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