Expand zero-dual blossom before assigning label T
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@ -1071,83 +1071,28 @@ class _MatchingContext:
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# Delete the expanded blossom.
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self.nontrivial_blossom.remove(blossom)
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def expand_blossom_rec(
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self,
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blossom: _NonTrivialBlossom,
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stack: list[_NonTrivialBlossom]
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) -> None:
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"""Expand the specified blossom and recursively expand any
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sub-blossoms that have dual variable zero.
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Use the stack object instead of making direct recursive calls.
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"""
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assert blossom.parent is None
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# Examine sub-blossoms.
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for sub in blossom.subblossoms:
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# Mark the sub-blossom as a top-level blossom.
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sub.parent = None
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if isinstance(sub, _NonTrivialBlossom):
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# Non-trivial sub-blossom.
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# If its dual variable is zero, expand it recursively.
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if sub.dual_var == 0:
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stack.append(sub)
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else:
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# This sub-blossom will not be expanded;
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# it now becomes top-level. Update its vertices
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# to point to this sub-blossom.
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for x in sub.vertices():
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self.vertex_top_blossom[x] = sub
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else:
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# Trivial sub-blossom. Mark it as top-level vertex.
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self.vertex_top_blossom[sub.base_vertex] = sub
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# Deletion of the expanded blossom will be handled in
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# the function "expand_zero_dual_blossoms()".
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def expand_zero_dual_blossoms(self) -> None:
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"""Expand all blossoms with zero dual variable (recursively).
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Note that this function runs at the end of a stage.
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Blossoms are not labeled. Least-slack edges are not tracked.
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def expand_unlabeled_blossom(self, blossom: _NonTrivialBlossom) -> None:
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"""Expand the specified unlabeled blossom.
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This function takes time O(n).
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"""
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# Use an explicit stack to avoid deep recursion.
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# The stack contains a list of blossoms to be expanded.
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stack: list[_NonTrivialBlossom] = []
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assert blossom.parent is None
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assert blossom.label == _LABEL_NONE
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# Find top-level blossoms with zero slack.
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for blossom in self.nontrivial_blossom:
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if blossom.parent is None:
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# We typically expand only S-blossoms that were created after
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# the most recent delta step. Those blossoms have _exactly_
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# zero dual. So this comparison is reliable, even in case
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# of floating point edge weights.
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if blossom.dual_var == 0:
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stack.append(blossom)
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# Convert sub-blossoms into top-level blossoms.
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for sub in blossom.subblossoms:
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assert sub.label == _LABEL_NONE
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sub.parent = None
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# Skip the rest of this function if there are no blossoms to delete.
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if not stack:
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return
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if isinstance(sub, _NonTrivialBlossom):
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for x in sub.vertices():
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self.vertex_top_blossom[x] = sub
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else:
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self.vertex_top_blossom[sub.base_vertex] = sub
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# Expand blossoms.
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while stack:
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blossom = stack.pop()
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self.expand_blossom_rec(blossom, stack)
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# Mark the blossom for deletion.
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blossom.marker = True
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# Delete the expanded blossoms.
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# We do this in one pass over the array to ensure O(n) time.
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self.nontrivial_blossom = [blossom
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for blossom in self.nontrivial_blossom
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if not blossom.marker]
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# Delete the expanded blossom.
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self.nontrivial_blossom.remove(blossom)
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#
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# Augmenting:
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@ -1350,8 +1295,14 @@ class _MatchingContext:
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"""
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assert self.vertex_top_blossom[x].label == _LABEL_S
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# Assign label T to the unlabeled blossom.
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by = self.vertex_top_blossom[y]
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# Expand zero-dual blossoms before assigning label T.
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while isinstance(by, _NonTrivialBlossom) and (by.dual_var == 0):
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self.expand_unlabeled_blossom(by)
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by = self.vertex_top_blossom[y]
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# Assign label T to the unlabeled blossom.
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assert by.label == _LABEL_NONE
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by.label = _LABEL_T
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by.tree_edge = (x, y)
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@ -1646,11 +1597,6 @@ class _MatchingContext:
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if augmenting_path is not None:
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self.augment_matching(augmenting_path)
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# Expand all blossoms with dual variable zero.
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# These are typically S-blossoms, since T-blossoms normally
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# get expanded as soon as their dual variable hits zero.
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self.expand_zero_dual_blossoms()
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# Remove all labels, clear queue.
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self.reset_stage()
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@ -191,6 +191,32 @@ class TestMaximumWeightMatching(unittest.TestCase):
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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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# 5--[2]--3--[4]
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# / |
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# [0]--5--[1] 5
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# \ |
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# 5--[3]--3--[5]
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#
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self.assertEqual(
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mwm([(0,1,5), (1,2,5), (1,3,5), (2,3,5), (2,4,3), (3,5,3)]),
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[(0,1), (2,4), (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 test_fail_bad_input(self):
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"""bad input values"""
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with self.assertRaises(TypeError):
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