352 lines
14 KiB
Python
352 lines
14 KiB
Python
# This module contains a VF2-inspired graph matching algorithm
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# It defines its own Graph type, and can be used standalone (no dependencies on the rest of muMLE framework)
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# Author: Joeri Exelmans
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import itertools
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from util.timer import Timer
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# like finding the 'strongly connected componenets', but edges are navigable in any direction
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def find_connected_components(graph):
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next_component = 0
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vtx_to_component = {}
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component_to_vtxs = []
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for vtx in graph.vtxs:
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if vtx in vtx_to_component:
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continue
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vtx_to_component[vtx] = next_component
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vtxs = []
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component_to_vtxs.append(vtxs)
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add_recursively(vtx, vtxs, vtx_to_component, next_component)
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next_component += 1
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return (vtx_to_component, component_to_vtxs)
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def add_recursively(vtx, vtxs: list, d: dict, component: int, already_visited: set = set()):
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if vtx in already_visited:
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return
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already_visited.add(vtx)
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vtxs.append(vtx)
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d[vtx] = component
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for edge in vtx.outgoing:
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add_recursively(edge.tgt, vtxs, d, component, already_visited)
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for edge in vtx.incoming:
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add_recursively(edge.src, vtxs, d, component, already_visited)
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class Graph:
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def __init__(self):
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self.vtxs = []
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self.edges = []
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class Vertex:
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def __init__(self, value):
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self.incoming = []
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self.outgoing = []
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self.value = value
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def __repr__(self):
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return f"V({self.value})"
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class Edge:
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def __init__(self, src: Vertex, tgt: Vertex, label=None):
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self.src = src
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self.tgt = tgt
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self.label = label
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# Add ourselves to src/tgt vertices
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self.src.outgoing.append(self)
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self.tgt.incoming.append(self)
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def __repr__(self):
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if self.label != None:
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return f"({self.src}--{self.label}->{self.tgt})"
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else:
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return f"({self.src}->{self.tgt})"
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class MatcherState:
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def __init__(self):
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self.mapping_vtxs = {} # guest -> host
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self.mapping_edges = {} # guest -> host
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self.r_mapping_vtxs = {} # host -> guest
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self.r_mapping_edges = {} # host -> guest
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self.h_unmatched_vtxs = []
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self.g_unmatched_vtxs = []
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# boundary is the most recently added (to the mapping) pair of (guest -> host) vertices
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self.boundary = None
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@staticmethod
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def make_initial(host, guest, pivot):
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state = MatcherState()
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state.h_unmatched_vtxs = [vtx for vtx in host.vtxs if vtx not in pivot.values()]
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state.g_unmatched_vtxs = [vtx for vtx in guest.vtxs if vtx not in pivot.keys()]
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state.mapping_vtxs = pivot
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state.r_mapping_vtxs = { v: k for k,v in state.mapping_vtxs.items() }
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return state
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# Grow the match set (creating a new copy)
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def grow_edge(self, host_edge, guest_edge):
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new_state = MatcherState()
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new_state.mapping_vtxs = self.mapping_vtxs
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new_state.mapping_edges = dict(self.mapping_edges)
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new_state.mapping_edges[guest_edge] = host_edge
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new_state.r_mapping_vtxs = self.r_mapping_vtxs
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new_state.r_mapping_edges = dict(self.r_mapping_edges)
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new_state.r_mapping_edges[host_edge] = guest_edge
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new_state.h_unmatched_vtxs = self.h_unmatched_vtxs
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new_state.g_unmatched_vtxs = self.g_unmatched_vtxs
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return new_state
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# Grow the match set (creating a new copy)
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def grow_vtx(self, host_vtx, guest_vtx):
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new_state = MatcherState()
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new_state.mapping_vtxs = dict(self.mapping_vtxs)
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new_state.mapping_vtxs[guest_vtx] = host_vtx
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new_state.mapping_edges = self.mapping_edges
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new_state.r_mapping_vtxs = dict(self.r_mapping_vtxs)
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new_state.r_mapping_vtxs[host_vtx] = guest_vtx
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new_state.r_mapping_edges = self.r_mapping_edges
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new_state.h_unmatched_vtxs = [h_vtx for h_vtx in self.h_unmatched_vtxs if h_vtx != host_vtx]
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new_state.g_unmatched_vtxs = [g_vtx for g_vtx in self.g_unmatched_vtxs if g_vtx != guest_vtx]
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new_state.boundary = (guest_vtx, host_vtx)
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return new_state
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def make_hashable(self):
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return frozenset(itertools.chain(
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((gv,hv) for gv,hv in self.mapping_vtxs.items()),
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((ge,he) for ge,he in self.mapping_edges.items()),
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))
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def __repr__(self):
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# return self.make_hashable().__repr__()
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return "VTXS: "+self.mapping_vtxs.__repr__()+"\nEDGES: "+self.mapping_edges.__repr__()
