Add generators: chain, hardcard.f, t.f, tt.f

tests/generate/hardcard.py

@@ -0,0 +1,62 @@
+#!/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.
+ 
+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).
+"""
+
+import argparse
+
+
+def main():
+
+    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()
+

tests/generate/make_slow_graph.py

@@ -70,12 +70,14 @@ def write_dimacs_graph(
 
 
 def make_dense_slow_graph(n: int) -> list[tuple[int, int, int]]:
-    """Generate a dense (not complete) graph with N vertices.
+    """Generate a dense graph with N vertices.
+
+    The graph contains O(n**2) edges and triggers O(n**2) delta steps.
 
     N must be divisible by 4.
 
-    Number of edges = M = (N**2/16 + N/2).
+    Number of edges = M = N**2/16 + N/2
-    Number of delta steps required to solve the matching = (M - 1).
+    Number of delta steps required to solve the matching = M - 1
     """
 
     assert n % 4 == 0
@@ -118,10 +120,12 @@ def make_dense_slow_graph(n: int) -> list[tuple[int, int, int]]:
 def make_sparse_slow_graph(n: int) -> list[tuple[int, int, int]]:
     """Generate a sparse graph with N vertices.
 
+    The graph contains just O(n) edges but still triggers O(n**2) delta steps.
+
     N must be 4 modulo 8.
 
-    Number of edges = M = (5/4 * N - 3).
+    Number of edges = M = 5/4 * N - 3
-    Number of delta steps required to solve the matching ~ (N**2 / 16).
+    Number of delta steps required to solve the matching = N**2/16 + 3/4*N - 3
     """
 
     assert n >= 12
@@ -233,20 +237,40 @@ def make_sparse_slow_graph(n: int) -> list[tuple[int, int, int]]:
     return edges
 
 
+def make_chain_graph(n: int) -> list[tuple[int, int, int]]:
+    """Generate a graph with N vertices connected into a simple chain.
+
+    The graph contains O(n) edges and triggers O(n) delta steps.
+    To force a large number of delta steps, N must be even.
+
+    Number of edges = M = N - 1
+    Number of delta steps required to solve the matching = N - 2
+    """
+
+    assert n >= 2
+
+    edges: list[tuple[int, int, int]] = []
+
+    for i in range(n - 1):
+        w = n + i % 2
+        edges.append((i, i + 1, w))
+
+    return edges
+
+
 def main() -> int:
     """Main program."""
 
     parser = argparse.ArgumentParser()
     parser.description = "Generate a difficult graph."
 
-    parser.add_argument("--structure",
-                        action="store",
-                        choices=("sparse", "dense"),
-                        default="sparse",
-                        help="choose graph structure")
     parser.add_argument("--check",
                         action="store_true",
                         help="solve the matching and count delta steps")
+    parser.add_argument("structure",
+                        action="store",
+                        choices=("sparse", "dense", "chain"),
+                        help="graph structure")
     parser.add_argument("n",
                         action="store",
                         type=int,
@@ -283,6 +307,18 @@ def main() -> int:
 
         edges = make_dense_slow_graph(args.n)
 
+    elif args.structure == "chain":
+
+        if args.n < 2:
+            print("ERROR: Number of vertices must be >= 2", file=sys.stderr)
+            return 1
+
+        if args.n % 2 != 0:
+            print("ERROR: Number of vertices must be even", file=sys.stderr)
+            return 1
+
+        edges = make_chain_graph(args.n)
+
     else:
         assert False
 

tests/generate/triangles.py

@@ -0,0 +1,92 @@
+#!/usr/bin/env python3
+
+r"""
+Generate a graph that consists of interconnected triangles.
+
+The graph is a chain of triangles, connected either at 1 vertex
+or at 3 vertices.
+
+Example of triangles connected at one vertex:
+
+   [1]-------[4]       [7]           [10]-------[13]
+    | \       | \       | \         / |          |  \
+    |  [3]    |  [6]    |  [9]---[12] |          |  [15]
+    | /       | /       | /         \ |          |  /
+   [2]       [5]-------[8]           [11]       [14]-----
+
+Example of triangles connected at 3 vertices:
+
+   [1]-------[4]-------[7]-------[10]-------[13]
+    | \       | \       | \       |  \       |  \
+    |  [3]----|--[6]----|--[9]----|--[12]----|--[15]
+    | /       | /       | /       |  /       |  /
+   [2]-------[5]-------[8]-------[11]-------[14]
+
+Based on Fortran programs "t.f" and "tt.f"
+by N. Ritchey and B. Mattingly, Youngstown State University, 1991.
+
+Rewritten in Python by Joris van Rantwijk, 2023.
+
+For the original Fortran code, see
+  http://archive.dimacs.rutgers.edu/pub/netflow/generators/matching/t.f
+  http://archive.dimacs.rutgers.edu/pub/netflow/generators/matching/tt.f
+
+Output to stdout in DIMACS edge format.
+All edges have weight 1.
+
+Input parameter:    K = number of triangles
+Input parameter:    C = 1 to connect triangles by 1 corner
+                    C = 3 to connect triangles by 3 corners
+Number of vertices: N = 3*K
+Number of edges:    M = 3*K + C*(K-1)
+"""
+
+import argparse
+
+
+def main():
+
+    parser = argparse.ArgumentParser()
+    parser.description = (
+        "Generate a graph that consists of interconnected triangles.")
+
+    parser.add_argument("k",
+                        action="store",
+                        type=int,
+                        help="size parameter; N = 3*K, M = 3*K+C*(K-1)")
+    parser.add_argument("c",
+                        action="store",
+                        type=int,
+                        choices=(1, 3),
+                        help="number of corners to connect")
+
+    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 = 3 * k
+    m = 3 * k + args.c * (k - 1)
+
+    print(f"p edge {n} {m}")
+
+    for i in range(k):
+        x = 3 * i + 1
+        print(f"e {x} {x+1} 1")
+        print(f"e {x} {x+2} 1")
+        print(f"e {x+1} {x+2} 1")
+
+    if args.c == 1:
+        for i in range(k - 1):
+            x = 3 * i + i % 3 + 1
+            print(f"e {x} {x+3} 1")
+
+    elif args.c == 3:
+        for x in range(1, 3 * k - 2):
+            print(f"e {x} {x+3} 1")
+
+
+if __name__ == "__main__":
+    main()