Expand zero-dual blossom before assigning label T

python/mwmatching.py

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

python/test_mwmatching.py

@@ -191,6 +191,32 @@ class TestMaximumWeightMatching(unittest.TestCase):
         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"""
+        #
+        #                5--[2]--3--[4]
+        #               /    |
+        #    [0]--5--[1]     5
+        #               \    |
+        #                5--[3]--3--[5]
+        #
+        self.assertEqual(
+            mwm([(0,1,5), (1,2,5), (1,3,5), (2,3,5), (2,4,3), (3,5,3)]),
+            [(0,1), (2,4), (3,5)])
+
+    def test47_expand_unlabeled_outer(self):
+        """expand outer blossom before assigning label T"""
+        #
+        #  [3]--10--[1]--15--[2]--12--[5]
+        #          _/  \_     |        |
+        #        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)])
+
     def test_fail_bad_input(self):
         """bad input values"""
         with self.assertRaises(TypeError):