60 lines
2.0 KiB
Python
60 lines
2.0 KiB
Python
# cogirth-packing gap of projections of graphic matroids
|
|
|
|
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 cogirthip(bases, integral=true):
|
|
model = gp.Model("mip1",env=env)
|
|
# model.Params.LogToConsole = 0
|
|
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
|
|
|
|
|
|
cnt=0 # actual number of instances tested
|
|
maxgap=0
|
|
f = lambda g: g.is_connected()
|
|
for N in range(4,10):
|
|
for g in filter(f, graphs(N)):
|
|
A=g.incidence_matrix()
|
|
n,m = A.dimensions()
|
|
# enumerate all vectors in F_2^n with even number of 1s
|
|
V = VectorSpace(GF(2), N)
|
|
for v in filter(lambda v: v.hamming_weight() % 2 == 0 and v!=0, V):
|
|
cnt=cnt+1
|
|
v_col=matrix(v).transpose()
|
|
A_t=A.augment(v_col)
|
|
# print(A_t)
|
|
M=Matroid(matrix=A_t,field=GF(2))/m #contract the last element
|
|
# print(M)
|
|
bases=M.bases()
|
|
strength=cogirthip(bases,integral=false)
|
|
cogirth =cogirthip(bases,integral=true)
|
|
gap = cogirth/strength
|
|
# maxgap=max(gap,maxgap)
|
|
if gap > maxgap:
|
|
maxgap = gap
|
|
print(f"find a large gap: {gap}")
|
|
with open("projection.out", "a") as file:
|
|
file.write("##################################\n"
|
|
+str(gap)+"\n"+str(A_t)
|
|
+"\n##################################\n")
|
|
if cnt%100==0:
|
|
print(f"#{cnt}, n={n}, max gap = {maxgap}") |