k_u
for service in self.service_chains[s_idx]:
for node in self.service_nodes[service]:
fst_half, snd_half = str(service) + "_" + str(
node), '_' + str(service) + "_" + str(node)
for h, t in list(multilevel_graph.out_edges(fst_half)):
multilevel_graph.add_edge(
snd_half,
t,
weight=multilevel_graph[h][t]['weight'])
multilevel_graph.remove_edge(h, t)
multilevel_graph.add_edge(
fst_half,
snd_half,
weight=self.sessions[s_idx].res[service]['cpu'])
# Add the source node S into G'
# Connect S to all nodes of the first column in G' and set the cost as corresponding shortest path
first_service = self.service_chains[s_idx][0]
for tail in self.service_nodes[first_service]:
multilevel_graph.add_edge(
self.sessions[s_idx].src,
str(first_service) + "_" + str(tail),
weight=apsp_length[self.sessions[s_idx].src][tail])
feasible_solution = (float('inf'), [], [])
last_service = self.service_chains[s_idx][-1]
for v in self.service_nodes[last_service]:
if self.nodes[v].services[last_service].resources_cap['cpu'] - \
(self.nodes[v].services[last_service].used_cap['cpu'] +
self.sessions[s_idx].res[last_service]['cpu']) < 0:
continue
# Find the shortest path y from S to v in G' and get [w_l_n_u]
last_node_v = "_" + str(last_service) + "_" + str(v)
# Build a Steiner tree to cover v and all destinations
st = steiner_tree(copy_graph,
[v] + list(self.sessions[s_idx].dsts),
weight='BandwidthCost')
# Convert steiner_tree into directed graph
s_tree = nx.DiGraph()
s_tree_path = set()
for dst in self.sessions[s_idx].dsts:
s_tree.add_edge(dst, "sink", weight=0)
for h, t in st:
s_tree.add_edge(
h,
t,
weight=copy_graph[h][t]['BandwidthCost'] *
self.sessions[s_idx].bw)
s_tree.add_edge(
t,
h,
weight=copy_graph[t][h]['BandwidthCost'] *
self.sessions[s_idx].bw)
for path in nx.all_simple_paths(s_tree,
source=v,
target="sink"):
for i, n in enumerate(path[:-2]):
s_tree_path.add((n, path[i + 1]))
# steiner_tree cost
accum_cost = 0
for h, t in s_tree_path:
accum_cost += copy_graph[h][t][
'BandwidthCost'] * self.sessions[s_idx].bw
shortest_path = nx.dijkstra_path(multilevel_graph,
self.sessions[s_idx].src,
last_node_v,
weight='weight')[1:]
candidate_solution = [self.sessions[s_idx].src]
for i, service in enumerate(
self.service_chains[s_idx][:-1]):
# Check where l_j is deployed in an overloaded node, if so,
# find a new node with the minimum sum of setup cost and connection cost to deploy l_j
node = int(shortest_path[i * 2][len(str(service)) +
1:])
if self.nodes[node].services[service].resources_cap['cpu'] - \
(self.nodes[node].services[service].used_cap['cpu'] +
self.sessions[s_idx].res[service]['cpu']) < 0:
other_nodes_cost = []
for other_node in set(
self.service_nodes[service]) - {node}:
if self.nodes[other_node].services[service].resources_cap['cpu'] - \
(self.nodes[other_node].services[service].used_cap['cpu'] +
self.sessions[s_idx].res[service]['cpu']) < 0:
continue
prev_service = "_" + self.service_chains[s_idx][i - 1] + "_" + str(candidate_solution[-1]) \
if i != 0 else candidate_solution[-1]
next_service = self.service_chains[s_idx][
i + 1] + "_" + shortest_path[
(i + 1) * 2][len(str(service)) + 1:]
vk = multilevel_graph[prev_service][
str(service) + "_" +
str(other_node)]['weight']
vm = multilevel_graph[
"_" + str(service) + "_" +
str(other_node)][next_service]['weight']
other_nodes_cost.append(
(self.sessions[s_idx].res[service]['cpu'] +
vk + vm, other_node))
if not other_nodes_cost:
# print ">>>>>Cannot find solution!solution!!!!"
break
_, best_candidate = max(other_nodes_cost)
candidate_solution.append(best_candidate)
else:
candidate_solution.append(node)
candidate_solution.append(v) # add last node
# Cannot find solution with v!!!!!
if len(candidate_solution) < 1 + len(
self.service_chains[s_idx]):
continue
# source to last VNF cost
for i, node in enumerate(candidate_solution[:-1]):
accum_cost += apsp_length[node][candidate_solution[i +
1]]
if accum_cost < feasible_solution[0]:
feasible_solution = (accum_cost, candidate_solution,
s_tree_path)
# Cannot find solution!!!!!
try:
if len(feasible_solution[1]) < 1 + len(
self.service_chains[s_idx]):
raise ResourceOverloaded
except ResourceOverloaded:
print "ResourceOverloaded!!!!!!!!!!!!!!"
