62 lines
1.8 KiB
Python
62 lines
1.8 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 representative_vectors(m, n):
|
|
for w1 in range(m+1):
|
|
for w2 in range(n+1):
|
|
v = [0]*(m+n)
|
|
v[:w1] = [1]*w1
|
|
v[m:m+w2] = [1]*w2
|
|
yield tuple(v)
|
|
|
|
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
|
|
# f = lambda g: g.is_connected()
|
|
for N in range(2,10):
|
|
for M in range(N,10):
|
|
g=graphs.CompleteBipartiteGraph(N,M)
|
|
A=g.incidence_matrix()
|
|
n,m = A.dimensions()
|
|
maxgap = 0
|
|
for v in representative_vectors(N,M):
|
|
# cnt=cnt+1
|
|
v_col=matrix(v).transpose()
|
|
A_t=A.augment(v_col)
|
|
# print(A_t)
|
|
MM=Matroid(matrix=A_t,field=GF(2))/m #contract the last element
|
|
# print(M)
|
|
bases=MM.bases()
|
|
strength=cogirthip(bases,integral=false)
|
|
cogirth =cogirthip(bases,integral=true)
|
|
gap = cogirth/strength
|
|
if gap > maxgap:
|
|
maxgap = gap
|
|
maxcol = v
|
|
|
|
print(f"K_{{{N},{M}}}, gap = {maxgap}, column = {maxcol}")
|