Pattern matching: return all the matches (instead of the first one found)

pattern_matching/main.py

@@ -31,31 +31,34 @@ if __name__ == '__main__':
 	"""
 	The main function called when running from the command line.
 	"""
-	nr_of_vertices		= 50
+	nr_of_vertices		= 10
-	nr_of_diff_types_v	= 10
+	nr_of_diff_types_v	= 0
-	nr_of_edges			= 150
+	nr_of_edges			= 20
-	nr_of_diff_types_e	= 10
+	nr_of_diff_types_e	= 0
 
 	dv      = [random.randint(0, nr_of_diff_types_v) for _ in range(nr_of_vertices)]
-	# dv		= np.random.random_integers(0, nr_of_diff_types_v, nr_of_vertices)
 	de      = [random.randint(0, nr_of_diff_types_e) for _ in range(nr_of_edges)]
-	# de		= np.random.random_integers(0, nr_of_diff_types_e, nr_of_edges)
 	dc_inc	= [random.randint(0, nr_of_vertices-1) for _ in range(nr_of_edges)]
-	# dc_inc	= np.random.random_integers(0, nr_of_vertices-1, nr_of_edges)
 	dc_out	= [random.randint(0, nr_of_vertices-1) for _ in range(nr_of_edges)]
-	# dc_out	= np.random.random_integers(0, nr_of_vertices-1, nr_of_edges)
 
 	# override random graph by copy pasting output from terminal
-	dv		= [ 10,5,4,0,8,6,8,0,4,8,5,5,7,0,10,0,5,6,10,4,0,3,0,8,2,7,5,8,1,0,2,10,0,0,1,6,8,4,7,6,4,2,10,10,6,4,6,0,2,7 ]
+	# dv		= [ 10,5,4,0,8,6,8,0,4,8,5,5,7,0,10,0,5,6,10,4,0,3,0,8,2,7,5,8,1,0,2,10,0,0,1,6,8,4,7,6,4,2,10,10,6,4,6,0,2,7 ]
-	de		= [ 8,10,8,1,6,7,4,3,5,2,0,0,9,6,0,3,8,3,2,7,2,3,10,8,10,8,10,2,5,5,10,6,7,5,1,2,1,2,2,3,7,7,2,1,7,2,9,10,8,1,9,4,1,3,1,1,8,2,2,9,10,9,1,9,4,10,10,10,9,3,5,3,6,6,9,1,2,6,3,2,4,10,9,6,5,6,2,4,3,2,4,10,6,2,8,8,0,5,1,7,3,4,3,8,7,3,0,8,3,3,8,5,10,5,9,3,1,10,3,2,6,3,10,0,5,10,9,10,0,1,4,7,10,3,1,9,1,2,3,7,4,3,7,8,8,4,5,10,1,4 ]
+	# de		= [ 8,10,8,1,6,7,4,3,5,2,0,0,9,6,0,3,8,3,2,7,2,3,10,8,10,8,10,2,5,5,10,6,7,5,1,2,1,2,2,3,7,7,2,1,7,2,9,10,8,1,9,4,1,3,1,1,8,2,2,9,10,9,1,9,4,10,10,10,9,3,5,3,6,6,9,1,2,6,3,2,4,10,9,6,5,6,2,4,3,2,4,10,6,2,8,8,0,5,1,7,3,4,3,8,7,3,0,8,3,3,8,5,10,5,9,3,1,10,3,2,6,3,10,0,5,10,9,10,0,1,4,7,10,3,1,9,1,2,3,7,4,3,7,8,8,4,5,10,1,4 ]
-	dc_inc	= [ 0,25,18,47,22,25,16,45,38,25,5,45,15,44,17,46,6,17,35,8,16,29,48,47,25,34,4,20,24,1,47,44,8,25,32,3,16,6,33,21,6,13,41,10,17,25,21,33,31,30,5,4,45,26,16,42,12,25,29,3,32,30,14,26,11,13,7,13,3,43,43,22,48,37,20,28,15,40,19,33,43,16,49,36,11,25,9,42,3,22,16,40,42,44,27,30,1,18,10,35,19,6,9,43,37,38,45,19,41,14,37,45,0,31,29,31,24,20,44,46,8,45,43,3,38,38,35,12,19,45,7,34,20,28,12,17,45,17,35,49,20,21,49,1,35,38,38,36,33,30 ]
+	# dc_inc	= [ 0,25,18,47,22,25,16,45,38,25,5,45,15,44,17,46,6,17,35,8,16,29,48,47,25,34,4,20,24,1,47,44,8,25,32,3,16,6,33,21,6,13,41,10,17,25,21,33,31,30,5,4,45,26,16,42,12,25,29,3,32,30,14,26,11,13,7,13,3,43,43,22,48,37,20,28,15,40,19,33,43,16,49,36,11,25,9,42,3,22,16,40,42,44,27,30,1,18,10,35,19,6,9,43,37,38,45,19,41,14,37,45,0,31,29,31,24,20,44,46,8,45,43,3,38,38,35,12,19,45,7,34,20,28,12,17,45,17,35,49,20,21,49,1,35,38,38,36,33,30 ]
-	dc_out	= [ 9,2,49,49,37,33,16,21,5,46,4,15,9,6,14,22,16,33,23,21,15,31,37,23,47,3,30,26,35,9,29,21,39,32,22,43,5,9,41,30,31,30,37,33,31,34,23,22,34,26,44,36,38,33,48,5,9,34,13,7,48,41,43,26,26,7,12,6,12,28,22,8,29,22,24,27,16,4,31,41,32,15,19,20,38,0,26,18,43,46,40,17,29,14,34,14,32,17,32,47,16,45,7,4,35,22,42,11,38,2,0,29,4,38,17,44,9,23,5,10,31,17,1,11,16,5,37,27,35,32,45,16,18,1,14,4,42,24,43,31,21,38,6,34,39,46,20,1,38,47 ]
+	# dc_out	= [ 9,2,49,49,37,33,16,21,5,46,4,15,9,6,14,22,16,33,23,21,15,31,37,23,47,3,30,26,35,9,29,21,39,32,22,43,5,9,41,30,31,30,37,33,31,34,23,22,34,26,44,36,38,33,48,5,9,34,13,7,48,41,43,26,26,7,12,6,12,28,22,8,29,22,24,27,16,4,31,41,32,15,19,20,38,0,26,18,43,46,40,17,29,14,34,14,32,17,32,47,16,45,7,4,35,22,42,11,38,2,0,29,4,38,17,44,9,23,5,10,31,17,1,11,16,5,37,27,35,32,45,16,18,1,14,4,42,24,43,31,21,38,6,34,39,46,20,1,38,47 ]
+
+	dv = [0, 1, 0, 1, 0]
+	de = [0, 0, 0]
+	dc_inc = [0, 2, 4]
+	dc_out = [1, 3, 3]
 	
