def generalGreedy(G, k, p):
''' Finds initial seed set S using general greedy heuristic
Input: G -- networkx Graph object
k -- number of initial nodes needed
p -- propagation probability
Output: S -- initial set of k nodes to propagate
'''
import time
start = time.time()
R = 1 # number of times to run Random Cascade
S = [] # set of selected nodes
# add node to S if achieves maximum propagation for current chosen + this node
for i in range(k):
s = PQ() # priority queue
for v in G.nodes():
if v not in S:
s.add_task(v, 0) # initialize spread value
for j in range(R): # run R times Random Cascade
[priority, count, task] = s.entry_finder[v]
s.add_task(v, priority - runICmodel_n(G, S + [v], p)[0] /
R) # add normalized spread value
task, priority = s.pop_item()
S.append(task)
# print(i, k, time.time() - start)
return S
def degreeDiscountIC(G, k, Ep=0):
''' Finds initial set of nodes to propagate in Independent Cascade model (with priority queue)
Input: G -- networkx graph object
k -- number of nodes needed
p -- propagation probability
Output:
S -- chosen k nodes
'''
S = []
dd = PQ() # degree discount
t = dict() # number of adjacent vertices that are in S
d = dict() # degree of each vertex
# initialize degree discount
for u in G.nodes():
d[u] = sum([G[u][v]['weight'] for v in G[u]]) # each edge adds degree 1
# d[u] = len(G[u]) # each neighbor adds degree 1
dd.add_task(u, -d[u]) # add degree of each node
t[u] = 0
# add vertices to S greedily
for i in range(k):
u, priority = dd.pop_item() # extract node with maximal degree discount
S.append(u)
for v in G[u]:
if v not in S:
t[v] += G[u][v]['weight'] # increase number of selected neighbors
# print(t[v])
p = Ep[u][v]['weight']
priority = d[v] - 2*t[v] - (d[v] - t[v])*t[v]*p # discount of degree
dd.add_task(v, -priority)
return S
def degreeDiscountIAC3(G, k, Ep):
''' Finds initial set of nodes to propagate in Independent Cascade model (with priority queue)
Input: G -- networkx graph object
k -- number of nodes needed
Ep -- propagation probability graph
Output:
S -- chosen k nodes
'''
S = []
dd = PQ() # degree discount
t = dict() # number of adjacent vertices that are in S
d = dict() # degree of each vertex
# initialize degree discount
for u in G.nodes():
d[u] = sum([G[u][v]['weight'] * Ep[u][v]['weight']
for v in G[u]]) # each edge adds degree 1
# d[u] = len(G[u]) # each neighbor adds degree 1
dd.add_task(u, -d[u]) # add degree of each node
t[u] = 0
# add vertices to S greedily
for i in range(k):
u, priority = dd.pop_item(
) # extract node with maximal degree discount
S.append(u)
for v in G[u]:
if v not in S:
multi = 1
add = 0
for n in G.predecessors(v):
if n in S:
multi *= (1 - Ep[n][v])
for n in G[v]:
if n in S:
add -= Ep[v][n]
else:
add += Ep[v][n]
add += 1
priority = add * multi
dd.add_task(v, -priority)
return S
def degreeDiscountStar(G,k,Ep):
S = []
scores = PQ()
d = dict()
t = dict()
for u in G:
d[u] = sum([G[u][v]['weight']*Ep[u][v]['weight'] for v in G[u]])
t[u] = 0
score = -((1-Ep[u][v]['weight'])**t[u])*(1+(d[u]-t[u])*Ep[u][v]['weight'])
scores.add_task(u, score)
for iteration in range(k):
u, priority = scores.pop_item()
print(iteration, -priority)
S.append(u)
for v in G[u]:
if v not in S:
t[v] += G[u][v]['weight']
score = -((1-p)**t[u])*(1+(d[u]-t[u])*Ep[u][v]['weight'])
scores.add_task(v, score)
return S
def degreeDiscountIAC3(G, k, Ep): # config中默认配置这个为oracle
''' Finds initial set of nodes to propagate in Independent Cascade model (with priority queue)
Input: G -- networkx graph object
k -- number of nodes needed
Ep -- propagation probability graph, 传播概率图
Output:
S -- chosen k nodes
'''
S = []
dd = PQ() # degree discount
t = dict() # number of adjacent vertices that are in S
d = dict() # degree of each vertex
# initialize degree discount
for u in G.nodes():
d[u] = sum([G[u][v]['weight']*Ep[u][v]['weight'] for v in G[u]]) + 1 # each edge adds degree 1
# d[u] = len(G[u]) # each neighbor adds degree 1
dd.add_task(u, -d[u]) # add degree of each node. degree最大，则-d[u]最小，则排在heap的前面(默认小根堆min-heap)
t[u] = 0
# add vertices to S greedily
for i in range(k):
u, priority = dd.pop_item() # extract node with maximal degree discount
S.append(u)
for v in G[u]:
if v not in S:
multi = 1
add = 0
for n in G.predecessors(v): # 前缀结点(有边指向v的结点)
if n in S: # 这些结点在S中，但是并没有激活v，的概率
multi *= (1 - Ep[n][v]['weight'])
for n in G[v]:
if n in S:
continue
else:
add += Ep[v][n]['weight']
add += 1
priority = add * multi
dd.add_task(v, -priority)
return S
def Greedy(G, k, p):
"""
Input: G -- networkx Graph object
k -- number of initial nodes needed
p -- propagation probability
Output: S -- initial set of k nodes to propagate
"""
R = 1 # number of times to run Random Cascade
S = [] # set of selected nodes
# add node to S if achieves maximum propagation for current chosen + this node
for i in range(k):
s = PQ() # priority queue
for v in G.nodes():
if v not in S:
s.add_task(v, 0) # initialize spread value
for j in range(R): # run R times Random Cascade
[priority, count, task] = s.entry_finder[v]
s.add_task(v, priority - runIC(G, S + [v], p)[0] /
R) # add normalized spread value
task, priority = s.pop_item()
S.append(task)
return S
