def probability_anyone(n, p, k):
"""
Returns the probability (aproximated) that in a G(n,p) i.e. ER-model a
random set of size k uniqely determines some vertex.
Input:(int, float, int)
Output: float
"""
exitos = 0
total = num_experiments
for i in range(0, total):
G = nx.gnp_random_graph(n, p)
A = random_set(k, n)
exitos = exitos + does_this_uniquely_det_someone(G, A)
return exitos / float(total)
def probability_rigid_expansion(n, p, k):
"""
Returns the probability (aproximated) that in a G(n,p) i.e. ER-model a
random set of size k generates a rigid expansion
Input: int n, float p, int k
Output: float
"""
successes = 0
total = 50
for i in range(0, total):
G = nx.gnp_random_graph(n, p)
A = random_set(k, n)
successes = successes + does_it_expands(G, A)
return successes / float(total)
def sample_jump(n, p, k, size):
"""
Input: Graph G (dictionary), set A
Output: Array
"""
S = [0] * (size)
if k * log(2) < log(n - k) + (k * p) * log(2):
method = 1
else:
method = 2
for i in range(size):
G = nx.fast_gnp_random_graph(n, p)
A = random_set(k, n)
S[i] = jump_experiment(G, A, method)
return S
def probability_subset(n, p, k, m):
"""
Returns the probability (aproximated) that in a G(n,p) i.e. ER-model a
random set of size k uniquely determines some vertex.
Input:(int, float, int)
Output: float
"""
successes = 0
if m == 0:
return 0
else:
for i in range(0, num_experiments):
G = nx.fast_gnp_random_graph(n, p)
A = random_set(k, n)
successes = successes + does_subset_uniquely_det_someone(G, A, m)
return successes / float(num_experiments)
def vector_success_jump(n, p, k):
"""
Input: Graph G (dictionary), set A
Output: Int
"""
V = [0] * (n + 1)
if k * log(2) < log(n - k) + (k * p) * log(2):
method = 1
else:
method = 2
for i in range(numExp):
G = nx.fast_gnp_random_graph(n, p)
A = random_set(k, n)
V[jump_experiment(G, A, method)] += 1
return [x / numExp for x in V]
def probability_last(n, p, k):
"""
Returns the empirical probability that in a G(n,p) i.e. ER-model a
random set of size k uniqely determines the nth-vertex.
Input:(int, float, int)
Output: float
"""
exitos = 0
total = num_experiments
if k == n:
return 0
else:
for i in range(0, total):
G = nx.gnp_random_graph(n, p)
A = random_set(k, n - 1)
exitos = exitos + is_this_uniquely_det(G, A, n - 1)
return exitos / float(total)
from numpy import log
from time import clock
import networkx as nx
import numpy as np
import matplotlib.pyplot as plt
from math import floor
def calculate_mean_expansion_time(n, p, k, case, number_of_experiments):
"""
Input: n (int), p (float), k(int), case(dict), number_of_experiments(int)
Output: Mean time, float
"""
sumation = 0
for e in range(number_of_experiments):
A = random_set(k, n)
starting_time = clock()
if(case['optimizations'] == "none"):
G = er_graph(n,p)
rigid_expansion(G,A,p,False,False)
else:
G = nx.fast_gnp_random_graph(n, p)
rigid_expansion(G,A,p,False,True)
sumation += clock() - starting_time
return 1000 * sumation/number_of_experiments
def time_execution_performance(n, p, samples_size, log_scale=False):
"""
Plots a mean time rigid expansions experiments varing n, p and k.
Input: n (max graph size), p (list), samples_size(int)
Output: Mean time, float