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class MatcherVF2:
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# Guest is the pattern
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def __init__(self, host, guest, compare_fn):
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self.host = host
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self.guest = guest
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self.compare_fn = compare_fn
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# with Timer("find_connected_components - guest"):
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self.guest_vtx_to_component, self.guest_component_to_vtxs = find_connected_components(guest)
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# print("number of guest connected components:", len(self.guest_component_to_vtxs))
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def match(self, pivot={}):
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yield from self._match(
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state=MatcherState.make_initial(self.host, self.guest, pivot),
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already_visited=set())
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def _match(self, state, already_visited, indent=0):
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# input()
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def print_debug(*args):
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pass
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# print(" "*indent, *args) # uncomment to see a trace of the matching process
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print_debug("match")
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# Keep track of the states in the search space that we already visited
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hashable = state.make_hashable()
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if hashable in already_visited:
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print_debug(" SKIP - ALREADY VISITED")
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# print_debug(" ", hashable)
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return
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# print_debug(" ", [hash(a) for a in already_visited])
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# print_debug(" ADD STATE")
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# print_debug(" ", hash(hashable))
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already_visited.add(hashable)
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if len(state.mapping_vtxs) == len(self.guest.vtxs) and len(state.mapping_edges) == len(self.guest.edges):
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print_debug("GOT MATCH:")
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print_debug(" ", state.mapping_vtxs)
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print_debug(" ", state.mapping_edges)
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yield state
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return
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def read_edge(edge, direction):
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if direction == "outgoing":
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return edge.tgt
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elif direction == "incoming":
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return edge.src
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else:
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raise Exception("wtf!")
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def attempt_grow(direction, indent):
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for g_matched_vtx, h_matched_vtx in state.mapping_vtxs.items():
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print_debug('attempt_grow', direction)
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for g_candidate_edge in getattr(g_matched_vtx, direction):
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print_debug('g_candidate_edge:', g_candidate_edge)
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g_candidate_vtx = read_edge(g_candidate_edge, direction)
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# g_to_skip_vtxs.add(g_candidate_vtx)
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if g_candidate_edge in state.mapping_edges:
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print_debug(" skip, guest edge already matched")
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continue # skip already matched guest edge
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for h_candidate_edge in getattr(h_matched_vtx, direction):
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if g_candidate_edge.label != h_candidate_edge.label:
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print_debug(" labels differ")
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continue
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print_debug('h_candidate_edge:', h_candidate_edge)
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if h_candidate_edge in state.r_mapping_edges:
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print_debug(" skip, host edge already matched")
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continue # skip already matched host edge
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print_debug('grow edge', g_candidate_edge, ':', h_candidate_edge, id(g_candidate_edge), id(h_candidate_edge))
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new_state = state.grow_edge(h_candidate_edge, g_candidate_edge)
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h_candidate_vtx = read_edge(h_candidate_edge, direction)
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yield from attempt_match_vtxs(
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new_state,
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g_candidate_vtx,
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h_candidate_vtx,
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indent+1)
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print_debug('backtrack edge', g_candidate_edge, ':', h_candidate_edge, id(g_candidate_edge), id(h_candidate_edge))
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def attempt_match_vtxs(state, g_candidate_vtx, h_candidate_vtx, indent):
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print_debug('attempt_match_vtxs')
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if g_candidate_vtx in state.mapping_vtxs:
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if state.mapping_vtxs[g_candidate_vtx] != h_candidate_vtx:
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print_debug(" nope, guest already mapped (mismatch)")
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return # guest vtx is already mapped but doesn't match host vtx
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if h_candidate_vtx in state.r_mapping_vtxs:
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if state.r_mapping_vtxs[h_candidate_vtx] != g_candidate_vtx:
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print_debug(" nope, host already mapped (mismatch)")
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return # host vtx is already mapped but doesn't match guest vtx
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g_outdegree = len(g_candidate_vtx.outgoing)
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h_outdegree = len(h_candidate_vtx.outgoing)
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if g_outdegree > h_outdegree:
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print_debug(" nope, outdegree")
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return
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g_indegree = len(g_candidate_vtx.incoming)
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h_indegree = len(h_candidate_vtx.incoming)
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if g_indegree > h_indegree:
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print_debug(" nope, indegree")
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return
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if not self.compare_fn(g_candidate_vtx, h_candidate_vtx):
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print_debug(" nope, bad compare")
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return
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new_state = state.grow_vtx(
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h_candidate_vtx,
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g_candidate_vtx)
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print_debug('grow vtx', g_candidate_vtx, ':', h_candidate_vtx, id(g_candidate_vtx), id(h_candidate_vtx))
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yield from self._match(new_state, already_visited, indent+1)
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print_debug('backtrack vtx', g_candidate_vtx, ':', h_candidate_vtx, id(g_candidate_vtx), id(h_candidate_vtx))
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print_debug('preferred...')
