testing my 2 factor conjecture

cogirth_callback.sage

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+from sage.all import *
+from sage.matroids.all import *
+from sage.graphs.all import *
+import gurobipy as gp
+from gurobipy import GRB
+
+env = gp.Env(empty=True)
+env.setParam("OutputFlag",0)
+env.start()
+
+def base_hittingset_with_callback(M, integral=true):
+    # model
+    model = gp.Model("mip1",env=env)
+    groundset = M.groundset()
+    x = dict()
+    if integral:
+        for e in groundset: x[e]=model.addVar(vtype=GRB.BINARY)
+    else:
+        for e in groundset: x[e]=model.addVar(vtype=GRB.CONTINUOUS,lb=0,ub=1)
+    # there is no lazy constraint for LP...
+    for B in M.bases():
+        model.addConstr(gp.quicksum([x[e] for e in B])>=1)
+    model.setObjective(gp.quicksum([x[e] for e in groundset]), GRB.MINIMIZE)
+    # callback
+    def callback_func(model, where):
+        if integral and where == GRB.Callback.MIPSOL:
+            sol_values = {key: model.cbGetSolution(var) 
+                          for key, var in x.items()}
+            # find min weight base in the matroid
+            base = frozenset()
+            minweight=0
+            for e in sorted(groundset, key=lambda ee: sol_values[ee]):
+                if M.is_independent(base.union([e])):
+                    base=base.union([e])
+                    minweight=minweight+sol_values[e]
+            if minweight < 1:
+                model.cbLazy(gp.quicksum([x[e] for e in base])>=1)
+    # solve
+    if integral:
+        model.Params.Heuristics = 0
+        model.Params.LazyConstraints = 1
+        model.optimize(callback_func)
+    else:
+        model.optimize()
+    return model.ObjVal
+
+# tests
+if __name__ == "__main__":
+    def cogirthip(bases, integral=true):
+        model = gp.Model("mip1",env=env)
+        groundset=frozenset()
+        for B in bases: groundset=groundset|frozenset(B)
+        x = dict()
+        if integral:
+            for e in groundset: x[e]=model.addVar(vtype=GRB.BINARY)
+        else:
+            for e in groundset: x[e]=model.addVar(vtype=GRB.CONTINUOUS,lb=0)
+        model.setObjective(gp.quicksum([x[e] for e in groundset]), GRB.MINIMIZE)
+        for B in bases:
+            model.addConstr(gp.quicksum([x[e] for e in B])>=1)
+        model.optimize()
+        return model.ObjVal
+    f = lambda g: g.is_connected()
+    for N in range(4,10):
+        for g in filter(f, graphs(N)):
+            M=Matroid(g)
+            cb=base_hittingset_with_callback(M)
+            bf=cogirthip(M.bases())
+            if randint(0,100)==1:
+                print(f"callback:{cb}, bf:{bf}")
+            if abs(cb-bf) > 0.01:
+                print(f"callback:{cb}, bf:{bf}")
+                exit(1)