continue
traversed_edges = defaultdict(int)
# Build tree from feasible solution
feasible_solution_tree = nx.DiGraph()
for node_id, node in enumerate(feasible_solution[1][:-1]):
path = nx.shortest_path(
copy_graph,
source=node,
target=feasible_solution[1][node_id + 1],
weight='BandwidthCost')
for i, h in enumerate(path[:-1]):
traversed_edges[(h, path[i + 1])] += 1
feasible_solution_tree.add_edge(
h,
path[i + 1],
weight=copy_graph[h][path[i + 1]]['BandwidthCost']
* self.sessions[s_idx].bw)
for h, t in feasible_solution[2]:
traversed_edges[(h, t)] += 1
feasible_solution_tree.add_edge(
h,
t,
weight=copy_graph[h][t]['BandwidthCost'] *
self.sessions[s_idx].bw)
####################################################################################
#
# Algorithm 3 The Optimize Phase Algorithm (OPA)
#
####################################################################################
_, candidate_solution, s_tree_path = feasible_solution
# print "self.sessions[s_idx]", self.sessions[s_idx]
curr_service_node = []
for s_id, service_node in enumerate(candidate_solution[1:]):
curr_service_node.append(
(self.service_chains[s_idx][s_id], service_node))
# Find all connection nodes in X_0
connection_nodes = set(self.sessions[s_idx].dsts)
for dst in self.sessions[s_idx].dsts:
connection_nodes -= set(
nx.descendants(feasible_solution_tree, dst))
for j, service in reversed(
list(enumerate(self.service_chains[s_idx]))):
for connection_node in list(connection_nodes):
connection_nodes.remove(connection_node)
for other_node in set(self.service_nodes[service]) - {
connection_node
}:
# if l_j can be deployed in other nodes according to the rule in Section IV-C then
if self.nodes[other_node].services[service].resources_cap['cpu'] - \
(self.nodes[other_node].services[service].used_cap['cpu'] +
self.sessions[s_idx].res[service]['cpu']) < 0:
continue
old_cost = apsp_length[candidate_solution[
j + 1]][connection_node]
new_cost = apsp_length[candidate_solution[j]][other_node] + \
apsp_length[other_node][connection_node] + 0
if new_cost < old_cost:
curr_service_node.append((service, other_node))
# Old link from VNF to connection node
old_path = apsp_path[candidate_solution[
j + 1]][connection_node]
for i, t in reversed(
list(enumerate(old_path[1:]))):
if feasible_solution_tree.has_edge(
old_path[i], t
) and feasible_solution_tree.edges(
old_path[i]
) <= 1 and feasible_solution_tree.edges(
t) <= 1:
feasible_solution_tree.remove_edge(
old_path[i], t)
traversed_edges[(old_path[i], t)] -= 1
if feasible_solution_tree.has_node(
old_path[i]) and len(
feasible_solution_tree.edges(
old_path[i])) > 1:
break
# New link from new VNF to connection node
new_path = apsp_path[other_node][
connection_node]
for i, h in enumerate(new_path[:-1]):
try:
feasible_solution_tree.add_edge(
h,
new_path[i + 1],
weight=copy_graph[h][new_path[
i + 1]]['BandwidthCost'] *
self.sessions[s_idx].bw)
except:
print "i, h", i, h
for hh, tt in copy_graph.edges():
print hh, tt
traversed_edges[(h, new_path[i + 1])] += 1
# New link from previous VNF to new VNF
new_path = apsp_path[
candidate_solution[j]][other_node]
for i, h in enumerate(new_path[:-1]):
feasible_solution_tree.add_edge(
h,
new_path[i + 1],
weight=copy_graph[h][new_path[
i + 1]]['BandwidthCost'] *
self.sessions[s_idx].bw)
traversed_edges[(h, new_path[i + 1])] += 1
connection_nodes.add(other_node)
break
# Add link from source to connection nodes
for connection_node in connection_nodes:
new_path = apsp_path[
self.sessions[s_idx].src][connection_node]
for i, h in enumerate(new_path[:-1]):
feasible_solution_tree.add_edge(
h,
new_path[i + 1],
weight=copy_graph[h][new_path[i +
1]]['BandwidthCost']
* self.sessions[s_idx].bw)
traversed_edges[(h, new_path[i + 1])] += 1
print "self.sessions[s_idx]", self.sessions[s_idx].addr
memo = defaultdict(float)
try:
# Update service used_cap
for service, node in curr_service_node:
print "service, node", service, node
self.nodes[node].services[service].used_cap[
'cpu'] += self.sessions[s_idx].res[service]['cpu']
memo[service] += self.sessions[s_idx].res[service][
'cpu']
if self.nodes[node].services[service].used_cap[
'cpu'] > self.nodes[node].services[
service].resources_cap['cpu']:
raise ResourceOverloaded
except ResourceOverloaded:
print "ResourceOverloaded!!!!!!!!!!!!!!"
