def test_bfs_properties_undirected(graph):
"""
In any breadth-first search tree, all edges either (1) are in the
tree, (2) connect two vertices in the same level of the tree, or
(3) connect two vertices from adjacent levels of the tree
"""
g = UndirectedGraph(graph())
visitor = AggregateVisitor(visitors={ParentEdge:None, Depth:None})
traverse(g.vertices(), visitor, breadth_first_generator(g))
tree_edges = set([e for e in visitor.ParentEdge.itervalues() \
if e is not None])
for e in g.edges():
if e not in tree_edges:
u_depth = visitor.Depth[e[0]]
v_depth = visitor.Depth[e[1]]
assert u_depth == v_depth or abs(u_depth - v_depth) == 1
def test_graph_splits_undirected(graph):
"""
In any depth-first search tree of an undirected graph, any
edge (root, X) in the depth-first search tree partitions
the graph: there are no edges between any vertex visited
before X and any vertices visited after X in the original graph.
"""
g = UndirectedGraph(graph())
visitor = AggregateVisitor(visitors={Parent : None,
ParentEdge : None,
DiscoverTime : None})
traverse(g.vertices(), visitor, depth_first_generator(g))
root = [v for v,time in visitor.DiscoverTime.iteritems() if time == 0][0]
root_edges = [visitor.ParentEdge[v] for v in g.vertices() \
if v != root and visitor.Parent[v] == root]
for x,y in root_edges:
before = [v for v in g.vertices() \
if visitor.DiscoverTime[v] < visitor.DiscoverTime[y] \
and v != root]
after = [v for v in g.vertices() \
if visitor.DiscoverTime[v] > visitor.DiscoverTime[y]]
for b in before:
for a in after:
assert [e for e in g.edges(source=b, target=a)] == []
assert [e for e in g.edges(source=a, target=b)] == []
def __init__(self, g):
self.g = UndirectedGraph(g)
v = {LowPoint:None, LeastAncestor:None, Parent:None, ParentEdge:None}
self.vis = AggregateVisitor(backend=self.g, visitors=v)
traverse(self.g.vertices(), self.vis, depth_first_generator(self.g))
self.vertices_by_lowpoint = \
sorted(self.g.vertices(),
key=partial(getitem, self.vis.LowPoint))
self.vertices_by_dfs_num = \
sorted(self.g.vertices(),
key=partial(getitem, self.vis.DiscoverTime))
self.face_handle = {}
self.df_face_handle = {}
self.canonical_df_child = dict((v,v) for v in self.g.vertices())
self.pertinent_roots = dict((v,[]) for v in self.g.vertices())
self.separated_df_child_list = dict((v,[]) for v in self.g.vertices())
self.self_loops = []
self.backedges = dict((v,[]) for v in self.g.vertices())
self.backedge_flag = dict((v,-1) for v in self.g.vertices())
self.visited = dict((v,-1) for v in self.g.vertices())
for v in self.g.vertices():
parent = self.vis.Parent.get(v)
parent_edge = self.vis.ParentEdge.get(v)
handle_list = [] if parent is None else [parent_edge]
self.face_handle[v] = face_handle(v, handle_list[:])
self.df_face_handle[v] = face_handle(parent, handle_list[:])
PRINT('Parent: %s' % self.vis.Parent, 1)
for v in self.g.vertices():
PRINT('ParentEdge %s: %s' % (v, self.vis.ParentEdge.get(v)), 1)
for v in self.g.vertices():
PRINT('DiscoverTime %s: %s' % (v, self.vis.DiscoverTime.get(v)), 1)
for v in self.g.vertices():
PRINT('LowPoint %s: %s' % (v, self.vis.LowPoint.get(v)), 1)
PRINT('Vertices by dfs num: %s' % self.vertices_by_dfs_num)
class boyer_myrvold(object):
def __init__(self, g):
self.g = UndirectedGraph(g)
v = {LowPoint:None, LeastAncestor:None, Parent:None, ParentEdge:None}
self.vis = AggregateVisitor(backend=self.g, visitors=v)
traverse(self.g.vertices(), self.vis, depth_first_generator(self.g))
self.vertices_by_lowpoint = \
sorted(self.g.vertices(),
key=partial(getitem, self.vis.LowPoint))
self.vertices_by_dfs_num = \
sorted(self.g.vertices(),
key=partial(getitem, self.vis.DiscoverTime))
self.face_handle = {}
self.df_face_handle = {}
self.canonical_df_child = dict((v,v) for v in self.g.vertices())
self.pertinent_roots = dict((v,[]) for v in self.g.vertices())
self.separated_df_child_list = dict((v,[]) for v in self.g.vertices())
self.self_loops = []
self.backedges = dict((v,[]) for v in self.g.vertices())
self.backedge_flag = dict((v,-1) for v in self.g.vertices())
self.visited = dict((v,-1) for v in self.g.vertices())
for v in self.g.vertices():
parent = self.vis.Parent.get(v)
parent_edge = self.vis.ParentEdge.get(v)
handle_list = [] if parent is None else [parent_edge]
self.face_handle[v] = face_handle(v, handle_list[:])
self.df_face_handle[v] = face_handle(parent, handle_list[:])
PRINT('Parent: %s' % self.vis.Parent, 1)
for v in self.g.vertices():
PRINT('ParentEdge %s: %s' % (v, self.vis.ParentEdge.get(v)), 1)
for v in self.g.vertices():
PRINT('DiscoverTime %s: %s' % (v, self.vis.DiscoverTime.get(v)), 1)
