386 lines
11 KiB
Python
386 lines
11 KiB
Python
|
#!/usr/bin/env python3
|
||
|
|
|
||
|
|
"""
|
||
|
|
Calculate maximum weighted matching of graphs in DIMACS format.
|
||
|
|
"""
|
||
|
|
|
||
|
|
from __future__ import annotations
|
||
|
|
|
||
|
|
import sys
|
||
|
|
import argparse
|
||
|
|
import math
|
||
|
|
import os.path
|
||
|
|
from typing import Optional, TextIO
|
||
|
|
|
||
|
|
from max_weight_matching import (
|
||
|
|
maximum_weight_matching,
|
||
|
|
adjust_weights_for_maximum_cardinality_matching)
|
||
|
|
|
||
|
|
|
||
|
|
def parse_int_or_float(s: str) -> int|float:
|
||
|
|
"""Convert a string to integer or float value."""
|
||
|
|
try:
|
||
|
|
return int(s)
|
||
|
|
except ValueError:
|
||
|
|
pass
|
||
|
|
return float(s)
|
||
|
|
|
||
|
|
|
||
|
|
def read_dimacs_graph(f: TextIO) -> list[tuple[int, int, int|float]]:
|
||
|
|
"""Read a graph in DIMACS edge list format."""
|
||
|
|
|
||
|
|
edges: list[tuple[int, int, float]] = []
|
||
|
|
|
||
|
|
for s in f:
|
||
|
|
words = s.strip().split()
|
||
|
|
|
||
|
|
if not words[0]:
|
||
|
|
# Skip empty line.
|
||
|
|
continue
|
||
|
|
|
||
|
|
if words[0].startswith("c"):
|
||
|
|
# Skip comment line.
|
||
|
|
pass
|
||
|
|
|
||
|
|
elif words[0] == "p":
|
||
|
|
# Handle "problem" line.
|
||
|
|
if len(words) != 4:
|
||
|
|
raise ValueError(
|
||
|
|
f"Expecting DIMACS edge format but got {s.strip()!r}")
|
||
|
|
if words[1] != "edge":
|
||
|
|
raise ValueError(
|
||
|
|
f"Expecting DIMACS edge format but got {words[1]!r}")
|
||
|
|
|
||
|
|
elif words[0] == "e":
|
||
|
|
# Handle "edge" line.
|
||
|
|
if len(words) != 4:
|
||
|
|
raise ValueError(f"Expecting edge but got {s.strip()!r}")
|
||
|
|
i = int(words[1])
|
||
|
|
j = int(words[2])
|
||
|
|
w = parse_int_or_float(words[3])
|
||
|
|
edges.append((i, j, w))
|
||
|
|
|
||
|
|
else:
|
||
|
|
raise ValueError(f"Unknown line type {words[0]!r}")
|
||
|
|
|
||
|
|
return edges
|
||
|
|
|
||
|
|
|
||
|
|
def read_dimacs_graph_file(filename: str) -> list[tuple[int, int, int|float]]:
|
||
|
|
"""Read a graph from file or stdin."""
|
||
|
|
if filename:
|
||
|
|
with open(filename, "r") as f:
|
||
|
|
try:
|
||
|
|
return read_dimacs_graph(f)
|
||
|
|
except ValueError as exc:
|
||
|
|
raise ValueError(f"{exc} in {filename!r}") from None
|
||
|
|
else:
|
||
|
|
try:
|
||
|
|
return read_dimacs_graph(sys.stdin)
|
||
|
|
except ValueError as exc:
|
||
|
|
raise ValueError(f"{exc} in (stdin)") from None
|
||
|
|
|
||
|
|
|
||
|
|
def read_dimacs_matching(
|
||
|
|
f: TextIO
|
||
|
|
) -> tuple[int|float, list[tuple[int, int]]]:
|
||
|
|
"""Read a matching solution in DIMACS format."""