 	gg	= GraphGenerator(dv, de, dc_inc, dc_out, debug)
 
 	graph	= gg.getRandomGraph()
-	pattern	= gg.getRandomPattern(5, 15, debug=debug)
 
+	print(graph.vertices)
+	pattern	= gg.getRandomPattern(3, 15, debug=debug)
+	print(pattern.vertices)
 
 	# override random pattern by copy pasting output from terminal to create
 	# pattern, paste it in the createConstantPattern function in the generator.py
@@ -70,10 +73,12 @@ if __name__ == '__main__':
 	#PM	= PatternMatching('SP')
 	# PM	= PatternMatching('Ullmann')
 	PM	= PatternMatching('VF2')
-	v,e = PM.match(pattern, graph)
+	matches = PM.match(pattern, graph)
+	print("found", len(matches), "matches:", matches)
 
 	# regenerate graph, to show matched pattern
-	graphToDot.printGraph('randomGraph.dot', graph, v, e)
+	for i, (v,e) in enumerate(matches):
+		graphToDot.printGraph(f'randomGraph-{i}.dot', graph, v, e)
 
 	if debug:
 		print(len(v))

pattern_matching/patternMatching.py

@@ -36,6 +36,7 @@ class PatternMatching(object):
 		self.result			= None
 		self.previous		= []
 		self.optimize		= optimize
+		self.results        = []
 
 	def match(self, pattern, graph):
 		"""
@@ -68,6 +69,7 @@ class PatternMatching(object):
 		self.bound_vertices	= {}
 		self.bound_edges	= {}
 		self.result			= None
+		self.results        = []
 
 		return result
 
@@ -845,7 +847,21 @@ class PatternMatching(object):
 				"""
 				# all candidate pair (n, m) represent graph x pattern
 
