/usr/lib/python3/dist-packages/networkx/algorithms/tests/test_matching.py is in python3-networkx 1.11-1ubuntu2.
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import math
from nose.tools import *
import networkx as nx
class TestMatching:
def setUp(self):
pass
def test_trivial1(self):
"""Empty graph"""
G = nx.Graph()
assert_equal(nx.max_weight_matching(G),{})
def test_trivial2(self):
"""Self loop"""
G = nx.Graph()
G.add_edge(0, 0, weight=100)
assert_equal(nx.max_weight_matching(G),{})
def test_trivial3(self):
"""Single edge"""
G = nx.Graph()
G.add_edge(0, 1)
assert_equal(nx.max_weight_matching(G),
{0: 1, 1: 0})
def test_trivial4(self):
"""Small graph"""
G = nx.Graph()
G.add_edge('one', 'two', weight=10)
G.add_edge('two', 'three', weight=11)
assert_equal(nx.max_weight_matching(G),
{'three': 'two', 'two': 'three'})
def test_trivial5(self):
"""Path"""
G = nx.Graph()
G.add_edge(1, 2, weight=5)
G.add_edge(2, 3, weight=11)
G.add_edge(3, 4, weight=5)
assert_equal(nx.max_weight_matching(G),
{2: 3, 3: 2})
assert_equal(nx.max_weight_matching(G, 1),
{1: 2, 2: 1, 3: 4, 4: 3})
def test_floating_point_weights(self):
"""Floating point weights"""
G = nx.Graph()
G.add_edge(1, 2, weight=math.pi)
G.add_edge(2, 3, weight=math.exp(1))
G.add_edge(1, 3, weight=3.0)
G.add_edge(1, 4, weight=math.sqrt(2.0))
assert_equal(nx.max_weight_matching(G),
{1: 4, 2: 3, 3: 2, 4: 1})
def test_negative_weights(self):
"""Negative weights"""
G = nx.Graph()
G.add_edge(1, 2, weight=2)
G.add_edge(1, 3, weight=-2)
G.add_edge(2, 3, weight=1)
G.add_edge(2, 4, weight=-1)
G.add_edge(3, 4, weight=-6)
assert_equal(nx.max_weight_matching(G),
{1: 2, 2: 1})
assert_equal(nx.max_weight_matching(G, 1),
{1: 3, 2: 4, 3: 1, 4: 2})
def test_s_blossom(self):
"""Create S-blossom and use it for augmentation:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 8), (1, 3, 9),
(2, 3, 10), (3, 4, 7) ])
assert_equal(nx.max_weight_matching(G),
{1: 2, 2: 1, 3: 4, 4: 3})
G.add_weighted_edges_from([ (1, 6, 5), (4, 5, 6) ])
assert_equal(nx.max_weight_matching(G),
{1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1})
def test_s_t_blossom(self):
"""Create S-blossom, relabel as T-blossom, use for augmentation:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 9), (1, 3, 8), (2, 3, 10),
(1, 4, 5), (4, 5, 4), (1, 6, 3) ])
assert_equal(nx.max_weight_matching(G),
{1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1})
G.add_edge(4, 5, weight=3)
G.add_edge(1, 6, weight=4)
assert_equal(nx.max_weight_matching(G),
{1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1})
G.remove_edge(1, 6)
G.add_edge(3, 6, weight=4)
assert_equal(nx.max_weight_matching(G),
{1: 2, 2: 1, 3: 6, 4: 5, 5: 4, 6: 3})
def test_nested_s_blossom(self):
"""Create nested S-blossom, use for augmentation:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 9), (1, 3, 9), (2, 3, 10),
(2, 4, 8), (3, 5, 8), (4, 5, 10),
(5, 6, 6) ])
assert_equal(nx.max_weight_matching(G),
{1: 3, 2: 4, 3: 1, 4: 2, 5: 6, 6: 5})
def test_nested_s_blossom_relabel(self):
"""Create S-blossom, relabel as S, include in nested S-blossom:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 10), (1, 7, 10), (2, 3, 12),
(3, 4, 20), (3, 5, 20), (4, 5, 25),
(5, 6, 10), (6, 7, 10), (7, 8, 8) ])
assert_equal(nx.max_weight_matching(G),
{1: 2, 2: 1, 3: 4, 4: 3, 5: 6, 6: 5, 7: 8, 8: 7})
def test_nested_s_blossom_expand(self):
"""Create nested S-blossom, augment, expand recursively:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 8), (1, 3, 8), (2, 3, 10),
(2, 4, 12),(3, 5, 12), (4, 5, 14),
(4, 6, 12), (5, 7, 12), (6, 7, 14),
(7, 8, 12) ])
assert_equal(nx.max_weight_matching(G),
{1: 2, 2: 1, 3: 5, 4: 6, 5: 3, 6: 4, 7: 8, 8: 7})
def test_s_blossom_relabel_expand(self):
"""Create S-blossom, relabel as T, expand:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 23), (1, 5, 22), (1, 6, 15),
(2, 3, 25), (3, 4, 22), (4, 5, 25),
(4, 8, 14), (5, 7, 13) ])
assert_equal(nx.max_weight_matching(G),
