def test_clique_removal():
graph = nx.complete_graph(10)
i, cs = apxa.clique_removal(graph)
idens = nx.density(graph.subgraph(i))
eq_(idens, 0.0, "i-set not found by clique_removal!")
for clique in cs:
cdens = nx.density(graph.subgraph(clique))
eq_(cdens, 1.0, "clique not found by clique_removal!")
graph = nx.trivial_graph(nx.Graph())
i, cs = apxa.clique_removal(graph)
idens = nx.density(graph.subgraph(i))
eq_(idens, 0.0, "i-set not found by ramsey!")
# we should only have 1-cliques. Just singleton nodes.
for clique in cs:
cdens = nx.density(graph.subgraph(clique))
eq_(cdens, 0.0, "clique not found by clique_removal!")
graph = nx.barbell_graph(10, 5, nx.Graph())
i, cs = apxa.clique_removal(graph)
idens = nx.density(graph.subgraph(i))
eq_(idens, 0.0, "i-set not found by ramsey!")
for clique in cs:
cdens = nx.density(graph.subgraph(clique))
eq_(cdens, 1.0, "clique not found by clique_removal!")
def test_clique_removal():
graph = nx.complete_graph(10)
i, cs = apxa.clique_removal(graph)
idens = nx.density(graph.subgraph(i))
eq_(idens, 0.0, "i-set not found by clique_removal!")
for clique in cs:
cdens = nx.density(graph.subgraph(clique))
eq_(cdens, 1.0, "clique not found by clique_removal!")
graph = nx.trivial_graph(nx.Graph())
i, cs = apxa.clique_removal(graph)
idens = nx.density(graph.subgraph(i))
eq_(idens, 0.0, "i-set not found by ramsey!")
# we should only have 1-cliques. Just singleton nodes.
for clique in cs:
cdens = nx.density(graph.subgraph(clique))
eq_(cdens, 0.0, "clique not found by clique_removal!")
graph = nx.barbell_graph(10, 5, nx.Graph())
i, cs = apxa.clique_removal(graph)
idens = nx.density(graph.subgraph(i))
eq_(idens, 0.0, "i-set not found by ramsey!")
for clique in cs:
cdens = nx.density(graph.subgraph(clique))
eq_(cdens, 1.0, "clique not found by clique_removal!")
def test_trivial_graph(self):
G = nx.trivial_graph()
independent_set, cliques = clique_removal(G)
assert is_independent_set(G, independent_set)
assert all(is_clique(G, clique) for clique in cliques)
# In fact, we should only have 1-cliques, that is, singleton nodes.
assert all(len(clique) == 1 for clique in cliques)
def test_trivial_graph(self):
G = nx.trivial_graph()
independent_set, cliques = clique_removal(G)
assert_true(is_independent_set(G, independent_set))
assert_true(all(is_clique(G, clique) for clique in cliques))
# In fact, we should only have 1-cliques, that is, singleton nodes.
assert_true(all(len(clique) == 1 for clique in cliques))
def maximum_independent_set(G):
"""Returns an approximate maximum independent set.
Parameters
----------
G : NetworkX graph
Undirected graph
Returns
-------
iset : Set
The apx-maximum independent set
Notes
-----
Finds the $O(|V|/(log|V|)^2)$ apx of independent set in the worst case.
References
----------
.. [1] Boppana, R., & Halldórsson, M. M. (1992).
Approximating maximum independent sets by excluding subgraphs.
BIT Numerical Mathematics, 32(2), 180–196. Springer.
"""
iset, _ = clique_removal(G)
return iset
def maximum_independent_set(G):
"""Returns an approximate maximum independent set.
Parameters
----------
G : NetworkX graph
Undirected graph
Returns
-------
iset : Set
The apx-maximum independent set
Notes
-----
Finds the $O(|V|/(log|V|)^2)$ apx of independent set in the worst case.
References
----------
.. [1] Boppana, R., & Halldórsson, M. M. (1992).
Approximating maximum independent sets by excluding subgraphs.
BIT Numerical Mathematics, 32(2), 180–196. Springer.
"""
iset, _ = clique_removal(G)
return iset
def solve_mcq_approximation(G):
"""
最大クリーク問題を既存の近似解法で解く
(Reference: Approximating Maximum Independent Sets by Excluding Subgraphs)
入力
G: 無向グラフ
出力
なし
# ><><><><><><><><><><><><><><><><><><><><><
# ><><><><><><><><><><><><><><><><><><><><><
# ><><><><><><><><><><><><><><><><><><><><><
"""
if G is None:
raise ValueError("Expected NetworkX graph!")