+				candidate = frozenset(itertools.chain(
+					((i, j) for i,j in VF2_obj.mapping.items()),
+					# ((self.reverseMapH[i], self.reverseMapP[j]) for i,j in VF2_obj.mapping.items()),
+					[(h[n],p[m])],
+				))
+
+				if candidate in self.alreadyVisited:
+				# print(self.indent*"  ", "candidate:", candidate)
+				# for match in self.alreadyVisited.get(index_M, []):
+					# if match == candidate:
+						return False # already visited this (partial) match -> skip
+
+
 				if feasibilityTest(H, P, h, p, VF2_obj, n, m):
+					print(self.indent*"  ","adding to match:", n, "->", m)
 					# adapt VF2_obj
 					VF2_obj.core_graph[n]	= True
 					VF2_obj.core_pattern[m]	= True
@@ -855,17 +871,30 @@ class PatternMatching(object):
 					addOutNeighbours(P[m], VF2_obj.N_out_pattern, index_M)
 					addIncNeighbours(P, m, VF2_obj.N_inc_pattern, index_M)
 
-					if findM(H, P, h, p, VF2_obj, index_M + 1):
+					if index_M > 0:
-						return True
+						# remember our partial match (shallow copy) so we don't visit it again
+						self.alreadyVisited.add(frozenset([ (i, j) for i,j in VF2_obj.mapping.items()]))
+						# self.alreadyVisited.setdefault(index_M, set()).add(frozenset([ (self.reverseMapH[i], self.reverseMapP[j]) for i,j in VF2_obj.mapping.items()]))
+						# print(self.alreadyVisited)
 
-					# else, cleanup, adapt VF2_obj
+					self.indent += 1
-					VF2_obj.core_graph[n]	= False
+					if findM(H, P, h, p, VF2_obj, index_M + 1):
-					VF2_obj.core_pattern[m]	= False
+						# return True
-					del VF2_obj.mapping[h[n]]
+						print(self.indent*"  ","found match", len(self.results), ", continuing...")
-					delNeighbours(VF2_obj.N_out_graph, index_M)
+					self.indent -= 1
-					delNeighbours(VF2_obj.N_inc_graph, index_M)
+
-					delNeighbours(VF2_obj.N_out_pattern, index_M)
+					if True:
-					delNeighbours(VF2_obj.N_inc_pattern, index_M)
+					# else:
+						print(self.indent*"  ","backtracking... remove", n, "->", m)
+
+						# else, backtrack, adapt VF2_obj
+						VF2_obj.core_graph[n]	= False
+						VF2_obj.core_pattern[m]	= False
+						del VF2_obj.mapping[h[n]]
+						delNeighbours(VF2_obj.N_out_graph, index_M)
+						delNeighbours(VF2_obj.N_inc_graph, index_M)
+						delNeighbours(VF2_obj.N_out_pattern, index_M)
+						delNeighbours(VF2_obj.N_inc_pattern, index_M)
 
 				return False
 
@@ -879,12 +908,15 @@ class PatternMatching(object):
 					# skip graph vertices that are not in VF2_obj.N_out_graph
 					# (or already matched)
 					if N_graph[n] == -1 or VF2_obj.core_graph[n]:
+						# print(self.indent*"  ","    skipping")
 						continue
+					print(self.indent*"  ","  n:", n)
 					for m in range(0, len(N_pattern)):
 						# skip graph vertices that are not in VF2_obj.N_out_pattern
 						# (or already matched)
 						if N_pattern[m] == -1 or VF2_obj.core_pattern[m]:
 							continue
+						print(self.indent*"  ","  m:", m)
 						if matchPhase(H, P, h, p, index_M, VF2_obj, n, m):
 							return True
 
