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PGM results and bipartite code

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This commit is contained in:
Yu Cong
2025-10-23 10:21:26 +08:00
parent dd06bbec21
commit 301670b350
3 changed files with 179 additions and 5 deletions
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61
bipartite.sage Normal file
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@@ -0,0 +1,61 @@
# 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 = {v}")

108
projection.out Normal file
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@@ -0,0 +1,108 @@
##################################
1.0
[1 0 0 1]
[0 1 0 1]
[0 0 1 0]
[1 1 1 0]
##################################
##################################
1.3333333333333333
[1 0 0 1]
[0 1 0 1]
[0 0 1 1]
[1 1 1 1]
##################################
##################################
1.4999999999999998
[1 0 0 0 1]
[0 1 0 0 1]
[0 0 1 0 1]
[0 0 0 1 1]
[1 1 1 1 0]
##################################
##################################
1.5
[1 1 0 0 0 0 1]
[0 0 1 1 0 0 1]
[0 0 0 0 1 1 1]
[1 0 1 0 1 0 0]
[0 1 0 1 0 1 1]
##################################
##################################
1.7142857142857137
[1 1 0 0 0 0 0 1]
[0 0 1 1 0 0 0 1]
[0 0 0 0 1 1 0 1]
[1 0 1 0 1 0 1 1]
[0 1 0 1 0 1 1 0]
##################################
##################################
1.7142857142857142
[1 1 0 0 0 0 0 1]
[0 0 1 1 0 0 0 1]
[0 0 0 0 1 1 0 1]
[0 0 0 0 0 0 1 1]
[1 0 1 0 1 0 0 0]
[0 1 0 1 0 1 1 0]
##################################
##################################
2.0
[1 1 0 0 0 0 0 0 1]
[0 0 1 1 0 0 0 0 1]
[0 0 0 0 1 1 0 0 1]
[0 0 0 0 0 0 1 1 1]
[1 0 1 0 1 0 1 0 0]
[0 1 0 1 0 1 0 1 0]
##################################
##################################
2.1333333333333337
[1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1]
[0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1]
[0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1]
[0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1]
[0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1]
##################################
##################################
2.1428571428571423
[1 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 1 1 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 1 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 0 1]
[1 0 0 1 0 0 1 0 0 1 0 0 1 0 1]
[0 1 0 0 1 0 0 1 0 0 1 0 0 1 1]
[0 0 1 0 0 1 0 0 1 0 0 1 1 1 0]
##################################
##################################
2.1818181818181817
[1 1 0 0 0 0 0 0 0 0 0 1]
[0 0 1 1 0 0 0 0 0 0 0 1]
[0 0 0 0 1 1 0 0 0 0 0 1]
[0 0 0 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 1 1 0 1]
[1 0 1 0 1 0 0 0 0 0 1 1]
[0 1 0 1 0 0 1 0 1 0 0 0]
[0 0 0 0 0 1 0 1 0 1 1 0]
##################################
##################################
2.181818181818182
[1 1 0 0 0 0 0 0 0 0 0 1]
[0 0 1 1 0 0 0 0 0 0 0 1]
[0 0 0 0 1 1 0 0 0 0 0 1]
[0 0 0 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 1 1 0 1]
[1 0 1 0 1 0 0 0 0 0 1 0]
[0 1 0 1 0 0 1 0 1 0 0 1]
[0 0 0 0 0 1 0 1 0 1 1 0]
##################################
##################################
2.4000000000000004
[1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1]
[1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1]
[0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1]
[0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1]
##################################

15
projection.sage
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@@ -29,8 +29,9 @@ def cogirthip(bases, integral=true):
cnt=0 # actual number of instances tested
maxgap=0
f = lambda g: g.is_connected()
for N in range(8,20):
for N in range(4,10):
for g in filter(f, graphs(N)):
A=g.incidence_matrix()
n,m = A.dimensions()
@@ -47,9 +48,13 @@ for N in range(8,20):
strength=cogirthip(bases,integral=false)
cogirth =cogirthip(bases,integral=true)
gap = cogirth/strength
if gap > 3.01:
print(f"bad example! gap={gap}")
# 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(str(gap)+"\n"+str(A_t)+"\n")
file.write("##################################\n"
+str(gap)+"\n"+str(A_t)
+"\n##################################\n")
if cnt%100==0:
print(f"#{cnt},n={n},m={m}")
print(f"#{cnt}, n={n}, max gap = {maxgap}")