def gen_m_graph(q: ConjunctiveQuery) -> nx.DiGraph:
"""
Computes the M-graph of a given ConjunctiveQuery q.
:param q: A ConjunctiveQuery
:return: Generated M-Graph
"""
atoms = q.get_atoms()
g = nx.DiGraph()
for atom1 in atoms:
g.add_node(atom1)
closure = transitive_closure(set(atom1.variables()),
q.get_consistent_fd())
for atom2 in [atom for atom in atoms if atom != atom1]:
if set(q.get_key_vars(atom2)).issubset(closure):
g.add_edge(atom1, atom2)
return g
def find_bad_internal_fd(
q: ConjunctiveQuery) -> FrozenSet[FunctionalDependency]:
"""
Given a non saturated ConjunctiveQuery, returns the FunctionalDependencies culprit of it's non saturation.
:param q: A ConjunctiveQuery.
:return: A FrozenSet containing the FunctionalDependencies culprit of the non saturation of q.
"""
res = frozenset()
possible_starts = []
possible_ends = []
for fd in q.get_all_fd().set:
if fd.left not in possible_starts:
possible_starts.append(fd.left)
if fd.right not in possible_ends:
possible_ends.append(fd.right)
for left in possible_starts:
for right in possible_ends:
test_fd = FunctionalDependency(left, right)
if fd_is_internal(test_fd, q):
if right not in transitive_closure(set(left),
q.get_consistent_fd()):
res = res.union(frozenset([test_fd]))
return res