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# -*- coding: utf-8 -*-
import networkx as nx
from nose.tools import assert_equal, assert_raises
class TestNetworkSimplex:
def test_simple_digraph(self):
G = nx.DiGraph()
G.add_node('a', demand = -5)
G.add_node('d', demand = 5)
G.add_edge('a', 'b', weight = 3, capacity = 4)
G.add_edge('a', 'c', weight = 6, capacity = 10)
G.add_edge('b', 'd', weight = 1, capacity = 9)
G.add_edge('c', 'd', weight = 2, capacity = 5)
flowCost, H = nx.network_simplex(G)
soln = {'a': {'b': 4, 'c': 1},
'b': {'d': 4},
'c': {'d': 1},
'd': {}}
assert_equal(flowCost, 24)
assert_equal(nx.min_cost_flow_cost(G), 24)
assert_equal(H, soln)
assert_equal(nx.min_cost_flow(G), soln)
assert_equal(nx.cost_of_flow(G, H), 24)
def test_negcycle_infcap(self):
G = nx.DiGraph()
G.add_node('s', demand = -5)
G.add_node('t', demand = 5)
G.add_edge('s', 'a', weight = 1, capacity = 3)
G.add_edge('a', 'b', weight = 3)
G.add_edge('c', 'a', weight = -6)
G.add_edge('b', 'd', weight = 1)
G.add_edge('d', 'c', weight = -2)
G.add_edge('d', 't', weight = 1, capacity = 3)
assert_raises(nx.NetworkXUnbounded, nx.network_simplex, G)
def test_sum_demands_not_zero(self):
G = nx.DiGraph()
G.add_node('s', demand = -5)
G.add_node('t', demand = 4)
G.add_edge('s', 'a', weight = 1, capacity = 3)
G.add_edge('a', 'b', weight = 3)
G.add_edge('a', 'c', weight = -6)
G.add_edge('b', 'd', weight = 1)
G.add_edge('c', 'd', weight = -2)
G.add_edge('d', 't', weight = 1, capacity = 3)
assert_raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
def test_no_flow_satisfying_demands(self):
G = nx.DiGraph()
G.add_node('s', demand = -5)
G.add_node('t', demand = 5)
G.add_edge('s', 'a', weight = 1, capacity = 3)
G.add_edge('a', 'b', weight = 3)
G.add_edge('a', 'c', weight = -6)
G.add_edge('b', 'd', weight = 1)
G.add_edge('c', 'd', weight = -2)
G.add_edge('d', 't', weight = 1, capacity = 3)
assert_raises(nx.NetworkXUnfeasible, nx.network_simplex, G)
def test_transshipment(self):
G = nx.DiGraph()
G.add_node('a', demand = 1)
G.add_node('b', demand = -2)
G.add_node('c', demand = -2)
G.add_node('d', demand = 3)
G.add_node('e', demand = -4)
G.add_node('f', demand = -4)
G.add_node('g', demand = 3)
G.add_node('h', demand = 2)
G.add_node('r', demand = 3)
G.add_edge('a', 'c', weight = 3)
G.add_edge('r', 'a', weight = 2)
G.add_edge('b', 'a', weight = 9)
G.add_edge('r', 'c', weight = 0)
G.add_edge('b', 'r', weight = -6)
G.add_edge('c', 'd', weight = 5)
G.add_edge('e', 'r', weight = 4)
G.add_edge('e', 'f', weight = 3)
G.add_edge('h', 'b', weight = 4)
G.add_edge('f', 'd', weight = 7)
G.add_edge('f', 'h', weight = 12)
G.add_edge('g', 'd', weight = 12)
G.add_edge('f', 'g', weight = -1)
G.add_edge('h', 'g', weight = -10)
flowCost, H = nx.network_simplex(G)
soln = {'a': {'c': 0},
'b': {'a': 0, 'r': 2},
'c': {'d': 3},
'd': {},
'e': {'r': 3, 'f': 1},
'f': {'d': 0, 'g': 3, 'h': 2},
'g': {'d': 0},
'h': {'b': 0, 'g': 0},
'r': {'a': 1, 'c': 1}}
assert_equal(flowCost, 41)
assert_equal(nx.min_cost_flow_cost(G), 41)
assert_equal(H, soln)
assert_equal(nx.min_cost_flow(G), soln)
assert_equal(nx.cost_of_flow(G, H), 41)
def test_max_flow_min_cost(self):
G = nx.DiGraph()
G.add_edge('s', 'a', bandwidth = 6)
G.add_edge('s', 'c', bandwidth = 10, cost = 10)
G.add_edge('a', 'b', cost = 6)
G.add_edge('b', 'd', bandwidth = 8, cost = 7)
G.add_edge('c', 'd', cost = 10)
G.add_edge('d', 't', bandwidth = 5, cost = 5)
soln = {'s': {'a': 5, 'c': 0},
'a': {'b': 5},
'b': {'d': 5},
'c': {'d': 0},
'd': {'t': 5},
't': {}}
flow = nx.max_flow_min_cost(G, 's', 't', capacity = 'bandwidth',
weight = 'cost')
assert_equal(flow, soln)
assert_equal(nx.cost_of_flow(G, flow, weight = 'cost'), 90)
def test_digraph1(self):
