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query_LowerBound.py
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query_LowerBound.py
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import networkx as nx
from networkx.algorithms import isomorphism
import networkx.algorithms.isomorphism as iso
from sets import Set
from cvxopt import matrix, solvers
from numpy import array, zeros, ones, log
import random
def findTightestLSim(U,F,UpB,LoB):
'''
U: set of remaining query graphs
F: set of feature graphs
UpB: for each feature, upper bound of SIP of feature-graph
LoB: for each feature, lower bound of SIP of feature-graph
'''
UpperB = list(UpB)
LowerB = list(LoB)
S = [] # S: for each feature, set of remaining query graphs which are sub-graphs
for f in range(0,len(F)):
s = Set([])
for rq in range(0,len(U)):
if checkSubGraphIsomorphismWithLabels(U[rq],F[f]):
s.add(rq+1)
S.append(s)
print S
# QP
q = zeros((len(S),len(S)),dtype=float)
for i in range(0,len(S)):
for j in range(i+1,len(S)):
q[i][j] = 0.5 * UpperB[i] * UpperB[j]
q[j][i] = 0.5 * UpperB[i] * UpperB[j]
Q = 2*matrix(q)
p = zeros(len(S),dtype=float)
for i in range(0,len(S)):
p[i] = -1.0 * LowerB[i]
P = matrix(p)
h = -1.0*ones(len(U)+2*len(S),dtype=float)
g = zeros((len(U)+2*len(S),len(S)),dtype=float)
for i in range(0,len(U)):
for j in range(0,len(S)):
if i+1 in S[j]:
g[i][j] = -1.0
for i in range(0,len(S)):
g[len(U)+i][i] = -1.0
g[len(U)+len(S)+i][i] = 1.0
h[len(U)+i] = 0.0
h[len(U)+len(S)+i] = 1.0
G = matrix(g)
H = matrix(h)
print Q
print P
print G
print H
sol=solvers.qp(Q, P, G, H)
probOfS = sol['x']
LSim = 0
covered = []
for i in range(0,int(2*log(len(U)))):
for s in range(0,len(S)):
if random.random() <= probOfS[s]:
if not s in covered:
covered.append(s)
currentSum = 0
for j in range(0,len(covered)):
currentSum = currentSum + UpperB[covered[j]]
LSim = LSim + LowerB[s] - UpperB[s]*currentSum
return LSim
def checkSubGraphIsomorphismWithLabels(G1,G2):
def checkTupleEquality(tuple_a,tuple_b):
if tuple_a[0]==tuple_b[0] and tuple_a[1]==tuple_b[1]:
return True
elif tuple_a[0]==tuple_b[1] and tuple_a[1]==tuple_b[0]:
return True
else:
return False
def nodeMatchWithVertexLabels(dictA,dictB):
return checkTupleEquality(dictA['label'],dictB['label'])
def findCommonNode(tuple_a,tuple_b):
for i in tuple_a:
if i in tuple_b:
return i
def generateLabeledLineGraph(G):
lineGraph=nx.line_graph(G)
for vertexIndex in lineGraph:
lineGraph.node[vertexIndex]['label']=(G.node[vertexIndex[0]]['label'],G.node[vertexIndex[1]]['label'])
for n,nbrsdict in lineGraph.adjacency_iter():
for nbr,eattr in nbrsdict.items():
lineGraph.edge[n][nbr]['label']=G.node[findCommonNode(n,nbr)]['label']
return lineGraph
em = iso.categorical_edge_match('label', 'miss')
lineGraphG1=generateLabeledLineGraph(G1)
lineGraphG2=generateLabeledLineGraph(G2)
GM=isomorphism.GraphMatcher(lineGraphG2,lineGraphG1,node_match=nodeMatchWithVertexLabels,edge_match=em)
return GM.subgraph_is_isomorphic()
rq1=nx.Graph()
rq1.add_node(1,label="A")
rq1.add_node(2,label="B")
rq1.add_node(3,label="C")
rq1.add_edge(1,2)
rq1.add_edge(2,3)
rq2=nx.Graph()
rq2.add_node(1,label="A")
rq2.add_node(2,label="B")
rq2.add_node(3,label="C")
rq2.add_edge(1,2)
rq2.add_edge(1,3)
rq3=nx.Graph()
rq3.add_node(1,label="A")
rq3.add_node(2,label="B")
rq3.add_node(3,label="C")
rq3.add_edge(2,3)
rq3.add_edge(1,3)
U = [rq1,rq2,rq3]
f1=nx.Graph()
f1.add_node(1,label="A")
f1.add_node(2,label="B")
f1.add_edge(1,2)
f2=nx.Graph()
f2.add_node(1,label="B")
f2.add_node(2,label="C")
f2.add_edge(1,2)
f3=nx.Graph()
f3.add_node(1,label="C")
f3.add_node(2,label="A")
f3.add_edge(1,2)
'''
f2=nx.Graph()
f2.add_node(1,label="A")
f2.add_node(2,label="B")
f2.add_node(3,label="C")
f2.add_edge(1,2)
f2.add_edge(2,3)
'''
F = [f1,f2]
UpperB = [0.36,0.15] # UpperB(f)
LowerB = [0.28,0.08] # LowerB(f)
print findTightestLSim(U,F,UpperB,LowerB)
f4=nx.Graph()
f4.add_node(1,label="C")
f4.add_node(2,label="A")
f4.add_node(3,label="B")
f4.add_node(4,label="B")
f4.add_edge(1,2)
f4.add_edge(2,3)
f4.add_edge(3,4)
f4.add_edge(4,1)
f4.add_edge(2,4)
F=[f1,f2,f4]
UpperB = [0.36,0.45,0.29]
LowerB = [0.28,0.08,0.19]
print findTightestLSim(U,F,UpperB,LowerB)
f5=nx.Graph()
f5.add_node(1,label="A")
f5.add_node(2,label="B")
f5.add_node(3,label="C")
f5.add_node(4,label="A")
f5.add_edge(1,2)
f5.add_edge(2,3)
f5.add_edge(3,4)
F=[f1,f2,f3,f4]
UpperB = [0.36,0.45,0.29,0.42]
LowerB = [0.32,0.38,0.23,0.38]
print findTightestLSim(U,F,UpperB,LowerB)