def test_max_flow_mst_cong_approx(s):
epsilon = 0.1
for i in range(20):
g = graph_util.diluted_complete_graph(10, 0.9)
if not g.has_edge(0, 1):
g.add_edge(0, 1, {'capacity': 1})
cong_approx = MstCongestionApprox(g.to_undirected())
sherman_flow = sherman.ShermanFlow(g, cong_approx)
_, flow_value = sherman_flow.max_st_flow(0, 1, epsilon)
actual_flow_value, _ = nx.maximum_flow(g.to_undirected(), 0, 1)
s.assertGreaterEqual(flow_value,
(1.0 - epsilon) * actual_flow_value)
s.assertLessEqual(flow_value, (1.0 + epsilon) * actual_flow_value)
def test_compute_B(s):
g = graph_util.complete_graph(5)
congestion_approximator = ConductanceCongestionApprox(g)
sherman_flow = sherman.ShermanFlow(g, congestion_approximator)
x = np.zeros(g.number_of_edges())
x[0] = 2
x[1] = -1.2
x[2] = -0.1
expected = np.zeros(g.number_of_nodes())
expected[0] = -2 + 1.2 + 0.1
expected[1] = 2
expected[2] = -1.2
expected[3] = -0.1
actual_Bx = sherman_flow.compute_B(x)
npt.assert_array_equal(expected, actual_Bx)
def test_max_flow_conductance_cong_approx(s):
epsilon = 0.1
n = 10
for p in [0.7, 0.8, 0.9, 1.0]:
for i in range(100):
g = graph_util.diluted_complete_graph(n, p)
if not g.has_edge(0, 1):
g.add_edge(0, 1, {'capacity': 1})
cong_approx = ConductanceCongestionApprox(g)
sherman_flow = sherman.ShermanFlow(g, cong_approx)
_, flow_value = sherman_flow.max_st_flow(0, 1, epsilon)
actual_flow_value, _ = nx.maximum_flow(g.to_undirected(), 0, 1)
s.assertGreaterEqual(flow_value,
(1.0 - epsilon) * actual_flow_value)
s.assertLessEqual(flow_value,
(1.0 + epsilon) * actual_flow_value)
def test_compute_C(s):
g = graph_util.complete_graph(5)
graph_util.set_edge_capacity(g, (0, 1), 12)
graph_util.set_edge_capacity(g, (0, 2), 13)
congestion_approximator = ConductanceCongestionApprox(g)
sherman_flow = sherman.ShermanFlow(g, congestion_approximator)
x = np.ones(g.number_of_edges())
x[0] = 2
x[1] = 3
expected = np.ones(g.number_of_edges())
expected[0] = 2 * 12
expected[1] = 3 * 13
npt.assert_array_equal(expected, sherman_flow.compute_C(x))
expected[0] = 2 / 12
expected[1] = 3 / 13
npt.assert_array_equal(expected, sherman_flow.compute_Cinv(x))
from __future__ import division
import numpy as np
import sys
import time
import graph_util
import sherman
from mst_congestion_approx import MstCongestionApprox
if len(sys.argv) != 3:
print 'usage: ' + sys.argv[0] + ' <num vertices> <epsilon>'
exit(1)
n = int(sys.argv[1])
epsilon = float(sys.argv[2])
print '%f-approximate max-flow on %d-complete graph\n' % (epsilon, n)
g = graph_util.complete_graph(n)
print 'n:', n
print 'm:', g.number_of_edges()
cong_approx = MstCongestionApprox(g.to_undirected())
sherman_flow = sherman.ShermanFlow(g, cong_approx)
start_time = time.clock()
flow, _ = sherman_flow.max_st_flow(0, 1, epsilon)
stop_time = time.clock()
print 'final flow:\n', flow
print 'time:', stop_time - start_time
exit(0)