for service, v in memo.items():
node = curr_service_node[service]
self.nodes[node].services[service].used_cap['cpu'] -= v
continue
memo = defaultdict(float)
# Update link usage
try:
print traversed_edges.items()
curr_cost = 0
sess_links = []
for l, count_link in traversed_edges.items():
for _ in range(count_link):
h, t = l
print h, t
sess_links.append((h, t))
self.links[(h, t)].used_cap += self.sessions[
s_idx].bw * self.links[(h, t)].bw_cost
memo[(h,
t)] += self.sessions[s_idx].bw * self.links[
(h, t)].bw_cost
if self.links[(h, t)].used_cap > self.links[(
h, t)].cap:
raise ResourceOverloaded
curr_cost += self.sessions[s_idx].bw * self.links[
(h, t)].bw_cost
self.total_routing_cost += self.sessions[
s_idx].bw * self.links[(h, t)].bw_cost
print self.sessions[s_idx].addr, "curr_cost", curr_cost
except ResourceOverloaded:
print "ResourceOverloaded!!!!!!!!!!!!!!"
for link_id, v in memo.items():
self.links[link_id].used_cap -= v
continue
# # Update the flow tcam
# for node, num_traverse in traversed_edges.items():
# h, t = node
# self.nodes[h].services['sdn_router'].used_cap['tcam'] = self.sessions[s_idx].res[service]['tcam'] * num_traverse
# self.nodes[t].services['sdn_router'].used_cap['tcam'] = self.sessions[s_idx].res[service]['tcam'] * num_traverse
# num_undirected_traversed_edges = defaultdict(int)
# for h, t in traversed_edges.keys():
# # h, t = key
# if (h, t) in num_undirected_traversed_edges or (t, h) in num_undirected_traversed_edges:
# continue
# num_undirected_traversed_edges[(h, t)] = traversed_edges[(h, t)] + traversed_edges[(t, h)]
curr_time = time.time() - session_start_time
self.update_session_cost(solution=self._solution,
session=self.sessions[s_idx],
links=sess_links,
time=curr_time)
self.session_completed += 1
except Exception as e:
raise e
finally:
print 'All DONE:', str(self.session_completed / len(self.sessions))
total_time = time.time() - start_time
print "Optimization time = ", str(total_time), " sec"
self._solution.total_time = total_time
return self._solution
def compute_all_pair_shortest_path(graphs_single_robot, trees_single_robot):
all_pairs_shortest_paths_per_robot = []
all_pairs_shortest_paths_per_robot_b = [
dict() for i in range(len(graphs_single_robot))
]
subgraph_nodes = [0] * len(graphs_single_robot)
for i in range(len(graphs_single_robot)):
all_pairs_shortest_paths_per_robot.append( \
nx.johnson(graphs_single_robot[i], weight='weight'))
subgraph_nodes[i] = random.sample(
graphs_single_robot[i].nodes,
math.ceil(len(graphs_single_robot[i].nodes) / 10))
if len(
subgraph_nodes[i]
) == 1: # single_source_bellman_ford gets stuck on single node graph, so this is an edge case