st1 = time.time()
cgraph = nx.complement(G)
et1 = time.time()
print('elapsed_time (complement) :', et1-st1)
st2 = time.time()
iset, _ = clique_removal(cgraph)
et2 = time.time()
print('elapsed_time (clique) :', et2-st2)
print(f'maximum clique number: {len(iset)}')
print(f'maximum clique: {iset}')
def nx_sim_score(self):
g = nx.Graph()
print "Vertices: %d" % len(self.v)
for node in self.v:
n = node[V_LABEL]
g.add_node(n)
print "Edges: %d" % len(self.e)
for edge in self.e:
g.add_edge(*edge)
maxw = 0
maxc = []
cnt = 0
sys.stdout.write("%d\r" % cnt)
'''
for clique in nx.find_cliques(g):
sys.stdout.write("%d\r" % cnt)
w = self.clique_weight([self.v_by_label(c) for c in clique])
if w > maxw:
maxw = w
maxc = clique
'''
from networkx.algorithms.approximation import max_clique, clique_removal
for c in clique_removal(g)[1]:
if len(c) > len(maxc):
maxc = c
maxw = self.clique_weight([self.v_by_label(c) for c in maxc])
jscore = self.jaccard_coef(len(maxc), self.g1order + self.g2order)
wscore = maxw / self.g1order
print "MaxW", maxw
print "JScore %d, %d", len(maxc), self.g1order + self.g2order, jscore
print "Wscore", wscore
return jscore, wscore
def nx_sim_score(self):
g = nx.Graph()
print "Vertices: %d" % len(self.v)
for node in self.v:
n = node[V_LABEL]
g.add_node(n)
print "Edges: %d" % len(self.e)
for edge in self.e:
g.add_edge(*edge)
maxw = 0
maxc = []
cnt = 0
sys.stdout.write("%d\r" % cnt)
'''
for clique in nx.find_cliques(g):
sys.stdout.write("%d\r" % cnt)
w = self.clique_weight([self.v_by_label(c) for c in clique])
if w > maxw:
maxw = w
maxc = clique
'''
from networkx.algorithms.approximation import max_clique, clique_removal
for c in clique_removal(g)[1]:
if len(c) > len(maxc):
maxc = c
maxw = self.clique_weight([self.v_by_label(c) for c in maxc])
jscore = self.jaccard_coef(len(maxc), self.g1order + self.g2order)
wscore = maxw / self.g1order
print "MaxW", maxw
print "JScore %d, %d", len(maxc), self.g1order+self.g2order, jscore
print "Wscore", wscore
return jscore, wscore
def NetworkX_approximate_clique_cover(graph_dict):
"""
NetworkX poly-time heuristic is based on
Boppana, R., & Halldórsson, M. M. (1992).
Approximating maximum independent sets by excluding subgraphs.
BIT Numerical Mathematics, 32(2), 180–196. Springer.
"""
G = nx.Graph()
for src in graph_dict:
for dst in graph_dict[src]:
G.add_edge(src, dst)
return approximation.clique_removal(G)[1]
def clique_approx_find_greedy_eliminate(graph: nx.Graph) -> list:
"""Perform minimum clique cover by approximatly find maximum clique and iteratively eliminate it.
Find the maximum clique with approximatino methods and iteratively eliminate it.
Args:
graph (nx.Graph): graph to solve
Returns:
list: list of node names for each clique
"""
_, clique_list = approx.clique_removal(graph)
clique_list = [list(item) for item in clique_list]
return clique_list
def max_set_ec2_deploy(graph_data):
'''
This code should be run on an Amazon EC2 instance or other cloud
computing platform. It actually runs max. ind. sets on the graph
file created above.'''
# Storing cardinality of largest set
cliques = approximation.clique_removal(graph)[1]
# Storing biggest cliques
biggest = max([len(cliques[x]) for x in range(len(cliques))])
# Adding 1 to get clinic number
cliques = np.array([list(x) for x in cliques if len(x) == biggest])
# Adding location identifier 'K'
cliques = cliques[:][:]+ 1
# Storing filepath
cliques = DataFrame(np.char.mod('K'+ '%04d', cliques))
# Writing to Excel file
filepath = wd + 'solutions.xlsx'
# Exporting
cliques.T.to_excel(filepath, index=False)
def test_barbell_graph(self):
G = nx.barbell_graph(10, 5)
independent_set, cliques = clique_removal(G)
assert is_independent_set(G, independent_set)
assert all(is_clique(G, clique) for clique in cliques)
def test_complete_graph(self):
G = nx.complete_graph(10)
independent_set, cliques = clique_removal(G)
assert is_independent_set(G, independent_set)
assert all(is_clique(G, clique) for clique in cliques)
def test_barbell_graph(self):
G = nx.barbell_graph(10, 5)
independent_set, cliques = clique_removal(G)
assert_true(is_independent_set(G, independent_set))
assert_true(all(is_clique(G, clique) for clique in cliques))
def test_complete_graph(self):
G = nx.complete_graph(10)
independent_set, cliques = clique_removal(G)
assert_true(is_independent_set(G, independent_set))
assert_true(all(is_clique(G, clique) for clique in cliques))