# From Bradley, S. P., Hax, A. C. and Magnanti, T. L. Applied
# Mathematical Programming. Addison-Wesley, 1977.
G = nx.DiGraph()
G.add_node(1, demand = -20)
G.add_node(4, demand = 5)
G.add_node(5, demand = 15)
G.add_edges_from([(1, 2, {'capacity': 15, 'weight': 4}),
(1, 3, {'capacity': 8, 'weight': 4}),
(2, 3, {'weight': 2}),
(2, 4, {'capacity': 4, 'weight': 2}),
(2, 5, {'capacity': 10, 'weight': 6}),
(3, 4, {'capacity': 15, 'weight': 1}),
(3, 5, {'capacity': 5, 'weight': 3}),
(4, 5, {'weight': 2}),
(5, 3, {'capacity': 4, 'weight': 1})])
flowCost, H = nx.network_simplex(G)
soln = {1: {2: 12, 3: 8},
2: {3: 8, 4: 4, 5: 0},
3: {4: 11, 5: 5},
4: {5: 10},
5: {3: 0}}
assert_equal(flowCost, 150)
assert_equal(nx.min_cost_flow_cost(G), 150)
assert_equal(H, soln)
assert_equal(nx.min_cost_flow(G), soln)
assert_equal(nx.cost_of_flow(G, H), 150)
def test_digraph2(self):
# Example from ticket #430 from mfrasca. Original source:
# http://www.cs.princeton.edu/courses/archive/spr03/cs226/lectures/mincost.4up.pdf, slide 11.
G = nx.DiGraph()
G.add_edge('s', 1, capacity=12)
G.add_edge('s', 2, capacity=6)
G.add_edge('s', 3, capacity=14)
G.add_edge(1, 2, capacity=11)
G.add_edge(2, 3, capacity=9)
G.add_edge(1, 4, capacity=5)
G.add_edge(1, 5, capacity=2)
G.add_edge(2, 5, capacity=4)
G.add_edge(2, 6, capacity=2)
G.add_edge(3, 6, capacity=31)
G.add_edge(4, 5, capacity=18)
G.add_edge(5, 5, capacity=9)
G.add_edge(4, 't', capacity=3)
G.add_edge(5, 't', capacity=7)
G.add_edge(6, 't', capacity=22)
flow = nx.max_flow_min_cost(G, 's', 't')
soln = {1: {2: 5, 4: 5, 5: 2},
2: {3: 6, 5: 3, 6: 2},
3: {6: 20},
4: {5: 2, 't': 3},
5: {5: 0, 't': 7},
6: {'t': 22},
's': {1: 12, 2: 6, 3: 14},
't': {}}
assert_equal(flow, soln)
def test_digraph3(self):
"""Combinatorial Optimization: Algorithms and Complexity,
Papadimitriou Steiglitz at page 140 has an example, 7.1, but that
admits multiple solutions, so I alter it a bit. From ticket #430
by mfrasca."""
G = G = nx.DiGraph()
G.add_edge('s', 'a', {0: 2, 1: 4})
G.add_edge('s', 'b', {0: 2, 1: 1})
G.add_edge('a', 'b', {0: 5, 1: 2})
G.add_edge('a', 't', {0: 1, 1: 5})
G.add_edge('b', 'a', {0: 1, 1: 3})
G.add_edge('b', 't', {0: 3, 1: 2})
"PS.ex.7.1: testing main function"
sol = nx.max_flow_min_cost(G, 's', 't', capacity=0, weight=1)
flow = sum(v for v in sol['s'].values())
assert_equal(4, flow)
assert_equal(23, nx.cost_of_flow(G, sol, weight=1))
assert_equal(sol['s'], {'a': 2, 'b': 2})
assert_equal(sol['a'], {'b': 1, 't': 1})
assert_equal(sol['b'], {'a': 0, 't': 3})
assert_equal(sol['t'], {})
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