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Antoine Castillon
DSS
Commits
38b79bf0
Commit
38b79bf0
authored
3 years ago
by
Antoine Castillon
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quick_del_edges.py
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38b79bf0
from
math
import
ceil
def
quick_quasi_cliques
(
G
,
gamma
,
min_size
):
def
test_indeg_exdeg
(
X
,
cand_exts
,
indeg_X
,
exdeg_X
):
"
verify that indeg_X[u] = d_X(u) and exdeg_X[u] = d_cand_exts(u) for all u, used only when debug = True
"
for
u
in
(
set
(
X
)
|
set
(
cand_exts
)):
if
indeg_X
[
u
]
!=
len
(
set
(
X
)
&
set
(
G
[
u
])):
print
(
"
Erreur indeg
"
,
indeg_X
[
u
],
len
(
set
(
X
)
&
set
(
G
[
u
])))
print
(
X
,
cand_exts
)
return
1
/
0
if
exdeg_X
[
u
]
!=
len
(
set
(
cand_exts
)
&
set
(
G
[
u
])):
print
(
"
Erreur exdeg
"
,
exdeg_X
[
u
],
len
(
set
(
cand_exts
)
&
set
(
G
[
u
])))
print
(
X
,
cand_exts
)
return
1
/
0
#print("ok",X,cand_exts)
def
is_quasi_clique
(
X
,
indeg_X
,
exdeg_X
,
bool_all_vertices
=
False
):
#bool_all_vertices = True if all current vertices are in X, False otherwise
"
verify that X is a gamma quasi-clique of G
"
if
len
(
X
)
<
min_size
:
return
False
seuil
=
ceil
(
gamma
*
(
len
(
X
)
-
1
))
for
u
in
X
:
d_X_u
=
indeg_X
[
u
]
+
(
exdeg_X
[
u
]
if
bool_all_vertices
else
0
)
if
debug
and
(
d_X_u
!=
len
(
set
(
X
)
&
set
(
G
[
u
]))):
print
(
"
Erreur
"
)
return
1
/
0
if
d_X_u
<
seuil
:
return
False
return
True
def
neighbourhood
(
v
,
k
,
current_vertices
):
"
compute the list of vertices k hops a far from v
"
current_vertices
=
set
(
current_vertices
)
dist
=
{}
for
u
in
current_vertices
:
dist
[
u
]
=
-
1
dist
[
v
]
=
0
l
=
[
v
]
N_k_v
=
[]
while
len
(
l
)
>
0
:
u
=
l
.
pop
(
0
)
N_k_v
.
append
(
u
)
if
dist
[
u
]
<
k
:
for
u2
in
current_vertices
&
set
(
G
[
u
]):
if
dist
[
u2
]
==
-
1
:
l
.
append
(
u2
)
dist
[
u2
]
=
dist
[
u
]
+
1
return
N_k_v
def
upper_lower_bounds
(
X
,
cand_exts
,
indeg_X
,
exdeg_X
):
"
compute L_X and U_X
"
if
debug
:
test_indeg_exdeg
(
X
,
cand_exts
,
indeg_X
,
exdeg_X
)
deg_min_X
=
min
([
indeg_X
[
u
]
+
exdeg_X
[
u
]
for
u
in
X
])
U_X_min
=
min
(
int
(
deg_min_X
/
gamma
)
+
1
-
len
(
X
),
len
(
cand_exts
))
indeg_cand_exts_sorted
=
sorted
([
indeg_X
[
u
]
for
u
in
cand_exts
],
key
=
lambda
x
:
-
x
)
# on trie cand_exts par indeg_X decroissant
sum_X_indeg_X
=
sum
([
indeg_X
[
u
]
for
u
