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maximum-weight-matching/python/tests/test_algorithm.py

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"""Unit tests for maximum weight matching."""
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import math
import unittest
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from unittest.mock import Mock
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from mwmatching import (
maximum_weight_matching as mwm,
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adjust_weights_for_maximum_cardinality_matching as adj)
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from mwmatching.algorithm import (
MatchingError, GraphInfo, Blossom, NonTrivialBlossom, MatchingContext,
verify_optimum)
class TestMaximumWeightMatching(unittest.TestCase):
"""Test maximum_weight_matching() function."""
def test10_empty(self):
"""empty input graph"""
self.assertEqual(mwm([]), [])
def test11_singleedge(self):
"""single edge"""
self.assertEqual(mwm([(0,1,1)]), [(0,1)])
def test12(self):
self.assertEqual(mwm([(1,2,10), (2,3,11)]), [(2,3)])
def test13(self):
self.assertEqual(
mwm([(1,2,5), (2,3,11), (3,4,5)]),
[(2,3)])
def test15_float(self):
"""floating point weigths"""
self.assertEqual(
mwm([(1,2,3.1415), (2,3,2.7183), (1,3,3.0), (1,4,1.4142)]),
[(2,3), (1,4)])
def test16_negative(self):
"""negative weights"""
self.assertEqual(
mwm([(1,2,2), (1,3,-2), (2,3,1), (2,4,-1), (3,4,-6)]),
[(1,2)])
def test20_sblossom(self):
"""create S-blossom and use it for augmentation"""
self.assertEqual(
mwm([(1,2,8), (1,3,9), (2,3,10), (3,4,7)]),
[(1,2), (3,4)])
def test20a_sblossom(self):
"""create S-blossom and use it for augmentation"""
self.assertEqual(
mwm([(1,2,8), (1,3,9), (2,3,10), (3,4,7), (1,6,5), (4,5,6)]),
[(2,3), (1,6), (4,5)])
def test21_tblossom(self):
"""create S-blossom, relabel as T-blossom, use for augmentation"""
self.assertEqual(
mwm([(1,2,9), (1,3,8), (2,3,10), (1,4,5), (4,5,4), (1,6,3)]),
[(2,3),(4,5),(1,6)])
def test21a_tblossom(self):
"""create S-blossom, relabel as T-blossom, use for augmentation"""
self.assertEqual(
mwm([(1,2,9), (1,3,8), (2,3,10), (1,4,5), (4,5,3), (1,6,4)]),
[(2,3), (4,5), (1,6)])
def test21b_tblossom(self):
"""create S-blossom, relabel as T-blossom, use for augmentation"""
self.assertEqual(
mwm([(1,2,9), (1,3,8), (2,3,10), (1,4,5), (4,5,3), (3,6,4)]),
[(1,2), (4,5), (3,6)])
def test22_s_nest(self):
"""create nested S-blossom, use for augmentation"""
self.assertEqual(
mwm([(1,2,9), (1,3,9), (2,3,10), (2,4,8), (3,5,8), (4,5,10), (5,6,6)]),
[(1,3), (2,4), (5,6)])
def test23_s_relabel_nest(self):
"""create S-blossom, relabel as S, include in nested S-blossom"""
self.assertEqual(
mwm([(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)]),
[(1,2), (3,4), (5,6), (7,8)])
def test24_s_nest_expand(self):
"""create nested S-blossom, augment, expand recursively"""
self.assertEqual(
mwm([(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)]),
[(1,2), (3,5), (4,6), (7,8)])
def test25_s_t_expand(self):
"""create S-blossom, relabel as T, expand"""