|
||
|
|
|
||
|
|
have_weight = False
|
||
|
|
weight: int|float = 0
|
||
|
|
pairs: list[tuple[int, int]] = []
|
||
|
|
|
||
|
|
for s in f:
|
||
|
|
words = s.strip().split()
|
||
|
|
|
||
|
|
if not words[0]:
|
||
|
|
# Skip empty line.
|
||
|
|
continue
|
||
|
|
|
||
|
|
if words[0].startswith("c"):
|
||
|
|
# Skip comment line.
|
||
|
|
pass
|
||
|
|
|
||
|
|
elif words[0] == "s":
|
||
|
|
# Handle "solution" line.
|
||
|
|
if len(words) != 2:
|
||
|
|
raise ValueError(
|
||
|
|
f"Expecting solution line but got {s.strip()}")
|
||
|
|
if have_weight:
|
||
|
|
raise ValueError("Duplicate solution line")
|
||
|
|
have_weight = True
|
||
|
|
weight = parse_int_or_float(words[1])
|
||
|
|
|
||
|
|
elif words[0] == "m":
|
||
|
|
# Handle "matching" line.
|
||
|
|
if len(words) != 3:
|
||
|
|
raise ValueError(
|
||
|
|
f"Expecting matched edge but got {s.strip()}")
|
||
|
|
i = int(words[1])
|
||
|
|
j = int(words[2])
|
||
|
|
pairs.append((i, j))
|
||
|
|
|
||
|
|
else:
|
||
|
|
raise ValueError(f"Unknown line type {words[0]!r}")
|
||
|
|
|
||
|
|
if not have_weight:
|
||
|
|
raise ValueError("Missing solution line")
|
||
|
|
|
||
|
|
return (weight, pairs)
|
||
|
|
|
||
|
|
|
||
|
|
def read_dimacs_matching_file(
|
||
|
|
filename: str
|
||
|
|
) -> tuple[int|float, list[tuple[int, int]]]:
|
||
|
|
"""Read a matching from file."""
|
||
|
|
with open(filename, "r") as f:
|
||
|
|
try:
|
||
|
|
return read_dimacs_matching(f)
|
||
|
|
except ValueError as exc:
|
||
|
|
raise ValueError(f"{exc} in {filename!r}") from None
|
||
|
|
|
||
|
|
|
||
|
|
def write_dimacs_matching(
|
||
|
|
f: TextIO,
|
||
|
|
weight: int|float,
|
||
|
|
pairs: list[tuple[int, int]]
|
||
|
|
) -> None:
|
||
|
|
"""Write a matching solution in DIMACS format."""
|
||
|
|
|
||
|
|
if isinstance(weight, int):
|
||
|
|
print("s", weight, file=f)
|
||
|
|
else:
|
||
|
|
print("s", f"{weight:.12g}", file=f)
|
||
|
|
|
||
|
|
for (i, j) in pairs:
|
||
|
|
print("m", i, j, file=f)
|
||
|
|
|
||
|
|
|
||
|
|
def write_dimacs_matching_file(
|
||
|
|
filename: str,
|
||
|
|
weight: int|float,
|
||
|
|
pairs: list[tuple[int, int]]
|
||
|
|
) -> None:
|
||
|
|
"""Write a matching to file or stdout."""
|
||
|
|
if filename:
|
||
|
|
with open(filename, "x") as f:
|
||
|
|
write_dimacs_matching(f, weight, pairs)
|
||
|
|
else:
|
||
|
|
write_dimacs_matching(sys.stdout, weight, pairs)
|
||
|
|
|
||
|
|
|
||
|
|
def calc_matching_weight(
|
||
|
|
edges: list[tuple[int, int, int|float]],
|
||
|
|
pairs: list[tuple[int, int]]
|
||
|
|
) -> int|float:
|
||
|
|
"""Verify that the matching is valid and calculate its weight.
|
||
|
|
|
||
|
|
Matched pairs are assumed to be in the same order as edges.
|
||
|
|
"""
|
||
|
|
|
||
|
|
weight: int|float = 0
|
||
|
|
|
||
|
|
edge_pos = 0
|
||
|
|
for pair in pairs:
|
||
|
|
while edge_pos < len(edges):
|
||
|
|
if edges[edge_pos][0:2] == pair:
|
||
|
|
break
|
||
|
|
edge_pos += 1
|
||
|
|
assert edge_pos <= len(edges)
|
||
|
|
(i, j, w) = edges[edge_pos]
|
||
|
|
assert pair == (i, j)
|
||
|
|
weight += w
|
||
|
|
edge_pos += 1
|
||
|
|
|
||
|
|
return weight
|
||
|
|
|
||
|
|
|
||
|
|
def generate_matching(
|
||
|
|
input_filename: str,
|
||
|
|
output_filename: str,
|
||
|
|
maxcard: bool
|
||
|
|
) -> None:
|
||
|
|
"""Calculate matching of one graph instance."""
