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maximum-weight-matching/tests/generate/hardcard.py

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#!/usr/bin/env python3
"""
Generate a graph that belongs to a class of worst-case graphs
described by Gabow.
Reference: H. N. Gabow, "An efficient implementation of Edmonds'
algorithm for maximum matching on graphs", JACM 23
(1976), pp. 221-234.
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Based on Fortran program "hardcard.f" by R. Bruce Mattingly, 1991.
Rewritten in Python by Joris van Rantwijk, 2023.
For the original Fortran code, see
http://archive.dimacs.rutgers.edu/pub/netflow/generators/matching/hardcard.f
Output to stdout in DIMACS edge format.
All edges have weight 1.
Input parameter: K
Number of vertices: N = 6*K
Number of edges: M = 8*K*K
The graph is constructed so that vertices 1 - 4*K form a complete subgraph.
For 1 <= I <= 2*K, vertex (2*I-1) is joined to vertex (4*K+I).
"""
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import sys
import argparse
def main():
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"""Main program."""
parser = argparse.ArgumentParser()
parser.description = "Generate a difficult graph"
parser.add_argument("k",
action="store",
type=int,
help="size parameter; N = 6*K, M = 4*K*K")
args = parser.parse_args()
if args.k < 1:
print("ERROR: K must be at least 1", file=sys.stderr)
sys.exit(1)
k = args.k
n = 6 * k
m = 8 * k * k
print(f"p edge {n} {m}")
for i in range(1, 4*k):
for j in range(i + 1, 4*k + 1):
print(f"e {i} {j} 1")
if i % 2 == 1:
j = 4 * k + (i + 1) // 2
print(f"e {i} {j} 1")
if __name__ == "__main__":
main()