self.assertEqual(
mwm([(1,2,23), (1,5,22), (1,6,15), (2,3,25), (3,4,22), (4,5,25), (4,8,14), (5,7,13)]),
[(1,6), (2,3), (4,8), (5,7)])
def test26_s_nest_t_expand(self):
"""create nested S-blossom, relabel as T, expand"""
self.assertEqual(
mwm([(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)]),
[(1,8), (2,3), (4,7), (5,6)])
def test30_tnasty_expand(self):
"""create blossom, relabel as T in more than one way, expand, augment"""
self.assertEqual(
mwm([(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)]),
[(2,3), (1,6), (4,8), (5,7), (9,10)])
def test31_tnasty2_expand(self):
"""again but slightly different"""
self.assertEqual(
mwm([(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)]),
[(2,3), (1,6), (4,8), (5,7), (9,10)])
def test32_t_expand_leastslack(self):
"""create blossom, relabel as T, expand such that a new least-slack S-to-free edge is produced, augment"""
self.assertEqual(
mwm([(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)]),
[(2,3), (1,6), (4,8), (5,7), (9,10)])
def test33_nest_tnasty_expand(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"""
self.assertEqual(
mwm([(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)]),
[(2,3), (4,6), (1,8), (5,9), (7,10), (11,12)])
def test34_nest_relabel_expand(self):
"""create nested S-blossom, relabel as S, expand recursively"""
self.assertEqual(
mwm([(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)]),
[(1,2), (3,5), (7,6), (8,10), (4,9)])
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def test41_nonmax_card(self):
"""leave some nodes unmatched"""
self.assertEqual(
mwm([(0,1,2), (0,4,3), (1,2,7), (1,5,2), (2,3,9), (2,5,4), (3,4,8), (3,5,4)]),
[(1,2), (3,4)])
def test42_s_nest_partial_expand(self):
"""create nested S-blossom, augment, expand only outer"""
#
# [0]--8--[1]--6--[3]--5--[5]
# \ | |
# \ 9 8
# 8 | |
# \--[2]--7--[4]
#
self.assertEqual(
mwm([(0,1,8), (0,2,8), (1,2,9), (1,3,6), (2,4,7), (3,4,8), (3,5,5)]),
[(0,1), (2,4), (3,5)])
def test43_s_nest_noexpand(self):
"""leave nested S-blossom with inner zero dual"""
#
# [1]--9--[2]
# | /
# 7 ___7
# | /
# [0] [5]--2--[6]
# | \___
# 7 7
# | \
# [3]--9--[4]
#
self.assertEqual(
mwm([(0,1,7), (0,2,7), (1,2,9), (0,3,7), (0,4,7), (3,4,9), (5,6,2)]),
[(1,2), (3,4), (5,6)])
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def test44_blossom_redundant_edge(self):
"""drop redundant edge while making a blossom"""
#
# [1]----9---[2]
# / | \
# 7 8 \
# / | 1
# [0]--6--[4]--9--[3] |
# \ |
# \----1----[5]
#
self.assertEqual(
mwm([(0,1,7), (0,4,6), (1,2,9), (2,3,8), (3,4,9), (2,5,1), (4,5,1)]),
[(1,2), (3,4)])
def test45_flip_order(self):
"""test that order of edges and vertices is irrelevant"""
edges = [(0,1,2), (0,4,3), (1,2,7), (1,5,1), (2,3,9), (2,5,4), (3,4,8), (3,5,4)]
self.assertEqual(mwm(edges), [(1,2), (3,4)])
self.assertEqual(mwm(list(reversed(edges))), [(3,4), (1,2)])
self.assertEqual(mwm([(y, x, w) for (x, y, w) in edges]), [(2,1), (4,3)])
edges = [(0,2,4), (0,3,4), (0,4,1), (1,2,8), (1,5,3), (2,3,9), (3,4,7), (4,5,2)]
self.assertEqual(mwm(edges), [(1,2), (3,4)])