{1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4})
def test_nested_s_blossom_relabel_expand(self):
"""Create nested S-blossom, relabel as T, expand:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 19), (1, 3, 20), (1, 8, 8),
(2, 3, 25), (2, 4, 18), (3, 5, 18),
(4, 5, 13), (4, 7, 7), (5, 6, 7) ])
assert_equal(nx.max_weight_matching(G),
{1: 8, 2: 3, 3: 2, 4: 7, 5: 6, 6: 5, 7: 4, 8: 1})
def test_nasty_blossom1(self):
"""Create blossom, relabel as T in more than one way, expand,
augment:
"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 45), (1, 5, 45), (2, 3, 50),
(3, 4, 45), (4, 5, 50), (1, 6, 30),
(3, 9, 35), (4, 8, 35), (5, 7, 26),
(9, 10, 5) ])
assert_equal(nx.max_weight_matching(G),
{1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
6: 1, 7: 5, 8: 4, 9: 10, 10: 9})
def test_nasty_blossom2(self):
"""Again but slightly different:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 45), (1, 5, 45), (2, 3, 50),
(3, 4, 45), (4, 5, 50), (1, 6, 30),
(3, 9, 35), (4, 8, 26), (5, 7, 40),
(9, 10, 5) ])
assert_equal(nx.max_weight_matching(G),
{1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
6: 1, 7: 5, 8: 4, 9: 10, 10: 9})
def test_nasty_blossom_least_slack(self):
"""Create blossom, relabel as T, expand such that a new
least-slack S-to-free dge is produced, augment:
"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 45), (1, 5, 45), (2, 3, 50),
(3, 4, 45), (4, 5, 50), (1, 6, 30),
(3, 9, 35), (4, 8, 28), (5, 7, 26),
(9, 10, 5) ])
assert_equal(nx.max_weight_matching(G),
{1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
6: 1, 7: 5, 8: 4, 9: 10, 10: 9})
def test_nasty_blossom_augmenting(self):
"""Create nested blossom, relabel as T in more than one way"""
# expand outer blossom such that inner blossom ends up on an
# augmenting path:
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 45), (1, 7, 45), (2, 3, 50),
(3, 4, 45), (4, 5, 95), (4, 6, 94),
(5, 6, 94), (6, 7, 50), (1, 8, 30),
(3, 11, 35), (5, 9, 36), (7, 10, 26),
(11, 12, 5) ])
assert_equal(nx.max_weight_matching(G),
{1: 8, 2: 3, 3: 2, 4: 6, 5: 9, 6: 4,
7: 10, 8: 1, 9: 5, 10: 7, 11: 12, 12: 11})
def test_nasty_blossom_expand_recursively(self):
"""Create nested S-blossom, relabel as S, expand recursively:"""
G = nx.Graph()
G.add_weighted_edges_from([ (1, 2, 40), (1, 3, 40), (2, 3, 60),
(2, 4, 55), (3, 5, 55), (4, 5, 50),
(1, 8, 15), (5, 7, 30), (7, 6, 10),
(8, 10, 10), (4, 9, 30) ])
assert_equal(nx.max_weight_matching(G),
{1: 2, 2: 1, 3: 5, 4: 9, 5: 3,
6: 7, 7: 6, 8: 10, 9: 4, 10: 8})
def test_maximal_matching():
graph = nx.Graph()
graph.add_edge(0, 1)
graph.add_edge(0, 2)
graph.add_edge(0, 3)
graph.add_edge(0, 4)
graph.add_edge(0, 5)
graph.add_edge(1, 2)
matching = nx.maximal_matching(graph)
vset = set(u for u, v in matching)
vset = vset | set(v for u, v in matching)
for edge in graph.edges_iter():
u, v = edge
ok_(len(set([v]) & vset) > 0 or len(set([u]) & vset) > 0, \
"not a proper matching!")
eq_(1, len(matching), "matching not length 1!")
graph = nx.Graph()
graph.add_edge(1, 2)
graph.add_edge(1, 5)
graph.add_edge(2, 3)
graph.add_edge(2, 5)
graph.add_edge(3, 4)
graph.add_edge(3, 6)
graph.add_edge(5, 6)
matching = nx.maximal_matching(graph)
vset = set(u for u, v in matching)
vset = vset | set(v for u, v in matching)
for edge in graph.edges_iter():
u, v = edge
ok_(len(set([v]) & vset) > 0 or len(set([u]) & vset) > 0, \
"not a proper matching!")
def test_maximal_matching_ordering():
# check edge ordering
G = nx.Graph()
G.add_nodes_from([100,200,300])
G.add_edges_from([(100,200),(100,300)])
matching = nx.maximal_matching(G)
assert_equal(len(matching), 1)
G = nx.Graph()
G.add_nodes_from([200,100,300])
G.add_edges_from([(100,200),(100,300)])
matching = nx.maximal_matching(G)
assert_equal(len(matching), 1)
G = nx.Graph()
G.add_nodes_from([300,200,100])
G.add_edges_from([(100,200),(100,300)])
matching = nx.maximal_matching(G)
assert_equal(len(matching), 1)
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