def bornesGloutonTriviale(G, C=[]):
cpt = 0
E = list(G.edges())
couvertures = []
e = E[0]
for i in range(2):
C_temp = C.copy()
C_temp.append(e[i])
Gbis = gr.suppression(gr.copie(G), e[i])
if gr.valeurDegreMax(Gbis) == 0:
couvertures.append(C_temp)
cpt += 1
else:
ac = ma.algo_couplage(Gbis)
ag = ma.algo_glouton(Gbis)
borneInf = len(ac) / 2
borneSup = len(ag)
if borneInf < borneSup:
c, cptemp = bornesGlouton(Gbis, C_temp)
couvertures.append(c)
cpt += cptemp + 1
else:
C_temp = C_temp + ag
couvertures.append(C_temp)
cpt += 1
if len(couvertures) == 0:
return C, cpt
elif len(couvertures) == 1 or (len(couvertures[0]) <= len(couvertures[1])):
C = couvertures[0]
else:
C = couvertures[1]
return C, cpt
def branchementAmeliorePlusPlusBornesGlouton(G, C=[], u=None):
cpt = 0
E = list(G.edges())
G_copie = gr.copie(G)
if u in G_copie.nodes():
gr.suppression(G_copie, u)
E = list(G_copie.edges())
if E == []:
C.append(u)
return C, cpt
couvertures = []
e = E[0]
dico = dict(gr.degres(G))
e_liste = list(e)
if dico[e[0]] < dico[e[1]]:
e_liste[0] = e[1]
e_liste[1] = e[0]
e = tuple(e_liste)
for i in range(2):
C_temp = C.copy()
C_temp.append(e[i])
Gbis = gr.suppression(gr.copie(G), e[i])
if gr.valeurDegreMax(Gbis) == 0:
couvertures.append(C_temp)
cpt += 1
elif dico[e[i]] == 1:
cpt += 1
else:
ac = ma.algo_couplage(Gbis)
ag = ma.algo_glouton(Gbis)
n = len(list(Gbis.nodes()))
m = len(list(Gbis.edges()))
b1 = m / gr.valeurDegreMax(Gbis)
b2 = len(ac) / 2
b3 = (2 * n - 1 - math.sqrt(((2 * n - 1)**2) - (8 * m))) / 2
borneInf = max([b1, b2, b3])
borneSup = len(ag)
if borneInf < borneSup:
if i == 0:
u = None
c, cptemp = branchementAmeliorePlusPlusBornesGlouton(
Gbis, C_temp, u)
elif i == 1:
u = e[0]
c, cptemp = branchementAmeliorePlusPlusBornesGlouton(
Gbis, C_temp, u)
couvertures.append(c)
cpt += cptemp + 1
else:
C_temp = C_temp + ag
couvertures.append(C_temp)
cpt += 1
if len(couvertures) == 0:
return C, cpt
elif len(couvertures) == 1 or (len(couvertures[0]) <= len(couvertures[1])):
C = couvertures[0]
else:
C = couvertures[1]
return C, cpt
def branchementAmelioreBornesGlouton(G, C=[], u=None):
cpt = 0
E = list(G.edges())
G_copie = gr.copie(G)
if u in G_copie.nodes():
gr.suppression(G_copie, u)
E = list(G_copie.edges())
if E == []:
C.append(u)
return C, cpt
couvertures = []
e = E[0]
for i in range(2):
C_temp = C.copy()
C_temp.append(e[i])
Gbis = gr.suppression(gr.copie(G), e[i])
if gr.valeurDegreMax(Gbis) == 0:
couvertures.append(C_temp)
cpt += 1
else:
ac = ma.algo_couplage(Gbis)
ag = ma.algo_glouton(Gbis)
n = len(list(Gbis.nodes()))
m = len(list(Gbis.edges()))
b1 = m / gr.valeurDegreMax(Gbis)
b2 = len(ac) / 2
b3 = (2 * n - 1 - math.sqrt(((2 * n - 1)**2) - (8 * m))) / 2
borneInf = max([b1, b2, b3])
borneSup = len(ag)
if borneInf < borneSup:
if i == 0: # première branche : pas de sommet u à ignorer
u = None
c, cptemp = branchementAmelioreBornesGlouton(
Gbis, C_temp, u)
elif i == 1: # deuxième branche : sommet u à ignorer
u = e[0]
c, cptemp = branchementAmelioreBornesGlouton(
Gbis, C_temp, u)
couvertures.append(c)
cpt += cptemp + 1
else:
C_temp = C_temp + ag
couvertures.append(C_temp)
cpt += 1
if len(couvertures) == 0:
return C, cpt
elif len(couvertures) == 1 or (len(couvertures[0]) <= len(couvertures[1])):
C = couvertures[0]
else:
C = couvertures[1]
return C, cpt
def rapportApproximation(p, Nmax, nbInstances):
x = np.linspace(1, Nmax, nbInstances)
yC = []
yG = []
for i in range(nbInstances):
n = int((i + 1) * Nmax / nbInstances)
g = gr.grapheAlea(n, p)
sol, cpt = branchementAmeliorePlusPlusBornesGlouton(g)
solC = ma.algo_couplage(g)
solG = ma.algo_glouton(g)
yC.append(len(solC) / len(sol))
yG.append(len(solG) / len(sol))
plt.title("Rapport d'approximation")
plt.xlabel("Taille n")
plt.ylabel("r-approché")
plt.plot(x, yC, c='blue', label='algo_couplage')
plt.plot(x, yG, c='red', label='algo_glouton')
plt.legend()
plt.show()
def bornesGlouton(G, C=[]):
cpt = 0
E = list(G.edges())
couvertures = []
e = E[0]
for i in range(2):
C_temp = C.copy()
C_temp.append(e[i])
Gbis = gr.suppression(gr.copie(G), e[i])
if gr.valeurDegreMax(Gbis) == 0:
couvertures.append(C_temp)
cpt += 1
else:
ac = ma.algo_couplage(Gbis)
ag = ma.algo_glouton(Gbis)
n = len(list(Gbis.nodes()))
m = len(list(Gbis.edges()))
b1 = m / gr.valeurDegreMax(Gbis)
b2 = len(ac) / 2
b3 = (2 * n - 1 - math.sqrt(((2 * n - 1)**2) - (8 * m))) / 2
borneInf = max([b1, b2, b3])
borneSup = len(ag)
if borneInf < borneSup:
c, cptemp = bornesGlouton(Gbis, C_temp)
couvertures.append(c)
cpt += cptemp + 1
else:
C_temp = C_temp + ag
couvertures.append(C_temp)
cpt += 1
if len(couvertures) == 0:
return C, cpt
elif len(couvertures) == 1 or (len(couvertures[0]) <= len(couvertures[1])):
C = couvertures[0]
else:
C = couvertures[1]
return C, cpt