def test46_expand_unlabeled_blossom(self):
"""expand blossom before assigning label T"""
#
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# 3--[1]
# / |
# [2]--1--[4] 7
# \ |
# 5--[3]--5--[5]
#
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self.assertIn(
mwm([(1,3,7), (1,4,3), (2,4,1), (3,4,5), (3,5,5)]),
([(1,3), (2,4)], [(1,4), (3,5)]))
def test47_expand_unlabeled_outer(self):
"""expand outer blossom before assigning label T"""
#
# [3]--10--[1]--15--[2]--12--[5]
# _/ \_ | |
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# 11 16_ 8 15
# / \ | |
# [4] [6]---7--[7]
#
self.assertEqual(
mwm([(1,2,15), (1,3,10), (1,4,11), (1,6,17), (2,5,12), (2,6,8), (5,7,15), (6,7,7)]),
[(1,4), (2,6), (5,7)])
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def test48_expand_unlabeled_nested(self):
"""expand nested blossom before assigning label T"""
#
# [5]--11--[1]--11 14--[3]
# | \ / |
# 12 [4] 14
# | / \ |
# [6]--11--[2]--12 11--[7]
#
self.assertEqual(
mwm([(1,2,12), (1,4,11), (1,5,11), (2,4,12), (2,6,11), (3,4,14), (3,7,14), (4,7,11)]),
[(1,5), (2,4), (3,7)])
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def test51_augment_blossom_nested(self):
"""augment nested blossoms with common base vertex"""
#
# 19--[1]--17--[4]--11--[7]
# / | |
# [3]--15--[2] 19 18
# \ | |
# 21--[5]--19--[6]
#
self.assertEqual(
mwm([(1,2,19), (1,4,17), (1,5,19), (2,3,15), (2,5,21), (4,6,18), (4,7,11), (5,6,19)]),
[(1,5), (2,3), (4,6)])
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def test52_augment_blossom_nested2(self):
"""augment nested blossoms"""
#
# [4]--15 19--[2]
# | \ / |
# 16 [1] 21
# | / \ |
# [5]--17 19--[3]
# |
# 10
# |
# [6]
#
self.assertEqual(
mwm([(1,2,19), (1,3,19), (1,4,15), (1,5,17), (2,3,21), (4,5,16), (5,6,10)]),
[(1,4), (2,3), (5,6)])
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def test61_triangles_n9(self):
"""t.f 9 nodes"""
#
# [1]------[4] [7]
# | \ | \ | \
# | [3] | [6] | [9]
# | / | / | /
# [2] [5]------[8]
#
result = mwm([(1,2,1), (1,3,1), (2,3,1), (4,5,1), (4,6,1), (5,6,1), (7,8,1), (7,9,1), (8,9,1), (1,4,1), (5,8,1)])
self.assertEqual(len(result), 4)
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def test_fail_bad_input(self):
"""bad input values"""
with self.assertRaises(TypeError):
mwm(15)
with self.assertRaises(TypeError):
mwm([15])
with self.assertRaises((TypeError, ValueError)):
mwm([(1,2)])
with self.assertRaises(TypeError):
mwm([(1.1, 2.5, 3)])
with self.assertRaises(ValueError):
mwm([(1, -2, 3)])
with self.assertRaises(TypeError):
mwm([(1, 2, "3")])
with self.assertRaises(ValueError):
mwm([(1, 2, math.inf)])
with self.assertRaises(ValueError):
mwm([(1, 2, 1e308)])
def test_fail_bad_graph(self):
"""bad input graph structure"""
with self.assertRaises(ValueError):
mwm([(0, 1, 2), (1, 1, 1)])
with self.assertRaises(ValueError):
mwm([(0, 1, 2), (1, 2, 1), (2, 1, 1)])
class TestCornerCases(unittest.TestCase):
"""Test cases that would catch certain errors in the algorithm.
These graphs were generated semi-automatically to fail when
specific bugs are introduced in the code.