in
X
])
sum_cand_exts
=
sum
(
indeg_cand_exts_sorted
[:
U_X_min
])
flag
=
False
for
t
in
range
(
U_X_min
,
0
,
-
1
):
if
sum_X_indeg_X
+
sum_cand_exts
>=
(
len
(
X
)
*
ceil
(
gamma
*
(
len
(
X
)
+
t
-
1
))):
U_X
=
t
flag
=
True
break
sum_cand_exts
-=
indeg_cand_exts_sorted
[
t
-
1
]
if
not
flag
:
U_X
=
0
indeg_min_X
=
min
([
indeg_X
[
u
]
for
u
in
X
])
t
=
0
while
(
indeg_min_X
+
t
)
<
ceil
(
gamma
*
(
len
(
X
)
+
t
-
1
))
and
t
<=
len
(
cand_exts
):
t
+=
1
L_X_min
=
t
flag
=
False
sum_cand_exts
=
sum
(
indeg_cand_exts_sorted
[:
L_X_min
-
1
])
for
t
in
range
(
L_X_min
,
len
(
cand_exts
)
+
1
):
sum_cand_exts
+=
indeg_cand_exts_sorted
[
t
-
1
]
if
sum_X_indeg_X
+
sum_cand_exts
>=
(
len
(
X
)
*
ceil
(
gamma
*
(
len
(
X
)
+
t
-
1
))):
L_X
=
t
flag
=
True
break
if
not
flag
:
L_X
=
len
(
cand_exts
)
+
1
return
U_X
,
L_X
def
compute_indeg_exdeg
(
X
,
cand_exts
):
"
compute indeg and exdeg
"
X
=
set
(
X
)
cand_exts
=
set
(
cand_exts
)
indeg
=
{}
exdeg
=
{}
for
u
in
(
X
|
cand_exts
):
N_u
=
set
(
G
[
u
])
indeg
[
u
]
=
len
(
X
&
N_u
)
exdeg
[
u
]
=
len
(
cand_exts
&
N_u
)
return
indeg
,
exdeg
def
update_indeg_exdeg
(
u
,
X
,
cand_exts
,
indeg
,
exdeg
,
update
):
"
update indeg and exdeg
"
if
update
==
'
del_X
'
:
# remove u from X
indeg
.
pop
(
u
)
exdeg
.
pop
(
u
)
for
neigh_u
in
((
set
(
X
)
|
set
(
cand_exts
))
&
set
(
G
[
u
])):
indeg
[
neigh_u
]
-=
1
if
update
==
'
del_cand_exts
'
:
# remove u from cand_exts
indeg
.
pop
(
u
)
exdeg
.
pop
(
u
)
for
neigh_u
in
((
set
(
X
)
|
set
(
cand_exts
))
&
set
(
G
[
u
])):
exdeg
[
neigh_u
]
-=
1
def
aux_quick
(
X
,
cand_exts
,
indeg_X
,
exdeg_X
):
# indeg_X[i] = nb of neigbhours of i in X
# exdeg_X[i] = nb of nieghbours of i in cand_exts
nonlocal
last_clique
global
id_rec
if
debug
:
print
(
"
id_rec:
"
,
id_rec
)
id_rec
+=
1
b_has_qclq
=
False
while
len
(
X
)
+
len
(
cand_exts
)
>=
min_size
:
current_vertices
=
set
(
X
+
cand_exts
)
if
current_vertices
.
issubset
(
last_clique
):
return
True
if
is_quasi_clique
(
current_vertices
,
indeg_X
,
exdeg_X
,
True
):
Quasi_Cliques
.
append
(
current_vertices
)
last_clique
=
current_vertices
current_vertices
=
list
(
current_vertices
)
G
.
remove_edges_from
([(
current_vertices
[
i
],
current_vertices
[
j
])
for
i
in
range
(
1
,
len
(
current_vertices
))
for
j
in
range
(
i
)])
return
True
if
len
(
cand_exts
)
==
0
:
return
b_has_qclq
v
=
cand_exts
.
