def forest_isomorphism(f1, f2):
#TODO: do this at a higher level, since both iso testers need it
if sum(1 for v in f1.vertices()) != sum(1 for v in f2.vertices()) or \
sum(1 for e in f1.edges()) != sum(1 for e in f2.edges()):
return None
results = []
for forest in (f1,f2):
generator = depth_first_generator(forest)
visitor = AggregateVisitor(backend=forest,
visitors={Depth:None})
traverse(root_vertices=graph.vertices(),
visitor=visitor,
generator=depth_first_generator(forest))
results.append(visitor.Depth)
f1_depth, f2_depth = results
f1_by_depths = ydict(backend=f1)
f2_by_depths = ydict(backend=f2)
max_depth = 0
for forest, depth, index_by_depths in [(f1, f1_depth, f1_by_depths),
(f2, f2_depth, f2_by_depths)]:
for v in forest.vertices():
d = depth[v]
max_depth = max(d, max_depth)
index_by_depths[d] = index_by_depths.setdefault(d, ydeque(backend=forest)).append(v)
prev_f1_canonical_id = ydict(backend=f1)
prev_f2_canonical_id = ydict(backend=f2)
if len(f1_by_depths[max_depth]) != len(f2_by_depths[max_depth]):
return
for v in f1_by_depths[max_depth]:
prev_f1_canonical_id[v] = 0
for v in f2_by_depths[max_depth]:
prev_f2_canonical_id[v] = 0
for depth in xrange(max_depth - 1, -1, -1):
f1_vertex_id = ydict(backend=f1)
f2_vertex_id = ydict(backend=f2)
if len(f1_by_depths[depth]) != len(f2_by_depths[depth]):
return
# don't do two-phase canonical id -> id transformation. instead, compute canonical ids
# on the fly by storing a lexicographically sorted list of ids and binary searching for
# existing ids each time
for v in f1_by_depths[depth]:
f1_vertex_id[v] = ydeque(backend=f2_vertex_id,
ysorted(backend=f2_vertex_id,
(prev_f1_canonical_id[w] for u,w in f1.edges(source=v))))
for v in f2_by_depths[depth]:
f2_vertex_id[v] = ydeque(backend=f2_vertex_id,
ysorted(backend=f2_vertex_id,
(prev_f2_canonical_id[w] for u,w in f2.edges(source=v))))
def isomorphism(g1, g2):
if sum(1 for v in g1.vertices()) != sum(1 for v in g2.vertices()) or \
sum(1 for e in g1.edges()) != sum(1 for e in g2.edges()):
return None
test_funcs = [partial(reachability_signature, reach=1),
partial(reachability_signature, reach=2),
partial(reachability_signature, reach=4)]
g1cf = canonical_form(g1, test_funcs)
g2cf = canonical_form(g2, test_funcs)
sorted_g1cf = ysorted(g1, g1cf.itervalues())
sorted_g2cf = ysorted(g2, g2cf.itervalues())
for x,y in izip(sorted_g1cf, sorted_g2cf):
if x != y:
return None
g2_cform_inv = function_inverse(g2cf, g2)
iso = ydict(backend=g1)
contexts = ydeque(backend=g1)
for v in g1.vertices():
g2_inv_image = ydeque(backend=contexts)
for image_element in g2_cform_inv[g1cf[v]]:
g2_inv_image.append(image_element)
contexts.append((v, g2_inv_image))
index = 0
while index >= 0 and index < len(contexts):
vertex = contexts[index][0]
if contexts[index][1]:
v_prime = contexts[index][1].popleft()
iso[vertex] = v_prime
if is_a_partial_isomorphism(g1, g2, iso):
index += 1
else:
if vertex in iso:
del iso[vertex]
g2_inv_image = ydeque(backend=contexts)
for image_element in g2_cform_inv[g1cf[vertex]]:
g2_inv_image.append(image_element)
(index, vertex, str([x for x in g2_inv_image]))
contexts[index] = (vertex, g2_inv_image)
index -= 1
if index < 0:
return None
else:
return iso
