def _recursive_cutting(g, p, res=[]):
"""helper function (recursive version)"""
k = math.ceil(len(g.nodes()) / p)
g_l, g_r = kernighan_lin_bisection(g, weight="rate")
for partition in g_l, g_r:
if len(partition) > k:
_recursive_cutting(g.subgraph(partition), p / 2, res)
else:
res.append(partition)
return res
def partition(self,x_mat): num_samples=x_mat.shape[0] assert(x_mat.shape[1]==self.num_all_labels+1) # the last dim of x_mat gives the id of the label # the other dims give that row of the coocc matrix label_ids=x_mat[:,-1] assert(np.all(label_ids<self.num_all_labels)) adj_mat=x_mat[:,:-1][:,label_ids] # no self edges np.fill_diagonal(adj_mat,0) similarity_graph=nx.from_numpy_matrix(np.matrix(adj_mat)) [p1,p2]=kernighan_lin_bisection(similarity_graph, partition=None, max_iter=self.max_iter, weight='weight') partitions=[p1,p2] return partitions
def detect_communities(M):
# Uses the Kernighan Lin bisection for
# community detection
nx_graph = get_undirected_nx_network(M)
# Try out partitions of all sizes
for size in range(1, len(M)):
partition = get_initial_partition(size)
partition = kernighan_lin_bisection(nx_graph, partition=partition, max_iter=100, weight='weight')
print "------"
print "Size:", size
print "Size a:", len(partition[0])
print "Size b:", len(partition[1])
print sorted(partition[0])
print sorted(partition[1])
print convert_community_to_continent(partition[0])
print convert_community_to_continent(partition[1])
def _iterative_cutting(g, p):
"""helper function (iterative version)"""
to_be_processed = [g]
K = math.ceil(len(g.nodes()) / p)
res = []
while len(to_be_processed) > 0:
g = to_be_processed.pop()
g_l, g_r = kernighan_lin_bisection(g, weight="rate")
for partition in g_l, g_r:
if len(partition) > K:
to_be_processed.append(g.subgraph(partition))
else:
res.append(partition)
return res
def getRackOrganization(mySources):
G_w = domainConfiguration.G.copy()
weightGraph_(G_w, mySources)
# racks_=asyn_lpa_communities(G, weight='weight')
# print racks_
# k = domainConfiguration.REPLICATIONFACTOR -1
# comp = nx.girvan_newman(G_w)
# limited = itertools.takewhile(lambda c: len(c) <= k, comp)
# for communities in limited:
# pass
# print(tuple(sorted(c) for c in communities))
# racks_= kernighan_lin_bisection(G_w)
# print racks_
racks_ = kernighan_lin_bisection(G_w, weight='weight')
# print racks_
return racks_
def cluster(self, dgraph, weight=None):
udgraph = super().to_undirected(dgraph.dgraph)
A, B = kernighan_lin_bisection(udgraph, weight=weight)
return [A, B]
def partition(virtual, algo="min_cut"):
"""Iterative min cut algorithm.
Iteratively partitions the graph according to the chosen algorithm (either min cut or min bisection)
until the size of the partition is under a certain threshold.
"""
class UnionFind:
"""Utility Class used by the MinCut algorithm."""
def __init__(self, nodes):
self.parents = {u: u for u in nodes}
self.ranks = {u: 0 for u in nodes}
self.subsets = {u: {u} for u in nodes}
def find(self, u):
return u if self.parents[u] == u else self.find(self.parents[u])
def union(self, u, v):
u_root, v_root = self.find(u), self.find(v)
if self.ranks[u_root] < self.ranks[v_root]:
self.parents[u_root] = v_root
self.subsets[v_root] |= self.subsets[u_root]
del self.subsets[u_root]
elif self.ranks[u_root] > self.ranks[v_root]:
self.parents[v_root] = u_root
self.subsets[u_root] |= self.subsets[v_root]
del self.subsets[v_root]
else:
self.parents[v_root] = u_root
self.ranks[u_root] += 1
self.subsets[u_root] |= self.subsets[v_root]
del self.subsets[v_root]
def min_cut(g):
"""Return a min cut of g.
The procedure is based on Karger's algorithm [1].
[1] D. Karger "Global Min-cuts in RNC and Other Ramifications of a Simple Mincut Algorithm".
Proc. 4th Annual ACM-SIAM Symposium on Discrete Algorithms 1993.
"""
edges = []
weights = []
sum_rate = 0
for (u, v) in g.edges():
edges.append((u, v))
rate = g[u][v]["rate"]
weights.append(rate)
sum_rate += rate
n_nodes = len(g.nodes())
uf = UnionFind(g.nodes())
sorted_edges = iter(
np.random.choice(
np.arange(len(edges)),
size=len(edges),
replace=False,
p=np.array(weights) / sum_rate,
))
while n_nodes > 2:
u, v = edges[next(sorted_edges)]
if uf.find(u) != uf.find(v):
n_nodes -= 1
uf.union(u, v)
return uf.subsets.values()
to_be_processed = [set(virtual.nodes())]
partitions = []
root = Node(
frozenset(virtual.nodes()),
cores=sum(virtual.req_cores(u) for u in virtual.nodes()),
memory=sum(virtual.req_memory(u) for u in virtual.nodes()),
)
t = Tree(root)
# to keep track of the Node associated to each of the partitions
partitions_nodes = {frozenset(virtual.nodes()): root}
while to_be_processed:
p = to_be_processed.pop()
if len(p) <= 1:
partitions.append(p)
else:
if algo == "min_cut":
p1, p2 = min_cut(virtual.g.subgraph(p))
elif algo == "bisection":
p1, p2 = kernighan_lin_bisection(virtual.g.subgraph(p),
weight="rate")
else:
raise ValueError("undefined")
# update tree
parent = partitions_nodes[frozenset(p)]
p1_node = Node(
frozenset(p1),
cores=sum(virtual.req_cores(u) for u in p1),
memory=sum(virtual.req_memory(u) for u in p1),
parent=parent,
)
p2_node = Node(
frozenset(p2),
cores=sum(virtual.req_cores(u) for u in p2),
memory=sum(virtual.req_memory(u) for u in p2),
parent=parent,
)
partitions_nodes[frozenset(p)].l = partitions_nodes[frozenset(
p1)] = p1_node
partitions_nodes[frozenset(p)].r = partitions_nodes[frozenset(
p2)] = p2_node
to_be_processed.append(p1)
to_be_processed.append(p2)
return t
wb = Workbook()
sheet = wb.active
list_performance = []
gg = []
n = 10
start_time_big = time.time()
for i in range(0, 1000 + 1):
v = n
e = random.randint(v, 2 * v)
G = nx.gnm_random_graph(v, e)
start_time = time.time()
kernighan_lin_bisection(G)
end_time = time.time()
list_performance.append((v, e, end_time - start_time))
gg.append(end_time - start_time)
end_time_big = time.time()
for row in list_performance:
sheet.append(row)
filepath = "/content/drive/My Drive/301_Project/" + str(v) + '_' + str(i)
wb.save(filepath)
t_val = t.ppf(0.95, i)
mean = 0
for i in range(len(gg)):
mean += gg[i]
def bisect(G):
Gp = G.copy()
Gp.remove_edges_from([(u, v) for u, v in G.edges()
if G[u][v]["weight"] < 0])
partition = kernighan_lin_bisection(Gp)
return partition