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yield from attempt_grow('outgoing', indent+1)
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yield from attempt_grow('incoming', indent+1)
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print_debug('least preferred...')
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if state.boundary != None:
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g_boundary_vtx, _ = state.boundary
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guest_boundary_component = self.guest_vtx_to_component[g_boundary_vtx]
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# only try guest vertices that are in a different component (all vertices in the same component are already discovered via 'attempt_grow')
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guest_components_to_try = (c for i,c in enumerate(self.guest_component_to_vtxs) if i != guest_boundary_component)
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# for the host vertices however, we have to try them from all components, because different connected components of our pattern (=guest) could be mapped onto the same connected component in the host
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else:
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guest_components_to_try = self.guest_component_to_vtxs
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for g_candidate_vtxs in guest_components_to_try:
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for g_candidate_vtx in g_candidate_vtxs:
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if g_candidate_vtx in state.mapping_vtxs:
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print_debug("skip (already matched)", g_candidate_vtx)
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continue
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for h_candidate_vtx in state.h_unmatched_vtxs:
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yield from attempt_match_vtxs(state, g_candidate_vtx, h_candidate_vtx, indent+1)
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if indent == 0:
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print_debug('visited', len(already_visited), 'states total')
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# demo time...
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if __name__ == "__main__":
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host = Graph()
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host.vtxs = [Vertex(0), Vertex(1), Vertex(2), Vertex(3)]
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host.edges = [
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Edge(host.vtxs[0], host.vtxs[1]),
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Edge(host.vtxs[1], host.vtxs[2]),
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Edge(host.vtxs[2], host.vtxs[0]),
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Edge(host.vtxs[2], host.vtxs[3]),
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Edge(host.vtxs[3], host.vtxs[2]),
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]
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guest = Graph()
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guest.vtxs = [
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Vertex('v != 3'), # cannot be matched with Vertex(3) - changing this to True, you get 2 morphisms instead of one
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Vertex('True')] # can be matched with any node
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guest.edges = [
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# Look for a simple loop:
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Edge(guest.vtxs[0], guest.vtxs[1]),
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# Edge(guest.vtxs[1], guest.vtxs[0]),
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]
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m = MatcherVF2(host, guest, lambda g_vtx, h_vtx: eval(g_vtx.value, {}, {'v':h_vtx.value}))
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import time
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durations = 0
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iterations = 1
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print("Patience...")
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for n in range(iterations):
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time_start = time.perf_counter_ns()
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matches = [mm for mm in m.match()]
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time_end = time.perf_counter_ns()
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time_duration = time_end - time_start
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durations += time_duration
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print(f'{iterations} iterations, took {durations/1000000:.3f} ms, {durations/iterations/1000000:.3f} ms per iteration')
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print("found", len(matches), "matches")
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for mm in matches:
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print("match:")
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print(" ", mm.mapping_vtxs)
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print(" ", mm.mapping_edges)
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print("######################")
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host = Graph()
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host.vtxs = [
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Vertex('pony'), # 1
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Vertex('pony'), # 3
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Vertex('bear'),
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Vertex('bear'),
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]
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host.edges = [
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# match:
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Edge(host.vtxs[0], host.vtxs[1]),
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Edge(host.vtxs[1], host.vtxs[0]),
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]
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guest = Graph()
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guest.vtxs = [
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Vertex('pony'), # 0
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Vertex('pony'), # 1
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Vertex('bear')]
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guest.edges = [
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Edge(guest.vtxs[0], guest.vtxs[1]),
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Edge(guest.vtxs[1], guest.vtxs[0]),
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]
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m = MatcherVF2(host, guest, lambda g_vtx, h_vtx: g_vtx.value == h_vtx.value)
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import time
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durations = 0
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iterations = 1
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print("Patience...")
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for n in range(iterations):
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time_start = time.perf_counter_ns()
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matches = [mm for mm in m.match()]
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time_end = time.perf_counter_ns()
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time_duration = time_end - time_start
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durations += time_duration
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print(f'{iterations} iterations, took {durations/1000000:.3f} ms, {durations/iterations/1000000:.3f} ms per iteration')
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print("found", len(matches), "matches")
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for mm in matches:
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print("match:")
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print(" ", mm.mapping_vtxs)
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print(" ", mm.mapping_edges)
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