"""
def test1(self):
pairs = mwm([(0,4,26), (1,3,31), (1,4,49)])
self.assertEqual(pairs, [(0,4), (1,3)])
def test2(self):
pairs = mwm([(0,2,42), (0,4,36), (2,3,26)])
self.assertEqual(pairs, [(0,4), (2,3)])
def test3(self):
pairs = mwm([(0,4,43), (1,4,28), (2,4,38)])
self.assertEqual(pairs, [(0,4)])
def test4(self):
pairs = mwm([(0,1,50), (0,3,46), (0,4,45)])
self.assertEqual(pairs, [(0,1)])
def test5(self):
pairs = mwm([(0,1,35), (0,3,36), (0,4,46)])
self.assertEqual(pairs, [(0,4)])
def test6(self):
pairs = mwm([(0,1,50), (0,4,51), (0,5,34), (1,2,43), (1,4,57), (2,5,47), (3,4,17)])
self.assertEqual(pairs, [(0,1), (2,5), (3,4)])
def test7(self):
pairs = mwm([(0,1,34), (0,3,19), (1,2,45), (1,3,30), (1,4,37), (2,4,36)])
self.assertEqual(pairs, [(0,1), (2,4)])
def test8(self):
pairs = mwm([(0,1,48), (0,3,42), (0,4,57), (1,3,51), (1,5,36), (2,3,23), (4,5,46)])
self.assertEqual(pairs, [(0,1), (2,3), (4,5)])
def test9(self):
pairs = mwm([(0,1,21), (0,2,25), (0,5,42), (1,4,40), (2,3,10), (2,5,40), (3,5,31), (4,5,58)])
self.assertEqual(pairs, [(0,2), (1,4), (3,5)])
def test10(self):
pairs = mwm([(0,2,7), (0,5,20), (1,2,50), (1,4,46), (2,3,35), (2,4,8), (2,5,25), (3,5,47)])
self.assertEqual(pairs, [(0,5), (1,4), (2,3)])
def test11(self):
pairs = mwm([(0,1,42), (0,2,60), (1,3,34), (1,4,58), (1,5,52), (2,5,60), (3,5,34), (4,5,57)])
self.assertEqual(pairs, [(0,2), (1,4), (3,5)])
def test12(self):
pairs = mwm([(0,1,23), (0,2,26), (0,3,22), (0,4,41), (2,4,36)])
self.assertEqual(pairs, [(0,1), (2,4)])
def test13(self):
pairs = mwm([(0,3,58), (0,4,49), (1,5,34), (2,3,22), (2,5,42), (4,5,36)])
self.assertEqual(pairs, [(0,4), (1,5), (2,3)])
def test14(self):
pairs = mwm([(0,1,29), (0,3,35), (0,4,42), (1,2,12), (2,4,29), (3,4,44)])
self.assertEqual(pairs, [(0,1), (3,4)])
def test15(self):
pairs = mwm([(0,4,53), (0,5,42), (1,4,45), (2,4,59), (2,6,39), (4,5,69), (4,6,52)])
self.assertEqual(pairs, [(0,5), (1,4), (2,6)])
def test16(self):
pairs = mwm([(0,2,13), (1,2,11), (2,3,39), (2,4,17), (3,4,35)])
self.assertEqual(pairs, [(0,2), (3,4)])
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def test17(self):
pairs = mwm([(0,1,48), (0,2,44), (0,4,48), (1,4,36), (3,4,31)])
self.assertEqual(pairs, [(0,2), (1,4)])
class TestAdjustWeightForMaxCardinality(unittest.TestCase):
"""Test adjust_weights_for_maximum_cardinality_matching() function."""