for v in self.g.vertices():
PRINT('LowPoint %s: %s' % (v, self.vis.LowPoint.get(v)), 1)
PRINT('Vertices by dfs num: %s' % self.vertices_by_dfs_num)
def planar_embedding(self):
for v in reversed(self.vertices_by_dfs_num):
self.store_old_face_handles()
self.walkup(v)
if not self.walkdown(v):
return False
self.clean_up_embedding()
return True
def walkup(self, v):
PRINT('--- Starting walkup from %s ---' % v, 1)
PRINT('--- edges to consider: %s ---' % \
[e for e in self.g.edges(source=v)])
for e in self.g.edges(source = v):
w = other_vertex(e, v)
PRINT('Looking at (v,w) = (%s,%s)' % (v,w), 4)
if v == w:
self.self_loops.append(e)
continue
if self.vis.DiscoverTime[w] < self.vis.DiscoverTime[v] or \
e == self.vis.ParentEdge[w]:
continue
self.backedges[w].append(e)
timestamp = self.vis.DiscoverTime[v]
self.backedge_flag[w] = timestamp
for face_itr in chain((w,),self.first_face_iter(w)):
PRINT('Traveler: %s' % face_itr)
if face_itr == v or self.visited[face_itr] == timestamp:
break
elif self.is_bicomp_root(face_itr):
PRINT('Setting visited/pertinent roots for %s' % face_itr)
dfs_child = self.canonical_df_child[face_itr]
parent = self.vis.Parent.get(dfs_child, dfs_child)
handle = self.df_face_handle[dfs_child]
PRINT('Handle: %s' % handle)
if handle.vertex is not None:
self.visited[handle.first_endpoint()] = timestamp
self.visited[handle.second_endpoint()] = timestamp
v_df_number = self.vis.DiscoverTime[v]
if self.vis.LowPoint[dfs_child] < v_df_number or \
self.vis.LeastAncestor[dfs_child] < v_df_number:
PRINT('Appending %s to %s''s prs' % (handle, parent))
self.pertinent_roots[parent].append(handle)
else:
PRINT("Prepending %s to %s's prs" % (handle, parent))
self.pertinent_roots[parent].insert(0,handle)
self.visited[face_itr] = timestamp
PRINT('--- Done with walkup from %s ---' % v, 1)
PRINT('Visited: %s' % self.visited, 1)
def walkdown(self, v):
PRINT('--- Starting walkdown from %s ---' % v, 1)
PRINT('pertinent roots: %s' % self.pertinent_roots[v], 1)
merge_stack = []
while self.pertinent_roots[v]:
root_handle = self.pertinent_roots[v].pop(0)
curr_handle = root_handle
PRINT('Traversing from handle %s' % curr_handle)
endpoints = []
PRINT('Traversal endpoints are %s and %s' % \
(curr_handle.first_endpoint(), curr_handle.second_endpoint()))
first_endpoint = curr_handle.first_endpoint()
second_endpoint = curr_handle.second_endpoint()
if first_endpoint == second_endpoint:
endpoints.append((curr_handle.vertex, first_endpoint))
else:
for endpoint in (first_endpoint, second_endpoint):
tail = curr_handle.vertex
for face_v in face_iterator(curr_handle.vertex,
endpoint,
self.face_handle):
if self.pertinent(face_v, v) or \
self.externally_active(face_v, v):
endpoints.append((tail, face_v))
break
tail = face_v
PRINT('Endpoints: %s' % endpoints)
first_tail, first_side_vertex = endpoints[0]
second_tail, second_side_vertex = endpoints[-1]
if self.internally_active(first_side_vertex, v):
chosen, chose_first_upper_path = first_side_vertex, True
elif self.internally_active(second_side_vertex, v):
chosen, chose_first_upper_path = second_side_vertex, False
elif self.pertinent(first_side_vertex, v):
chosen, chose_first_upper_path = first_side_vertex, True
elif self.pertinent(second_side_vertex, v):
chosen, chose_first_upper_path = second_side_vertex, False
else:
PRINT('NOT PLANAR!')
return False
PRINT('Chosen: %s, Chose first: %s' % \
(chosen, chose_first_upper_path))
PRINT('--- Done with walkdown from %s ---' % v, 1)
return True
def store_old_face_handles(self):
pass
def clean_up_embedding(self):
pass
def first_face_iter(self, v):
return face_iterator(v, self.face_handle[v].first_endpoint(),
self.face_handle)
def second_face_iter(self, v):
return face_iterator(v, self.face_handle[v].second_endpoint(),
self.face_handle)
def pertinent(self, w, v):
return self.backedge_flag[w] == self.vis.DiscoverTime[v] or \
self.pertinent_roots[w]
def externally_active(self, w, v):
v_num = self.vis.DiscoverTime[v]
return self.vis.LeastAncestor[w] < v_num or \
(self.separated_df_child_list[w] and \
self.vis.LowPoint[self.separated_df_child_list[w][0]] < v_num)
def internally_active(self, w, v):
return self.pertinent(w,v) and not self.externally_active(w,v)
def is_bicomp_root(self, v):
handle = self.face_handle[v]
if not handle.handle_list:
return True
first_endpoint = handle.first_endpoint()
second_endpoint = handle.second_endpoint()
if first_endpoint == second_endpoint:
return True # one-edge bicomp
if face_handle[first_endpoint].first_endpoint() != v and \
face_handle[first_endpoint].second_endpoint() != v:
return True
return False