pop
(
0
)
Y
=
X
+
[
v
]
cand_exts_Y
=
list
(
set
(
cand_exts
)
&
set
(
neighbourhood
(
v
,
2
,
current_vertices
)))
indeg_Y
,
exdeg_Y
=
compute_indeg_exdeg
(
Y
,
cand_exts_Y
)
flag_repeat_until
=
(
len
(
cand_exts_Y
)
>
0
)
U_Y
,
L_Y
=
len
(
cand_exts_Y
),
0
while
flag_repeat_until
:
U_Y
,
L_Y
=
upper_lower_bounds
(
Y
,
cand_exts_Y
,
indeg_Y
,
exdeg_Y
)
if
L_Y
>
U_Y
:
flag_repeat_until
=
False
break
for
u
in
X
:
maxi
=
max
(
exdeg_Y
[
u
],
L_Y
)
cond
=
(
indeg_Y
[
u
]
+
exdeg_Y
[
u
]
<
ceil
(
gamma
*
(
len
(
Y
)
+
maxi
-
1
)))
or
(
indeg_Y
[
u
]
+
U_Y
<
ceil
(
gamma
*
(
len
(
Y
)
+
U_Y
-
1
)))
if
cond
:
cand_exts_Y
=
[]
break
flag_repeat_until
=
False
cand_exts_Y_copy
=
cand_exts_Y
.
copy
()
for
u
in
cand_exts_Y_copy
:
maxi
=
max
(
exdeg_Y
[
u
],
L_Y
)
cond
=
(
indeg_Y
[
u
]
+
exdeg_Y
[
u
]
<
ceil
(
gamma
*
(
len
(
Y
)
+
maxi
-
1
)))
or
(
indeg_Y
[
u
]
+
U_Y
<
ceil
(
gamma
*
(
len
(
Y
)
+
U_Y
-
1
)))
if
cond
:
flag_repeat_until
=
True
cand_exts_Y
.
remove
(
u
)
update_indeg_exdeg
(
u
,
Y
,
cand_exts_Y
,
indeg_Y
,
exdeg_Y
,
'
del_cand_exts
'
)
if
debug
:
test_indeg_exdeg
(
Y
,
cand_exts_Y
,
indeg_Y
,
exdeg_Y
)
flag_repeat_until
=
flag_repeat_until
and
(
len
(
cand_exts_Y
)
>
0
)
and
(
len
(
cand_exts_Y
)
>=
L_Y
)
b_has_superqclq
=
False
if
(
L_Y
<=
U_Y
)
and
(
len
(
cand_exts_Y
)
>=
L_Y
)
and
(
len
(
Y
)
+
len
(
cand_exts_Y
)
>=
min_size
):
b_has_superqclq
=
aux_quick
(
Y
,
cand_exts_Y
,
indeg_Y
,
exdeg_Y
)
b_has_qclq
=
b_has_qclq
or
b_has_superqclq
if
(
not
b_has_superqclq
)
and
is_quasi_clique
(
Y
,
indeg_Y
,
exdeg_Y
,
False
):
set_Y
=
set
(
Y
)
if
not
(
set_Y
.
issubset
(
last_clique
)):
Quasi_Cliques
.
append
(
set_Y
)
last_clique
=
set_Y
G
.
remove_edges_from
([(
Y
[
i
],
Y
[
j
])
for
i
in
range
(
1
,
len
(
Y
))
for
j
in
range
(
i
)])
b_has_qclq
=
True
indeg_X
,
exdeg_X
=
compute_indeg_exdeg
(
X
,
cand_exts
)
if
debug
:
test_indeg_exdeg
(
X
,
cand_exts
,
indeg_X
,
exdeg_X
)
return
b_has_qclq
Quasi_Cliques
=
[]
last_clique
=
set
()
# last_clique is used to avoid some non maximal quasi-cliques
indeg_X
=
{}
# indeg_X[i] is the number of neighbours of i in X
exdeg_X
=
{}
# exdeg_X[i] is the number of neighbours of i in cand_exts
for
u
in
G
.
nodes
:
indeg_X
[
u
]
=
0
exdeg_X
[
u
]
=
len
(
G
[
u
])
aux_quick
([],
list
(
G
.
nodes
),
indeg_X
,
exdeg_X
)
return
Quasi_Cliques
debug
=
False
# significantly slow down the processing, use only when debugging
id_rec
=
0
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