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def test_empty(self):
self.assertEqual(adj([]), [])
def test_chain(self):
self.assertEqual(
adj([(0,1,2), (1,2,8), (2,3,3), (3,4,9), (4,5,1), (5,6,7), (6,7,4)]),
[(0,1,65), (1,2,71), (2,3,66), (3,4,72), (4,5,64), (5,6,70), (6,7,67)])
def test_chain_preadjusted(self):
self.assertEqual(
adj([(0,1,65), (1,2,71), (2,3,66), (3,4,72), (4,5,64), (5,6,70), (6,7,67)]),
[(0,1,65), (1,2,71), (2,3,66), (3,4,72), (4,5,64), (5,6,70), (6,7,67)])
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def test_flat(self):
self.assertEqual(
adj([(0,1,0), (0,4,0), (1,2,0), (1,5,0), (2,3,0), (2,5,0), (3,4,0), (3,5,0)]),
[(0,1,1), (0,4,1), (1,2,1), (1,5,1), (2,3,1), (2,5,1), (3,4,1), (3,5,1)])
def test14_maxcard(self):
self.assertEqual(
adj([(1,2,5), (2,3,11), (3,4,5)]),
[(1,2,30), (2,3,36), (3,4,30)])
def test16_negative(self):
self.assertEqual(
adj([(1,2,2), (1,3,-2), (2,3,1), (2,4,-1), (3,4,-6)]),
[(1,2,48), (1,3,44), (2,3,47), (2,4,45), (3,4,40)])
class TestMaximumCardinalityMatching(unittest.TestCase):
"""Test maximum cardinality matching."""
def test14_maxcard(self):
"""maximum cardinality"""
self.assertEqual(
mwm(adj([(1,2,5), (2,3,11), (3,4,5)])),
[(1,2), (3,4)])
def test16_negative(self):
"""negative weights"""
self.assertEqual(
mwm(adj([(1,2,2), (1,3,-2), (2,3,1), (2,4,-1), (3,4,-6)])),
[(1,3), (2,4)])
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def test43_maxcard(self):
"""maximum cardinality"""
self.assertIn(
mwm(adj([(0,1,2), (0,4,3), (1,2,7), (1,5,2), (2,3,9), (2,5,4), (3,4,8), (3,5,4)])),
([(0,1), (2,5), (3,4)],
[(0,4), (1,2), (3,5)]))
class TestGraphInfo(unittest.TestCase):
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"""Test GraphInfo helper class."""
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def test_empty(self):
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graph = GraphInfo([])
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self.assertEqual(graph.num_vertex, 0)
self.assertEqual(graph.edges, [])
self.assertEqual(graph.adjacent_edges, [])
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class TestVerificationFail(unittest.TestCase):
"""Test failure handling in verification routine."""
def _make_context(
self,
edges,
vertex_mate,
vertex_dual_2x,
nontrivial_blossom):
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ctx = Mock(spec=MatchingContext)
ctx.graph = GraphInfo(edges)
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ctx.vertex_mate = vertex_mate
ctx.vertex_dual_2x = vertex_dual_2x
ctx.nontrivial_blossom = nontrivial_blossom
return ctx
def test_success(self):
edges = [(0,1,10), (1,2,11)]
ctx = self._make_context(
edges,
vertex_mate=[-1, 2, 1],
vertex_dual_2x=[0, 20, 2],
nontrivial_blossom=[])
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verify_optimum(ctx)
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def test_asymmetric_matching(self):
edges = [(0,1,10), (1,2,11)]
ctx = self._make_context(
edges,
vertex_mate=[-1, 2, 0],
vertex_dual_2x=[0, 20, 2],
nontrivial_blossom=[])
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with self.assertRaises(MatchingError):
verify_optimum(ctx)
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def test_nonexistent_matched_edge(self):
edges = [(0,1,10), (1,2,11)]
ctx = self._make_context(
edges,
vertex_mate=[2, -1, 0],
vertex_dual_2x=[11, 11, 11],
nontrivial_blossom=[])
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with self.assertRaises(MatchingError):
verify_optimum(ctx)
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def test_negative_vertex_dual(self):
edges = [(0,1,10), (1,2,11)]
ctx = self._make_context(
edges,
vertex_mate=[-1, 2, 1],
vertex_dual_2x=[-2, 22, 0],
nontrivial_blossom=[])
