Lazy delta updates of S-blossom duals

python/mwmatching.py

@@ -444,7 +444,13 @@ class _NonTrivialBlossom(_Blossom):
 
         # Every non-trivial blossom has a variable in the dual LPP.
         #
+        # If this is a top-level S-blossom,
+        # "dual_var" is the value of the dual variable minus 2 times
+        # the running sum of delta steps.
+        #
+        # In all other cases,
         # "dual_var" is the current value of the dual variable.
+        #
         # New blossoms start with dual variable 0.
         self.dual_var: float = 0
 
@@ -542,7 +548,7 @@ class _MatchingContext:
         #
         # For an S-vertex "x",
         # "vertex_dual_2x[x]" is 2 times the dual variable of vertex "x"
-        # plus two times the running sum of delta updates.
+        # plus two times the running sum of delta steps.
         #
         # For a T-vertex "x", ... TODO
         self.vertex_dual_2x: list[float]
@@ -553,13 +559,13 @@ class _MatchingContext:
 
         # Queue containing edges between S-vertices in different top-level
         # blossoms. The priority of an edge is its slack plus two times the
-        # running sum of delta updates.
+        # running sum of delta steps.
         self.delta3_queue: PriorityQueue[int] = PriorityQueue()
         self.delta3_set: set[int] = set()
 
         # Queue containing top-level non-trivial T-blossoms.
         # The priority of a blossom is its dual plus two times the running
-        # sum of delta updates.
+        # sum of delta steps.
         self.delta4_queue: PriorityQueue[_NonTrivialBlossom] = PriorityQueue()
 
         # For each T-vertex or unlabeled vertex "x",
@@ -677,34 +683,36 @@ class _MatchingContext:
     #
 
     def assign_blossom_label_s(self, blossom: _Blossom) -> None:
-        """Assign label S to an unlabeled top-level blossom.
+        """Assign label S to an unlabeled top-level blossom."""
-
-        All vertices in the newly labeled blossom are added to the scan queue.
-        Dual variables are adjusted.
-        """
-
         assert blossom.parent is None
         assert blossom.label == _LABEL_NONE
-
-        # Assign label S.
         blossom.label = _LABEL_S
 
+        if isinstance(blossom, _NonTrivialBlossom):
+            blossom.dual_var -= self.delta_sum_2x
+
+    def remove_blossom_label_s(self, blossom: _Blossom) -> None:
+        """Remove label S from a top-level S-blossom."""
+        assert blossom.parent is None
+        assert blossom.label == _LABEL_S
+        blossom.label = _LABEL_NONE
+
+        if isinstance(blossom, _NonTrivialBlossom):
+            blossom.dual_var += self.delta_sum_2x
+
+    def assign_vertex_label_s(self, blossom: _Blossom) -> None:
+        """Adjust after assigning label S to previously unlabeled vertices."""
+
         # Adjust the vertex dual variables of the new S-vertices.
         vertices = blossom.vertices()
         for x in vertices:
             self.vertex_dual_2x[x] += self.delta_sum_2x
 
-        # Add all vertices inside the newly labeled S-blossom to the queue.
+        # Add the new S-vertices to the scan queue.
         self.scan_queue.extend(vertices)
 
-    def remove_blossom_label_s(self, blossom: _Blossom) -> None:
+    def remove_vertex_label_s(self, blossom: _Blossom) -> None:
-        """Remove label S from a top-level S-blossom."""
+        """Adjust after removing labels from S-vertices."""
-
-        assert blossom.parent is None
-        assert blossom.label == _LABEL_S
-
-        # Remove label.
-        blossom.label = _LABEL_NONE
 
         # Adjust the vertex dual variables of the former S-vertices.
         for x in blossom.vertices():
@@ -751,12 +759,11 @@ class _MatchingContext:
 
         # Remove blossom labels.
         for blossom in self.trivial_blossom + self.nontrivial_blossom:
-            if blossom.parent is None:
             if blossom.label == _LABEL_S:
                 self.remove_blossom_label_s(blossom)
+                self.remove_vertex_label_s(blossom)
             elif blossom.label == _LABEL_T:
                 self.remove_blossom_label_t(blossom)
-            blossom.label = _LABEL_NONE
             blossom.tree_edge = None
 
         # Clear the scan queue.
@@ -881,18 +888,20 @@ class _MatchingContext:
         # Blossom must start and end with an S-sub-blossom.
         assert subblossoms[0].label == _LABEL_S
 
-        # Relabel the T-sub-blossoms to S-sub-blossoms.
+        # Remove blossom labels.
-        # This also adds new S-vertices to the scan queue.
+        # Mark vertices inside former T-blossoms as S-vertices.
         for sub in subblossoms:
-            if sub.label == _LABEL_T:
+            if sub.label == _LABEL_S:
+                self.remove_blossom_label_s(sub)
+            elif sub.label == _LABEL_T:
                 self.remove_blossom_label_t(sub)
-                self.assign_blossom_label_s(sub)
+                self.assign_vertex_label_s(sub)
 
         # Create the new blossom object.
         blossom = _NonTrivialBlossom(subblossoms, path.edges)
 
         # Assign label S to the new blossom and link it to the tree.
-        blossom.label = _LABEL_S
+        self.assign_blossom_label_s(blossom)
         blossom.tree_edge = subblossoms[0].tree_edge
 
         # Insert into the blossom array.
@@ -1185,6 +1194,7 @@ class _MatchingContext:
         # Assign label S to the blossom that contains vertex "x".
         bx = self.vertex_top_blossom[x]
         self.assign_blossom_label_s(bx)
+        self.assign_vertex_label_s(bx)
 
         y = self.vertex_mate[x]
         if y == -1:
@@ -1325,7 +1335,7 @@ class _MatchingContext:
                 elif ylabel == _LABEL_S:
                     # Update tracking of least-slack edges between S-blossoms.
                     # Priority is edge slack plus 2 times the running sum of
-                    # delta updates.
+                    # delta steps.
                     if e not in self.delta3_set:
                         if self.graph.integer_weights:
                             # If all edge weights are integers, the slack of
@@ -1443,10 +1453,7 @@ class _MatchingContext:
         for blossom in self.nontrivial_blossom:
             if blossom.parent is None:
                 blabel = blossom.label
-                if blabel == _LABEL_S:
+                if blabel == _LABEL_T:
-                    # S-blossom: add 2*delta to dual variable.
-                    blossom.dual_var += delta_2x
-                elif blabel == _LABEL_T:
                     # T-blossom: subtract 2*delta from dual variable.
                     blossom.dual_var -= delta_2x