def display_size_matching_vs_greedy(nmax,p,p2,inst,inter):
plt.figure()
ax = plt.subplot(111)
width=5
stat=np.zeros(shape=(inter,inst))
stat2=np.zeros(shape=(inter,inst))
stat3=np.zeros(shape=(inter,inst))
stat4=np.zeros(shape=(inter,inst))
for i in range(1,inter+1):
for j in range(1,inst+1):
g=rndm(int(i*nmax/(inter+1)),p)
m=len(algo_matching(g))
n=len(algo_greedy(g))
g2=rndm(int(i*nmax/(inter+1)),p2)
q=len(algo_matching(g2))
r=len(algo_greedy(g2))
stat[i-1,j-1]= m
stat2[i-1,j-1]= n
stat3[i-1,j-1]= q
stat4[i-1,j-1]= r
stat,stat2,stat3,stat4=np.mean(stat,axis=1),np.mean(stat2,axis=1),np.mean(stat3,axis=1) ,np.mean(stat4,axis=1)
ax.bar([int(i*nmax/(inter+1)) for i in range(1,inter+1)],list(stat2),width,label='Algo glouton, p='+str(p))
ax.bar([int(i*nmax/(inter+1))+width for i in range(1,inter+1)],list(stat3),width,label='Algo glouton, p='+str(p2))
ax.bar([int(i*nmax/(inter+1))+2*width for i in range(1,inter+1)],list(stat),width,label='Algo couplage, p='+str(p))
ax.bar([int(i*nmax/(inter+1))+3*width for i in range(1,inter+1)],list(stat4),width,label='Algo couplage, p='+str(p2))
plt.legend()
plt.ylabel('Taille de la couverture renvoyée')
plt.xlabel('Taille des instances de Graph (nb de sommets)')
plt.show()
def find_couv_born(g,c_opt,c_curent):
binf=g.graph_lower_bound()+len(c_curent)
solrea=algo_greedy(g)+list(c_curent)
bsup=len(solrea)
if (bsup<len(c_opt)):
c_opt.clear()
c_opt.update(solrea)
if binf<len(c_opt) and (binf<bsup):
e=g.first_edge()
if e is not None:
i,j=e
gi=g.copy()
gi.delete_node(i)
gj=g.copy()
gj.delete_node(j)
c_i=c_curent.copy()
c_i.add(i)
c_j=c_curent.copy()
c_j.add(j)
binfi=gi.graph_lower_bound()+len(c_i)
binfj=gj.graph_lower_bound()+len(c_j)
if binfi<binfj :
find_couv_born(gi,c_opt,c_i)
find_couv_born(gj,c_opt,c_j)
else:
find_couv_born(gj,c_opt,c_j)
find_couv_born(gi,c_opt,c_i)
else:
if len(c_curent) < len(c_opt):
c_opt.clear()
c_opt.update(c_curent)
def iterative_branch_and_bound(g):
global minactuel
c_opt=np.linspace(0,1,len(g._out)+1)
stack = deque([g])
if g is None:
return
while stack:
gcurrent = stack.pop()
#print("graphe actuel:")
#print(gcurrent._out)
e=gcurrent.first_edge()
visites=gcurrent._visites
solrea=algo_greedy(gcurrent)+visites
#print("minactuel: "+str(minactuel))
#print("SOLREA --------")
#print(solrea)
bornesup=len(solrea)
borneinf=gcurrent.graph_lower_bound()+len(visites)
#print("Borne inf:")
#print(borneinf)
if (borneinf>=minactuel):
#print(borneinf)
#print(minactuel)
continue
#if (bornesup>minactuel):
# continue
if (bornesup<len(c_opt)):
c_opt=set(solrea)
minactuel=bornesup
if (bornesup<borneinf):
c_opt=set(solrea)
minactuel=bornesup
#print("Borne inf: "+str(borneinf))
if e is None:
if (len(gcurrent._visites) < len(c_opt)):
c_opt=set(gcurrent._visites)
if (borneinf<minactuel):
minactuel=borneinf
else:
i,j=e
#print("(i,j): "+str((i,j)))
gi,gj=gcurrent.copy(),gcurrent.copy()
gi.delete_node(i)
gj.delete_node(j)
gi._visites.append(i)
gj._visites.append(j)
binfi=gi.graph_lower_bound()
binfj=gj.graph_lower_bound()
#print("binfi, binfj: "+str(binfi)+" "+str(binfj))
#print(gi._out)
#print(gj._out)
if (binfi<binfj):
stack.extend([gj,gi])
else:
stack.extend([gi,gj])
return c_opt
def display_time_matching_vs_greedy(nmax,p,p2,inst,inter):
stat=np.zeros(shape=(inter,inst))
stat2=np.zeros(shape=(inter,inst))
stat3=np.zeros(shape=(inter,inst))
stat4=np.zeros(shape=(inter,inst))
for i in range(1,inter+1):
for j in range(1,inst+1):
g=rndm(int(i*nmax/(inter+1)),p)
start_time = time.time()
algo_matching(g)
end_time = time.time()
start_time2 = time.time()
algo_greedy(g)
end_time2 = time.time()
g2=rndm(int(i*nmax/(inter+1)),p2)
start_time3 = time.time()
algo_matching(g2)
end_time3 = time.time()
start_time4 = time.time()
algo_greedy(g2)
end_time4 = time.time()
stat[i-1,j-1]= end_time -start_time
stat2[i-1,j-1]= end_time2 -start_time2
stat3[i-1,j-1]= end_time3 -start_time3
stat4[i-1,j-1]= end_time4 -start_time4
stat,stat2,stat3,stat4=np.mean(stat,axis=1),np.mean(stat2,axis=1),np.mean(stat3,axis=1) ,np.mean(stat4,axis=1)
plt.plot([int(i*nmax/(inter+1)) for i in range(1,inter+1)],list(stat4),label='Algorithme glouton, p='+str(p2))
plt.plot([int(i*nmax/(inter+1)) for i in range(1,inter+1)],list(stat2),label='Algorithme glouton, p='+str(p))
plt.plot([int(i*nmax/(inter+1)) for i in range(1,inter+1)],list(stat3),label='Algorithme de couplage, p='+str(p2))
plt.plot([int(i*nmax/(inter+1)) for i in range(1,inter+1)],list(stat),label='Algorithme de couplage, p='+str(p))
plt.legend()
plt.yscale("log")
plt.ylabel('Moyenne de temps d\'exécution (s)')
plt.xlabel('Taille des instances de graphe (nb de sommets)')
plt.title("Durée d'exécution des algorithmes couplage et glouton ")
plt.show()
def find_couv_born_imp2(g,c_opt,c_curent):
binf=g.graph_lower_bound()+len(c_curent)
solrea=algo_greedy(g)+list(c_curent)
bsup=len(solrea)
if (bsup<len(c_opt)):
c_opt.clear()
c_opt.update(solrea)
if binf<len(c_opt) and (binf<bsup):
e=g.first_edge()
if e is not None:
i,j=e
degi=len(g._out[i])
degj=len(g._out[j])
gi=g.copy()
gi.delete_node(i)
gj=g.copy()
gj.delete_node(j)
c_i=c_curent.copy()
c_i.add(i)
c_j=c_curent.copy()
c_j.add(j)
binfi=gi.graph_lower_bound()+len(c_i)
binfj=gj.graph_lower_bound()+len(c_j)
if binfi<binfj or degi>degj:
find_couv_born_imp2(gi,c_opt,c_i)
c_j.update(set(gj._out[i]))
gj.delete_nodes([i]+gj._out[i])
find_couv_born_imp2(gj,c_opt,c_j)
else:
if binfi>binfj or degi<degj:
find_couv_born_imp2(gj,c_opt,c_j)
c_i.update(set(gi._out[j]))
gi.delete_nodes([j]+gi._out[j])
find_couv_born_imp2(gi,c_opt,c_i)
else:
if len(c_curent) < len(c_opt):
c_opt.clear()
c_opt.update(c_curent)