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with self.assertRaises(MatchingError):
verify_optimum(ctx)
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def test_unmatched_nonzero_dual(self):
edges = [(0,1,10), (1,2,11)]
ctx = self._make_context(
edges,
vertex_mate=[-1, 2, 1],
vertex_dual_2x=[9, 11, 11],
nontrivial_blossom=[])
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with self.assertRaises(MatchingError):
verify_optimum(ctx)
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def test_negative_edge_slack(self):
edges = [(0,1,10), (1,2,11)]
ctx = self._make_context(
edges,
vertex_mate=[-1, 2, 1],
vertex_dual_2x=[0, 11, 11],
nontrivial_blossom=[])
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with self.assertRaises(MatchingError):
verify_optimum(ctx)
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def test_matched_edge_slack(self):
edges = [(0,1,10), (1,2,11)]
ctx = self._make_context(
edges,
vertex_mate=[-1, 2, 1],
vertex_dual_2x=[0, 20, 11],
nontrivial_blossom=[])
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with self.assertRaises(MatchingError):
verify_optimum(ctx)
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def test_negative_blossom_dual(self):
#
# [0]--7--[1]--9--[2]--6--[3]
# \ /
# \----8-----/
#
edges = [(0,1,7), (0,2,8), (1,2,9), (2,3,6)]
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blossom = NonTrivialBlossom(
subblossoms=[Blossom(0), Blossom(1), Blossom(2)],
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edges=[0,2,1])
for sub in blossom.subblossoms:
sub.parent = blossom
blossom.dual_var = -1
ctx = self._make_context(
edges,
vertex_mate=[1, 0, 3, 2],
vertex_dual_2x=[4, 6, 8, 4],
nontrivial_blossom=[blossom])
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with self.assertRaises(MatchingError):
verify_optimum(ctx)
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def test_blossom_not_full(self):
#
# [3] [4]
# | |
# 8 8
# | |
# [0]--7--[1]--5--[2]
# \ /
# \----2-----/
#
edges = [(0,1,7), (0,2,2), (1,2,5), (0,3,8), (1,4,8)]
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blossom = NonTrivialBlossom(
subblossoms=[Blossom(0), Blossom(1), Blossom(2)],
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edges=[0,2,1])
for sub in blossom.subblossoms:
sub.parent = blossom
blossom.dual_var = 2
ctx = self._make_context(
edges,
vertex_mate=[3, 4, -1, 0, 1],
vertex_dual_2x=[4, 10, 0, 12, 6],
nontrivial_blossom=[blossom])
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with self.assertRaises(MatchingError):
verify_optimum(ctx)
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class TestValueRange(unittest.TestCase):
"""Test graphs that force big values for dual variables or edge slack."""
def test_big_blossom_dual(self):
"""Force modified blossom dual close to 2*maxweight."""
#
# [3]
# / \
# W-4/ \W
# 7 / \
# [1]-----[2]-----[4]
# | W-4
# 5|
# | 1
# [5]-----[6]
#
w = 100000
pairs = mwm([(1,2,7), (2,3,w-4), (2,4,w-4), (2,5,5), (3,4,w), (5,6,1)])
self.assertEqual(pairs, [(1,2), (3,4), (5,6)])
def test_negative_blossom_dual(self):
"""Force modified blossom dual close to -maxweight."""
#
# [3]
# / \
# 5/ \7
# 1 / \
# [1]-----[2]-----[4]
# | 5
# 1|
# | W
# [5]-----[6]
#
w = 100000
pairs = mwm([(1,2,1), (2,3,5), (2,4,5), (2,5,1), (3,4,7), (5,6,w)])
self.assertEqual(pairs, [(1,2), (3,4), (5,6)])
def test_big_edge_slack(self):
"""Force modified edge slack close to 3*maxweight."""
#
# 6 W W-2 5
# [1]-----[2]-----[3]-----[4]-----[5]
# | |
# |1 |1
# | |
# [6]-----[7]-----[8]-----[9]-----[10]
# 6 W W-2 5
#
w = 100000
pairs = mwm([(1,2,6), (1,6,1), (2,3,w), (3,4,w-2), (3,8,1), (4,5,5),
(6,7,6), (7,8,w), (8,9,w-2), (9,10,5)])
self.assertEqual(pairs, [(1,6), (2,3), (4,5), (7,8), (9,10)])
if __name__ == "__main__":
unittest.main()