# coding: utf-8 """ Author: Sten Vercamman Univeristy of Antwerp Example code for paper: Efficient model transformations for novices url: http://msdl.cs.mcgill.ca/people/hv/teaching/MSBDesign/projects/Sten.Vercammen The main goal of this code is to give an overview, and an understandable implementation, of known techniques for pattern matching and solving the sub-graph homomorphism problem. The presented techniques do not include performance adaptations/optimizations. It is not optimized to be efficient but rather for the ease of understanding the workings of the algorithms. The paper does list some possible extensions/optimizations. It is intended as a guideline, even for novices, and provides an in-depth look at the workings behind various techniques for efficient pattern matching. """ import graph # import numpy as np import math import collections import random class GraphGenerator(object): """ Generates a random Graph with dv an array containing all vertices (there type), de an array containing all edges (their type) and dc_inc an array representing the incoming edges (analogue for dc_out) """ def __init__(self, dv, de, dc_inc, dc_out, debug=False): if len(de) != len(dc_inc): raise ValueError('de and dc_inc should be the same length.') if len(de) != len(dc_out): raise ValueError('de and dc_out should be the same length.') self.dv = dv self.de = de self.dc_inc = dc_inc self.dc_out = dc_out # print for debugging, so you know the used values if debug: print('dv') print('[',','.join(map(str,dv)),']') print('_____') print('de') print('[',','.join(map(str,de)),']') print('_____') print('dc_inc') print('[',','.join(map(str,dc_inc)),']') print('_____') print('dc_out') print('[',','.join(map(str,dc_out)),']') print('_____') self.graph = graph.Graph() self.vertices = [] # create all the vertices: for v_type in self.dv: # v_type represents the type of the vertex self.vertices.append(self.graph.addCreateVertex('v' + str(v_type))) index = 0 # create all edges for e_type in self.de: # e_type represents the type of the edge src = self.vertices[self.dc_out[index]] # get src vertex tgt = self.vertices[self.dc_inc[index]] # get tgt vertex self.graph.addCreateEdge(src, tgt, 'e' + str(e_type)) # create edge index += 1 def getRandomGraph(self): return self.graph def getRandomPattern(self, max_nr_of_v, max_nr_of_e, start=0, debug=False): # create pattern pattern = graph.Graph() # map from graph to new pattern graph_to_pattern = {} # map of possible edges # we don't need a dict, but python v2.7 does not have an OrderedSet possible_edges = collections.OrderedDict() # set of chosen edges chosen_edges = set() # start node from graph g_node = self.vertices[start] p_node = pattern.addCreateVertex(g_node.type) # for debuging, print the order in which the pattern gets created and # connects it edges if debug: print('v'+str(id(p_node))+'=pattern.addCreateVertex('+"'"+str(g_node.type)+"'"+')') # save corrolation graph_to_pattern[g_node] = p_node def insertAllEdges(edges, possible_edges, chosen_edges): for edge in edges: # if we did not chose the edge if edge not in chosen_edges: # if inc_edge not in possible edges, add it with value 1 possible_edges[edge] = None def insertEdges(g_vertex, possible_edges, chosen_edges): insertAllEdges(g_vertex.incoming_edges, possible_edges, chosen_edges) insertAllEdges(g_vertex.outgoing_edges, possible_edges, chosen_edges) insertEdges(g_node, possible_edges, chosen_edges) while max_nr_of_v > len(graph_to_pattern) and max_nr_of_e > len(chosen_edges): candidate = None if len(possible_edges) == 0: break # get a random number between 0 and len(possible_edges) # We us a triangular distribution to approximate the fact that # the first element is the longest in the possible_edges and # already had the post chance of beeing choosen. # (The approximation is because the first few ellements where # added in