def read_cnf_file(filename: str) -> CNF:
with open(filename, "r") as cnfFile:
lines = list(filter(lambda line: line.strip(), cnfFile.readlines()))
cnf = CNF()
cnf.clauses = list(list())
for line in lines:
if len(line) > 20 and line[:20] == "c automorphism group":
cnf.automorphism_group_size = int(line.split()[-1])
elif line[0] == "c":
continue
elif line[0] == "p":
metadata = line.split()
cnf.number_of_literals = int(metadata[2])
cnf.number_of_clauses = int(metadata[3])
else:
cnf.clauses.append([int(x) for x in line.split()[:-1]])
return cnf
def produce_cnf(
problemType: str,
pattern_filename: str,
graph_filename: str,
target_dir: str = suggested_dir,
compute_automorph_size=True,
) -> str:
cnf_file_name = "{}/cnf-{}-h-{}-g-{}.cnf".format(
target_dir,
problemType.strip("--"),
pattern_filename.split("/")[-1].split(".")[0],
graph_filename.split("/")[-1].split(".")[0],
)
# if file already exists, return filename.
if path.isfile(cnf_file_name):
return cnf_file_name
# read input files
pattern = read_graph(pattern_filename)
graph = read_graph(graph_filename)
# create CNF:
cnf = CNF(number_of_literals=pattern.number_of_verticies *
graph.number_of_verticies,
clauses=list(list()))
def pair(a: int, v: int) -> int:
return (a - 1) * graph.number_of_verticies + v
# adding clauses to guarantee that each a is mapped to at least one vertex
for a in range(1, pattern.number_of_verticies + 1):
cnf.clauses.append(
list(pair(a, v) for v in range(1, graph.number_of_verticies + 1)))
for a in range(1, pattern.number_of_verticies + 1):
for v in range(1, graph.number_of_verticies + 1):
for w in range(v + 1, graph.number_of_verticies + 1):
cnf.clauses.append([-pair(a, v), -pair(a, w)])
# dictionary, to use for finding non existant pairs:
non_existant_pairs = {}
for i in range(1, graph.number_of_verticies + 1):
non_existant_pairs[i] = list(range(i, graph.number_of_verticies + 1))
for v, w in graph.edges:
assert v < w
non_existant_pairs[v].remove(w)
for a, b in pattern.edges:
for v, ws in non_existant_pairs.items():
for w in ws:
cnf.clauses.append([-pair(a, v), -pair(b, w)])
if pair(a, v) != pair(a, w) or pair(b, w) != pair(b, v):
cnf.clauses.append([-pair(a, w), -pair(b, v)])
# changed second pair to negative, not in the SS notes.
if problemType == "--emb":
for v in range(1, graph.number_of_verticies + 1):
for a in range(1, pattern.number_of_verticies + 1):
for b in range(a + 1, pattern.number_of_verticies + 1):
clause = [-pair(a, v), -pair(b, v)]
if clause not in cnf.clauses:
cnf.clauses.append(clause)
# count the automorphism group size, by counting embeddings of the pattern unto the pattern.
# embed it in a comment comment line on top.
auto_size = 0
if compute_automorph_size:
auto_size_problem = produce_cnf("--emb", pattern_filename,
pattern_filename, target_dir, False)
auto_size = int(count_sharp_file(auto_size_problem)[0])
cnf.number_of_clauses = len(cnf.clauses)
write_cnf_file(cnf, cnf_file_name, auto_size)
return cnf_file_name
