def random_model(n1, n2, k, cap):
"""
create a graph with the partition A of size n1
and partition B of size n2 using the random model
:param n1: size of partition A
:param n2: size of partition B
:param k: length of preference list for vertices in A
:param cap: capacity of a vertex in partition B
:return: bipartite graph with above properties
"""
def order_by_master_list(l, master_list):
return sorted(l, key=master_list.index)
g = Graph()
# create the sets R and H, r_1 ... r_n1, h_1 .. h_n2
R = set('r{}'.format(i) for i in range(1, n1 + 1))
H = set('h{}'.format(i) for i in range(1, n2 + 1))
for res in R:
g.residents.append(Resident(res))
for hosp in H:
g.hospitals.append(Hospital(hosp, 0, cap))
# prepare a master list
# master_list = list(h for h in H)
# random.shuffle(master_list)
pref_lists_H, pref_lists_R = collections.defaultdict(list), {}
for resident in R:
r_ind = resident[1:]
pref_list = random.sample(H, min(
len(H), k)) # random.randint(1, len(H))) # sample houses
pref_lists_R[
resident] = pref_list # order_by_master_list(pref_list, master_list)
# add these residents to the preference list for the corresponding hospital
for hospital in pref_list:
h_ind = hospital[1:]
pref_lists_H[hospital].append(resident)
g.edges.append(Edge(r_ind, h_ind))
res = g.get_resident(resident)
for hosp in pref_lists_R[resident]:
res.pref.append(g.get_hospital(hosp))
for hospital in H:
random.shuffle(pref_lists_H[hospital])
hosp = g.get_hospital(hospital)
for res in pref_lists_H[hospital]:
hosp.pref.append(g.get_resident(res))
return g
def seat_model_generator(n1, n2, k_low, k_up):
"""
create a graph with the partition R of size n1 and
partition H of size n2
:param n1: size of partition R
:param n2: size of partition H
:param k_low, k_up: range for length of resident preference lists
"""
def order_by_master_list(l, master_list):
return sorted(l, key=master_list.index)
possible_credits = [5, 10, 15, 20]
# set up geometric distribution among above possible hospital credits
probs = np.random.geometric(p=0.10, size=len(possible_credits))
probs = probs / np.sum(probs)
def get_hosp_credits():
return list(
np.random.choice(possible_credits, size=1, replace=False,
p=probs))[0]
def get_hosp_capacity_uniform():
# returns the average hospital capacity based on resident, hospital credits
res_cap_sum = 0
hosp_cred_sum = 0
for r in g.residents:
res_cap_sum += r.uq
for h in g.hospitals:
hosp_cred_sum += h.credits
return int(np.ceil((1.5 * res_cap_sum) / hosp_cred_sum))
def get_hosp_capacity_non_uniform(cap):
low = int(np.ceil(0.3 * cap))
high = int(np.ceil(1.7 * cap))
return random.randint(low, high)
g = Graph()
# default hospital capacity
cap = 60
# create the sets R and H, r_1 ... r_n1, h_1 .. h_n2
R = list('r{}'.format(i) for i in range(1, n1 + 1))
H = list('h{}'.format(i) for i in range(1, n2 + 1))
for res in R:
g.residents.append(Resident(res))
for hosp in H:
g.hospitals.append(Hospital(hosp, 0, cap, get_hosp_credits()))
# prepare a master list
master_list = list(r for r in R)
random.shuffle(master_list)
# setup a probability distribution over the hospitals
p = np.random.geometric(p=0.10, size=len(H))
# normalize the distribution
p = p / np.sum(p) # p is a ndarray, so this operation is correct
prob_dict = dict(zip(H, p))
master_list_h = sorted(H, key=lambda h: prob_dict[h], reverse=True)
pref_H, pref_R = collections.defaultdict(list), {}
for r in R:
# sample hospitals according to the probability distribution and without replacement
k = random.randint(k_low, k_up)
pref_R[r] = list(
np.random.choice(H, size=min(len(H), k), replace=False, p=p))
# add these residents to the preference list for the corresponding hospitals
for h in pref_R[r]:
pref_H[h].append(r)
for r in R:
pref_R[r] = order_by_master_list(pref_R[r], master_list_h)
# random.shuffle(pref_R[r])
res = g.get_resident(r)
for hosp in pref_R[r]:
res.pref.append(g.get_hospital(hosp))
for h in H:
pref_H[h] = order_by_master_list(pref_H[h], master_list)
# random.shuffle(pref_H[h])
hosp = g.get_hospital(h)
for res in pref_H[h]:
hosp.pref.append(g.get_resident(res))
g.init_resident_capacities()
# get average capacity for hospitals
cap = get_hosp_capacity_uniform()
for h in g.hospitals:
h.uq = get_hosp_capacity_non_uniform(cap)
# initialize class constraints for residents
g.init_all_resident_class()
# initialize master class constraints applicable to all residents
g.init_master_classes_disjoint()
return g
def mahadian_model(n1, n2, k, cap):
"""
create a graph with the partition R of size n1 and
partition H of size n2 using the model as described in
Marriage, Honesty, and Stability
Immorlica, Nicole and Mahdian, Mohammad
Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
:param n1: size of partition R
:param n2: size of partition H
:param k: length of preference list for the residents
:param cap: capacity of the hospitals
:return: bipartite graph with above properties
"""
def order_by_master_list(l, master_list):
return sorted(l, key=master_list.index)
g = Graph()
# create the sets R and H, r_1 ... r_n1, h_1 .. h_n2
R = list('r{}'.format(i) for i in range(1, n1 + 1))
H = list('h{}'.format(i) for i in range(1, n2 + 1))
# prepare a master list
master_list = list(r for r in R)
random.shuffle(master_list)
for res in R:
g.residents.append(Resident(res))
for hosp in H:
g.hospitals.append(Hospital(hosp, 0, cap))
# setup a probability distribution over the hospitals
p = np.random.geometric(p=0.10, size=len(H))
# normalize the distribution
p = p / np.sum(p) # p is a ndarray, so this operation is correct
prob_dict = dict(zip(H, p))
master_list_h = sorted(H, key=lambda h: prob_dict[h], reverse=True)
# print(prob_dict, master_list_h, sep='\n')
pref_H, pref_R = collections.defaultdict(list), {}
for r in R:
# sample women according to the probability distribution and without replacement
pref_R[r] = list(
np.random.choice(H, size=min(len(H), k), replace=False, p=p))
# add these man to the preference list for the corresponding women
r_ind = r[1:]
for h in pref_R[r]:
h_ind = h[1:]
pref_H[h].append(r)
g.edges.append(Edge(r_ind, h_ind))
for r in R:
pref_R[r] = order_by_master_list(pref_R[r], master_list_h)
res = g.get_resident(r)
for hosp in pref_R[r]:
res.pref.append(g.get_hospital(hosp))
for h in H:
pref_H[h] = order_by_master_list(pref_H[h], master_list)
#random.shuffle(pref_H[h])
hosp = g.get_hospital(h)
for res in pref_H[h]:
hosp.pref.append(g.get_resident(res))
return g