all_pairs_shortest_paths_per_robot_b[i][subgraph_nodes[i]
[0]] = dict()
all_pairs_shortest_paths_per_robot_b[i][subgraph_nodes[i][0]][
subgraph_nodes[i][0]] = [subgraph_nodes[i][0]]
else:
for j in range(len(subgraph_nodes[i])):
all_pairs_shortest_paths_per_robot_b[i][
subgraph_nodes[i][j]] = nx.single_source_bellman_ford(
graphs_single_robot[i],
subgraph_nodes[i][j],
target=None,
weight='weight')[1]
while len(all_pairs_shortest_paths_per_robot_b[i]) < len(
graphs_single_robot[i].nodes):
for node in list(all_pairs_shortest_paths_per_robot_b[i].keys()):
N = drrt_ao.adj(graphs_single_robot[i], node)
for neighbor in N:
if neighbor in all_pairs_shortest_paths_per_robot_b[i]:
continue
else:
all_pairs_shortest_paths_per_robot_b[i][
neighbor] = dict()
for key in all_pairs_shortest_paths_per_robot_b[i][
node].keys():
all_pairs_shortest_paths_per_robot_b[
i][neighbor][key] = list(
all_pairs_shortest_paths_per_robot_b[i]
[node][key]
) # attaching copy of the list of the neighbor
all_pairs_shortest_paths_per_robot_b[i][neighbor][
key].insert(0, neighbor)
if key == neighbor:
all_pairs_shortest_paths_per_robot_b[i][neighbor][
key] = all_pairs_shortest_paths_per_robot_b[
i][neighbor][key][:1]
for i in range(
len(graphs_single_robot)
): # A check to see the johnson and bellman ford dictionaries are equal
for key in all_pairs_shortest_paths_per_robot[i].keys():
if key not in all_pairs_shortest_paths_per_robot_b[i]:
print("check out")
else:
for inkey in all_pairs_shortest_paths_per_robot[i][key].keys():
if inkey not in all_pairs_shortest_paths_per_robot_b[i][
key]:
print("check in")
return all_pairs_shortest_paths_per_robot_b
G.add_edge(t[0] + 1, t[1] + 1, weight=euclidean(t[0], t[1]))
G.add_edge(t[1] + 1, t[2] + 1, weight=euclidean(t[1], t[2]))
G.add_edge(t[0] + 1, t[2] + 1, weight=euclidean(t[0], t[2]))
# Cycle check
for i in range(len(C) - 1):
e = [C[i], C[i + 1]]
if (e in G.edges()): # cycle edge on DG
CE_IN.append(e)
else:
CE_OUT.append(e)
C_length += euclidean(C[i] - 1, C[i + 1] - 1)
if (len(CE_OUT) > 0): C_valid = 0
# Calculate ditance between vertices and cycle
path = nx.johnson(G,
weight='weight') # or nx.all_pairs_dijkstra_path_length(G)
print("1. All Shortest Path (v-->cycle)")
print("vertex -- cycle_vertex ==> distance [path]")
for i in range(1, len(P) + 1):
if (i in C): continue
else:
min_dist = 1000 * 1000
min_idx = 0
for j in C:
cur_dist = 0
for k in range(len(path[i][j]) - 1):
cur_dist += G[path[i][j][k]][path[i][j][k + 1]]['weight']
if cur_dist < min_dist:
min_dist = cur_dist
min_idx = j
print(" ", i, "--", min_idx, "==>", round(min_dist, 3),
def all_pairs_paths(G):
print "Computing all pairs paths..."