|
||
|
|
|
||
|
|
edges = read_dimacs_graph_file(input_filename)
|
||
|
|
|
||
|
|
if maxcard:
|
||
|
|
edges_adj = adjust_weights_for_maximum_cardinality_matching(edges)
|
||
|
|
pairs = maximum_weight_matching(edges_adj)
|
||
|
|
else:
|
||
|
|
pairs = maximum_weight_matching(edges)
|
||
|
|
|
||
|
|
weight = calc_matching_weight(edges, pairs)
|
||
|
|
|
||
|
|
write_dimacs_matching_file(output_filename, weight, pairs)
|
||
|
|
|
||
|
|
|
||
|
|
def run_generate(
|
||
|
|
filenames: list[str],
|
||
|
|
outdir: Optional[str],
|
||
|
|
maxcard: bool
|
||
|
|
) -> int:
|
||
|
|
"""Calculate matching(s) and write output to disk or stdout."""
|
||
|
|
|
||
|
|
if len(filenames) == 0:
|
||
|
|
# Read from stdin; write to stdout.
|
||
|
|
generate_matching("", "", maxcard)
|
||
|
|
|
||
|
|
elif not outdir:
|
||
|
|
# Read from file, write to stdout.
|
||
|
|
assert len(filenames) == 1
|
||
|
|
generate_matching(filenames[0], "", maxcard)
|
||
|
|
|
||
|
|
else:
|
||
|
|
# Read from file, write to file.
|
||
|
|
for filename in filenames:
|
||
|
|
output_filename = os.path.join(
|
||
|
|
outdir,
|
||
|
|
os.path.splitext(os.path.basename(filename))[0] + ".out")
|
||
|
|
print(f"Processing {filename!r} -> {output_filename!r} ...",
|
||
|
|
end=" ")
|
||
|
|
sys.stdout.flush()
|
||
|
|
|
||
|
|
generate_matching(filename, output_filename, maxcard)
|
||
|
|
|
||
|
|
print(" OK")
|
||
|
|
sys.stdout.flush()
|
||
|
|
|
||
|
|
return 0
|
||
|
|
|
||
|
|
|
||
|
|
def verify_matching(filename: str, maxcard: bool, wfactor: float) -> bool:
|
||
|
|
"""Verify matching of one graph instance."""
|
||
|
|
|
||
|
|
print("Verifying", repr(filename), "...", end=" ")
|
||
|
|
sys.stdout.flush()
|
||
|
|
|
||
|
|
matching_filename = os.path.splitext(filename)[0] + ".out"
|
||
|
|
|
||
|
|
edges = read_dimacs_graph_file(filename)
|
||
|
|
(gold_weight, gold_pairs) = read_dimacs_matching_file(matching_filename)
|
||
|
|
|
||
|
|
edges_adj = edges
|
||
|
|
|
||
|
|
if wfactor != 1.0:
|
||
|
|
if wfactor.is_integer():
|
||
|
|
wfactor = round(wfactor)
|
||
|
|
edges_adj = [(i, j, w * wfactor) for (i, j, w) in edges_adj]
|
||
|
|
|
||
|
|
if maxcard:
|
||
|
|
edges_adj = adjust_weights_for_maximum_cardinality_matching(edges_adj)
|
||
|
|
|
||
|
|
pairs = maximum_weight_matching(edges_adj)
|
||
|
|
weight = calc_matching_weight(edges, pairs)
|
||
|
|
|
||
|
|
if maxcard:
|
||
|
|
if len(pairs) != len(gold_pairs):
|
||
|
|
print("FAILED",
|
||
|
|
f"(got {len(pairs)} pairs, expected {len(gold_pairs)}")
|
||
|
|
return False
|
||
|
|
|
||
|
|
if isinstance(weight, int) and isinstance(gold_weight, int):
|
||
|
|
good = (weight == gold_weight)
|
||
|
|
else:
|
||
|
|
good = math.isclose(weight, gold_weight, rel_tol=1e-9, abs_tol=1e-9)
|
||
|
|
|
||
|
|
if not good:
|
||
|
|
print(f"FAILED (got weight {weight}, expected {gold_weight}")
|
||
|
|
return False
|
||
|
|
|
||
|
|
print("OK")
|
||
|
|
return True
|
||
|
|
|
||
|
|
|
||
|
|
def run_verify(filenames: list[str], maxcard: bool, wfactor: float) -> int:
|
||
|
|
"""Verify matching(s)."""