the same itteration, but doing this exact is # computationally expensive.) if len(possible_edges) == 1: randie = 0 else: randie = int(round(random.triangular(1, len(possible_edges), len(possible_edges)))) - 1 candidate = list(possible_edges.keys())[randie] del possible_edges[candidate] chosen_edges.add(candidate) src = graph_to_pattern.get(candidate.src) tgt = graph_to_pattern.get(candidate.tgt) src_is_new = True if src != None and tgt != None: # create edge between source and target pattern.addCreateEdge(src, tgt, candidate.type) if debug: print('pattern.addCreateEdge('+'v'+str(id(src))+', '+'v'+str(id(tgt))+', '+"'"+str(candidate.type)+"'"+')') # skip adding new edges continue elif src == None: # create pattern vertex src = pattern.addCreateVertex(candidate.src.type) if debug: print('v'+str(id(src))+'=pattern.addCreateVertex('+"'"+str(candidate.src.type)+"'"+')') # map newly created pattern vertex graph_to_pattern[candidate.src] = src # create edge between source and target pattern.addCreateEdge(src, tgt, candidate.type) if debug: print('pattern.addCreateEdge('+'v'+str(id(src))+', '+'v'+str(id(tgt))+', '+"'"+str(candidate.type)+"'"+')') elif tgt == None: src_is_new = False # create pattern vertex tgt = pattern.addCreateVertex(candidate.tgt.type) if debug: print('v'+str(id(tgt))+'=pattern.addCreateVertex('+"'"+str(candidate.tgt.type)+"'"+')') # map newly created pattern vertex graph_to_pattern[candidate.tgt] = tgt # create edge between source and target pattern.addCreateEdge(src, tgt, candidate.type) if debug: print('pattern.addCreateEdge('+'v'+str(id(src))+', '+'v'+str(id(tgt))+', '+"'"+str(candidate.type)+"'"+')') else: raise RuntimeError('Bug: src or tgt of edge should be in out pattern') # select the vertex from the chosen edge that was not yet part of the pattern if src_is_new: new_vertex = candidate.src else: new_vertex = candidate.tgt # insert all edges from the new vertex insertEdges(new_vertex, possible_edges, chosen_edges) return pattern def createConstantPattern(): """ Use this to create the same pattern over and over again. """ # create pattern pattern = graph.Graph() # copy and paste printed pattern from debug output or create a pattern # below the following line: # ---------------------------------------------------------------------- v4447242448=pattern.addCreateVertex('v4') v4457323088=pattern.addCreateVertex('v6') pattern.addCreateEdge(v4447242448, v4457323088, 'e4') v4457323216=pattern.addCreateVertex('v8') pattern.addCreateEdge(v4457323216, v4447242448, 'e4') v4457323344=pattern.addCreateVertex('v7') pattern.addCreateEdge(v4457323216, v4457323344, 'e3') v4457323472=pattern.addCreateVertex('v7') pattern.addCreateEdge(v4457323344, v4457323472, 'e1') # ---------------------------------------------------------------------- return pattern def get_random_host_and_guest(nr_vtxs, nr_vtx_types, nr_edges, nr_edge_types, pattern_nr_vtxs=3, pattern_nr_edges=15): dv = [random.randint(0, nr_vtx_types) for _ in range(nr_vtxs)] de = [random.randint(0, nr_edge_types) for _ in range(nr_edges)] dc_inc = [random.randint(0, nr_vtxs-1) for _ in range(nr_edges)] dc_out = [random.randint(0, nr_vtxs-1) for _ in range(nr_edges)] return get_host_and_guest(dv, de, dc_inc, dc_out, pattern_nr_vtxs, pattern_nr_edges) def get_host_and_guest(dv, de, dc_inc, dc_out, pattern_nr_vtxs=3, pattern_nr_edges=15): gg = GraphGenerator(dv, de, dc_inc, dc_out) graph = gg.getRandomGraph() pattern = gg.getRandomPattern(pattern_nr_vtxs, pattern_nr_edges, debug=False) return (graph, pattern) def get_large_host_and_guest(): 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 ] 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 ] return get_host_and_guest(dv, de, dc_inc, dc_out) def get_small_host_and_guest(): dv = [0, 1, 0, 1, 0] de = [0, 0, 0] dc_inc = [0, 2, 4] dc_out = [1, 3, 3] return get_host_and_guest(dv, de, dc_inc, dc_out)