paths = nx.johnson(G, weight="weight")
return paths
def johnson_explored(G, source, destination):
return " -> ".join(nx.johnson(G)[source])
def test_single_node_graph(self):
G = nx.DiGraph()
G.add_node(0)
nx.johnson(G)
def test_single_node_graph(self):
G = nx.DiGraph()
G.add_node(0)
nx.johnson(G)
if eg[0] in cost_dict:
if eg[1] in cost_dict[eg[0]]:
eg[2]['negative_weight'] = -1 * eg[2]['weight']
idcs = np.random.choice(len(gp.nodes()), int(5 * 5 * 0.2), replace=False)
# print idcs
# スタート・ゴール・障害物を設定する
st, gl, obs = (0, 0), (30, 60), [list(gp.nodes())[i] for i in idcs[2:]]
# st, gl, obs = (0,0), (np.random.randint(g_dim[0]),np.random.randint(g_dim[1])), [list(gp.nodes())[i] for i in idcs[2:]]
obs = [list(gp.nodes())[i] for i in idcs[2:]]
path = nx.astar_path(gp, st, gl, cost)
length = nx.astar_path_length(gp, st, gl, cost)
path2 = nx.johnson(gp, weight='negative_weight')
print('johnson: {0}'.format(path2[st][gl]))
for p in path2[st][gl]:
if gp.node[p].get('color', '') == 'black':
print('Invalid path')
continue
gp.node[p]['color'] = 'orange'
previous_nd = st
longest_length = 0
for nd in path2[st][gl][:]:
if not (previous_nd == st and nd == st):
# longest_length += cost_dict[previous_nd][nd]
longest_length += gp[previous_nd][nd]['weight']
# print ('{0}-[{1}]→{2}'.format(previous_nd,cost_dict[previous_nd][nd],nd))
def optimize(self):
start_time = time.time()
############################
# Multi-Tree Routing Phase
############################
copy_graph = self.graph.copy()
# Sort the multicast tress according to their data rates in ascending order
self.sessions = sorted(self.app.get_sessions(),
key=lambda session: session.bw)
for s_idx, s_session in enumerate(self.sessions):
for link_id in set(self.app.links.items()) & set(
copy_graph.edges()):
if self.links[link_id].cap - (self.links[link_id].used_cap +
s_session.bw) < 0:
copy_graph.remove_edge(link_id[0], link_id[1])
# All to All node shortest distance
apsp = nx.johnson(copy_graph, weight='BandwidthCost')
# Remove session which cannot reach to every destination
if set(s_session.dsts) - set(apsp[s_session.src]):
continue
# Shortest path trees
session_tree = nx.DiGraph() # DAG - multicast tree
counted_link = set()
for dst in s_session.dsts:
for i, head_edge in enumerate(
apsp[s_session.src][dst][:-1]): # path
tail_edge = apsp[s_session.src][dst][i + 1]
session_tree.add_edge(head_edge,
tail_edge,
weight=self.graph[head_edge]
[tail_edge]['BandwidthCost'] *
s_session.bw)
# Add link usage
if (head_edge, tail_edge) not in counted_link:
self.links[(head_edge,
tail_edge)].used_cap += s_session.bw
counted_link.add((head_edge, tail_edge))
# # Add flow table
self.node_capacity[head_edge] |= {s_idx}
self.node_capacity[tail_edge] |= {s_idx}
# Find branching nodes
if len(session_tree.edges(head_edge)) > 1:
self.session_branch_nodes[s_idx].add(head_edge)
self.sessions_tree[s_idx] = session_tree
# Try to reroute all branch node
for s_idx, nodes in self.session_branch_nodes.items():
for node in list(nodes):
self.reroute(s_idx, node)
# self.reassess_tcam_cost()
# max_tcam = 0
# for node, sessions in self.node_capacity.items():
# if len(sessions)>max_tcam:
# max_tcam = len(sessions)
total_c = 0
for link_id, link in self.links.items():
total_c += link.used_cap
# print "max_tcam", max_tcam
print "self.sessions_tree", len(self.sessions_tree)
print "self.app.get_sessions()", len(self.app.get_sessions())
print 'All DONE:', len(self.app.get_sessions()) - len(
self.sessions_tree) == 0
# ############################
# # State-Node Assignment Phase
# ############################
#
# print "State-Node Assignment Phase"
#
# # Greedy Assigning Stage
# self.branch_state_node_sessions = defaultdict(set) # Reset sessions_branch_state_nodes
# self.session_branch_state_nodes = defaultdict(set)
# a = defaultdict(set)
# curr__a_cost = {s_idx: self.cost_t_a(s_idx, set()) for s_idx, _ in self.sessions_tree.items()}
# cost_t_a_cache = dict()
# for s_idx, _ in self.sessions_tree.items():
# cost_t_a_cache[s_idx] = defaultdict(float)
# # Find max x
# while True:
# max_x_cost, max_x_node, max_x_s_idx = -float('inf'), None, None
# for s_idx, _ in self.sessions_tree.items():
# for branch_node in self.session_branch_nodes[s_idx] - a[s_idx]:
# if len(self.branch_state_node_sessions[branch_node]) + 1 <= self.nodes[branch_node].services['sdn_router'].resources_cap['tcam']:
# if tuple({branch_node} | a[s_idx]) not in cost_t_a_cache[s_idx]:
# cost_t_a_cache[s_idx][tuple({branch_node} | a[s_idx])] = \
# self.cost_t_a(s_idx, {branch_node} | a[s_idx])
# reduced_cost = curr__a_cost[s_idx] - cost_t_a_cache[s_idx][tuple({branch_node} | a[s_idx])]
# if reduced_cost > max_x_cost:
# max_x_cost, max_x_node, max_x_s_idx = reduced_cost, branch_node, s_idx
#
# if max_x_cost == -float('inf'):
# break
# a[max_x_s_idx].add(max_x_node) # AU{x}
# curr__a_cost[max_x_s_idx] -= max_x_cost # z(A)
# self.branch_state_node_sessions[max_x_node].add(max_x_s_idx)
# self.session_branch_state_nodes[max_x_s_idx].add(max_x_node)
#
# self.reassess_cost()
#
# total_c = 0
# for link_id, link in self.links.items():
# total_c += link.used_cap
#
# print "total_c", total_c
#
#
# # Local Search Stage
#
# print "Local Search Stage"
#
# # Identify the overloaded nodes
# overloaded_branch_state_nodes = defaultdict(set)
# for s_idx, branch_nodes in self.session_branch_nodes.items():
# for branch_node in branch_nodes:
# overloaded_branch_state_nodes[branch_node].add(s_idx)
# if len(overloaded_branch_state_nodes[branch_node]) > \
# self.nodes[branch_node].services['sdn_router'].resources_cap['tcam']:
# self.overloaded_set.add(branch_node)
#
# # Choose set of session in branch state node that reduce z_cost
# for u in self.overloaded_set:
# cost_no_overloaded_node = [(self.cost_t_a(s_idx, a[s_idx] - {u}) - self.cost_t_a(s_idx, a[s_idx] | {u}),
# s_idx) for s_idx in overloaded_branch_state_nodes[u]]
# cost_no_overloaded_node.sort()
#
# # Remove overloaded node from branch state
# self.branch_state_node_sessions[u] = set()
# for s_idx in self.session_branch_state_nodes:
# if u in self.session_branch_state_nodes[s_idx]:
# self.session_branch_state_nodes[s_idx].remove(u)
#
# for _ in range(self.nodes[u].services['sdn_router'].resources_cap['tcam']):
# _, best_t = cost_no_overloaded_node.pop()
# self.branch_state_node_sessions[u].add(best_t)
# self.session_branch_state_nodes[best_t].add(u)
# self.reassess_cost()
#
# for _, s_idx in cost_no_overloaded_node:
# # Reroute the rest tree
# self.reroute(s_idx, u)
#
# # If the amount of multicast flows in any edge exceeds the capacity constraint,
# # we also reroute its closest upstream state node u in a tree Ti
# # to w, such that the new path from w to v follows the link
# # capacity constraint.
# overloaded_links = {link_id for link_id, link in self.links.items() if link.used_cap > link.cap}
# for s_idx, s_session in self.sessions_tree.items():
# for h, t in list(overloaded_links):
# if (h, t) in s_session.edges():
# # find downstream
# down_streams = [t]
# while len(down_streams) > 0:
# v = down_streams.pop(0)
# if v in set(self.session_branch_nodes[s_idx]) | set(self.sessions[s_idx].dsts):
# # find downstream
# if self.reroute_path(s_idx, h, v):
# overloaded_links.remove((h, t))
# break
# else:
# down_streams += list(s_session.neighbors(v))
#
# # Remove session until link constraint is meant
# while len(overloaded_links) > 0:
# overloaded_link = overloaded_links.pop()
# for s_idx in reversed(list(self.sessions_tree)):
# if overloaded_link in self.sessions_tree[s_idx].edges():
# del self.sessions_tree[s_idx]
# self.reassess_cost()
# if self.links[overloaded_link].used_cap <= self.links[overloaded_link].cap:
# break
# total_c = 0
# for link_id, link in self.links.items():
# total_c += link.used_cap
#
# print "total_c", total_c
# print "total mtrsa session", len(self.sessions_tree)
# print "total session", len(self.app.get_sessions())
# print "unicast tunneling", self.max_count_unicast_tunneling()
#
# for id, node in self.nodes.items():
# print "used cam", id, node.services['sdn_router'].used_cap['tcam']
# Convert networkx to Solution
for s_idx, s_session in self.sessions_tree.items():
self._solution.get_tree(self.sessions[s_idx])
self.update_session_cost(solution=self._solution,
session=self.sessions[s_idx],
links=self.sessions_tree[s_idx].edges())
total_time = time.time() - start_time
self._solution.total_time = total_time
return self._solution
def all_pairs_paths(G):
print "Computing all pairs paths..."
paths = nx.johnson(G, weight="weight")
return paths
def use_johnson(self,s,t):
path = nx.johnson(self.G, source=s, target=t)
return path