@@ -899,35 +931,48 @@ class PatternMatching(object):
 					# skip vertices that are connected to the graph 
 					# (or already matched)
 					if not (VF2_obj.N_out_graph[n] == -1 and VF2_obj.N_inc_graph[n] == -1) or VF2_obj.core_graph[n]:
+						# print(self.indent*"  ","    skipping")
 						continue
+					print("  n:", n)
 					for m in range(0, len(VF2_obj.N_out_pattern)):
 						# skip vertices that are connected to the graph 
 						# (or already matched)
 						if not (VF2_obj.N_out_pattern[m] == -1 and VF2_obj.N_inc_pattern[m] == -1) or VF2_obj.core_pattern[m]:
+							# print(self.indent*"  ","      skipping")
 							continue
+						print(self.indent*"  ","    m:", m)
 						if matchPhase(H, P, h, p, index_M, VF2_obj, n, m):
 							return True
 
 				return False
 
+			print(self.indent*"  ","index_M:", index_M)
+
 			# We are at the end, we found an candidate.
 			if index_M == len(p):
+				print(self.indent*"  ","end...")
 				bound_graph_vertices	= {}
 				for vertex_bound, _ in VF2_obj.mapping.items():
 					bound_graph_vertices.setdefault(vertex_bound.type, set()).add(vertex_bound)
 
 				self.result	= self.matchNaive(vertices=bound_graph_vertices, edges=self.graph.edges)
+				if self.result != None:
+					self.results.append(self.result)
 				return self.result != None
 
-			# try the candidates is the preffered order
+			if index_M > 0:
-			# first try the adjacent vertices connected via the outgoing edges.
+				# try the candidates is the preffered order
-			if preferred(H, P, h, p, index_M, VF2_obj, VF2_obj.N_out_graph, VF2_obj.N_out_pattern):
+				# first try the adjacent vertices connected via the outgoing edges.
-				return True
+				print(self.indent*"  ","preferred L1")
+				if preferred(H, P, h, p, index_M, VF2_obj, VF2_obj.N_out_graph, VF2_obj.N_out_pattern):
+					return True
 
-			# then try the adjacent vertices connected via the incoming edges.
+				print(self.indent*"  ","preferred L2")
-			if preferred(H, P, h, p, index_M, VF2_obj, VF2_obj.N_inc_graph, VF2_obj.N_inc_pattern):
+				# then try the adjacent vertices connected via the incoming edges.
-				return True
+				if preferred(H, P, h, p, index_M, VF2_obj, VF2_obj.N_inc_graph, VF2_obj.N_inc_pattern):
+					return True
 
+			print(self.indent*"  ","leastPreferred")
 			# and lastly, try the vertices not connected to the currently matched vertices
 			if leastPreferred(H, P, h, p, index_M, VF2_obj):
 				return True
@@ -937,11 +982,23 @@ class PatternMatching(object):
 
 		# create adjecency matrix of the graph
 		H, h	= self.createAdjacencyMatrixMap(self.graph)
+		print("adjacency:", H)
+		print("h:", len(h))
 		# create adjecency matrix of the pattern
 		P, p	= self.createAdjacencyMatrixMap(self.pattern)
 
 		VF2_obj	= VF2_Obj(len(h), len(p))
 
+		self.indent = 0
+
+		# Only for debugging:
+		self.reverseMapH = { h[i] : i for i in range(len(h))}
+		self.reverseMapP = { p[i] : i for i in range(len(p))}
+
+		# Set of partial matches already explored - prevents us from producing the same match multiple times
+		# Encoded as a mapping from match size to the partial match
+		self.alreadyVisited = set()
+		
 		findM(H, P, h, p, VF2_obj)
 
-		return self.result
+		# return self.results

pattern_matching/run.sh

@@ -1,8 +1,11 @@
 #!/bin/sh
 
+rm *.svg
+rm *.dot
 python main.py
-dot randomGraph.dot -Tsvg > randomGraph.svg
+# dot randomGraph.dot -Tsvg > randomGraph.svg
-dot randomPattern.dot -Tsvg > randomPattern.svg
+for filename in randomGraph-*.dot; do
+  dot $filename -Tsvg > $filename.svg
+done
 
-firefox randomGraph.svg
+firefox *.svg
-firefox randomPattern.svg