|
||
|
|
|
||
|
|
num_passed = 0
|
||
|
|
failed_tests: list[str] = []
|
||
|
|
|
||
|
|
for filename in filenames:
|
||
|
|
if verify_matching(filename, maxcard, wfactor):
|
||
|
|
num_passed += 1
|
||
|
|
else:
|
||
|
|
failed_tests.append(filename)
|
||
|
|
sys.stdout.flush()
|
||
|
|
|
||
|
|
print("done.")
|
||
|
|
print(num_passed, "tests passed")
|
||
|
|
if failed_tests:
|
||
|
|
print(len(failed_tests), "tests failed:")
|
||
|
|
for filename in failed_tests:
|
||
|
|
print(" ", filename, "FAILED")
|
||
|
|
else:
|
||
|
|
print("All tests passed")
|
||
|
|
sys.stdout.flush()
|
||
|
|
|
||
|
|
return 1 if failed_tests else 0
|
||
|
|
|
||
|
|
|
||
|
|
def main() -> int:
|
||
|
|
"""Main program."""
|
||
|
|
|
||
|
|
parser = argparse.ArgumentParser()
|
||
|
|
parser.description = (
|
||
|
|
"Calculate maximum weighted matching of graphs in DIMACS format.")
|
||
|
|
|
||
|
|
parser.add_argument("--stdin",
|
||
|
|
action="store_true",
|
||
|
|
help="read graph from stdin")
|
||
|
|
parser.add_argument("--verify",
|
||
|
|
action="store_true",
|
||
|
|
help="verify existing output file(s)")
|
||
|
|
parser.add_argument("--maxcard",
|
||
|
|
action="store_true",
|
||
|
|
help="calculate maximum-cardinality matching")
|
||
|
|
parser.add_argument("--wfactor",
|
||
|
|
action="store",
|
||
|
|
type=float,
|
||
|
|
default=1.0,
|
||
|
|
help="adjust weights by specified factor")
|
||
|
|
parser.add_argument("--outdir",
|
||
|
|
action="store",
|
||
|
|
type=str,
|
||
|
|
help="directory to write output")
|
||
|
|
parser.add_argument("input",
|
||
|
|
nargs="*",
|
||
|
|
help="input file(s)")
|
||
|
|
|
||
|
|
args = parser.parse_args()
|
||
|
|
|
||
|
|
if args.stdin and args.verify:
|
||
|
|
print("ERROR: Can not verify when reading from stdin",
|
||
|
|
file=sys.stderr)
|
||
|
|
return 1
|
||
|
|
|
||
|
|
if (not args.stdin) and (not args.input):
|
||
|
|
parser.print_help(sys.stderr)
|
||
|
|
print(file=sys.stderr)
|
||
|
|
print("ERROR: Specify either --stdin or at least one input file",
|
||
|
|
file=sys.stderr)
|
||
|
|
return 1
|
||
|
|
|
||
|
|
if args.stdin and args.input:
|
||
|
|
print("ERROR: Specify either --stdin or input files, not both",
|
||
|
|
file=sys.stderr)
|
||
|
|
return 1
|
||
|
|
|
||
|
|
if len(args.input) > 1 and (not args.verify) and (not args.outdir):
|
||
|
|
print("ERROR: Need --outdir or --verify to process multiple inputs",
|
||
|
|
file=sys.stderr)
|
||
|
|
return 1
|
||
|
|
|
||
|
|
try:
|
||
|
|
if args.verify:
|
||
|
|
return run_verify(args.input, args.maxcard, args.wfactor)
|
||
|
|
else:
|
||
|
|
return run_generate(args.input, args.outdir, args.maxcard)
|
||
|
|
except (OSError, ValueError) as exc:
|
||
|
|
print("ERROR:", exc, file=sys.stderr)
|
||
|
|
return 1
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
sys.exit(main())
|