Use priority queue for delta4

cpp/mwmatching.h

@@ -430,7 +430,9 @@ struct NonTrivialBlossom : public Blossom<WeightType>
      */
     WeightType dual_var;
 
-    // TODO -- delta4_node
+    /** Top-level T-blossoms are elements in the delta4 queue. */
+    typedef PriorityQueue<WeightType, NonTrivialBlossom*> BlossomQueue;
+    typename BlossomQueue::Node delta4_node;
 
     /** Initialize a non-trivial blossom. */
     NonTrivialBlossom(
@@ -637,7 +639,12 @@ public:
     /** For each edge, a node in delta3_queue. */
     std::vector<typename EdgeQueue::Node> delta3_node;
 
-    // TODO -- delta4_queue
+    /**
+     * Queue of top-level non-trivial T-blossoms.
+     * Priority of a blossom is its modified dual variable.
+     */
+    typedef PriorityQueue<WeightType, NonTrivialBlossomT*> BlossomQueue;
+    BlossomQueue delta4_queue;
 
     // TODO -- vertex_sedge_queue
     // TODO -- vertex_sedge_node
@@ -961,12 +968,16 @@ public:
 
         blossom->label = LABEL_T;
 
-        // Unlabeled blossoms and T-blossoms use different rules
-        // for modified blossom duals. Adjust the modified dual variable
-        // to preserve the true blossom dual while switching labels.
         NonTrivialBlossomT* ntb = blossom->nontrivial();
         if (ntb) {
+            // Unlabeled blossoms and T-blossoms use different rules
+            // for modified blossom duals. Adjust the modified dual variable
+            // to preserve the true blossom dual while switching labels.
             ntb->dual_var += 2 * delta_sum;
+
+            // Top-level T-blossoms are tracked in the delta4 queue.
+            assert(! ntb->delta4_node.valid());
+            delta4_queue.insert(&ntb->delta4_node, ntb->dual_var, ntb);
         }
 
         // Unlabeled vertices and T-vertices use different rules for
@@ -1025,9 +1036,13 @@ public:
 
         blossom->label = LABEL_NONE;
 
-        // Adjust modified blossom dual to preserve true blossom dual.
         NonTrivialBlossomT* ntb = blossom->nontrivial();
         if (ntb) {
+            // Unlabeled blossoms are not tracked in the delta4 queue.
+            assert(ntb->delta4_node.valid());
+            delta4_queue.remove(&ntb->delta4_node);
+
+            // Adjust modified blossom dual to preserve true blossom dual.
             ntb->dual_var -= 2 * delta_sum;
         }
 
@@ -1756,14 +1771,17 @@ public:
         }
 
         // Compute delta4: half minimum dual of a top-level T-blossom.
-        for (NonTrivialBlossomT& blossom : nontrivial_blossom) {
+        // This takes time O(1).
-            if ((! blossom.parent) && (blossom.label == LABEL_T)) {
+        if (! delta4_queue.empty()) {
-                WeightType true_dual_var = blossom.dual_var - 2 * delta_sum;
+            NonTrivialBlossomT* blossom = delta4_queue.min_elem();
-                if (true_dual_var / 2 <= delta.value) {
+            assert(! blossom->parent);
-                    delta.kind = 4;
+            assert(blossom->label == LABEL_T);
-                    delta.value = true_dual_var / 2;
+            // Calculate true blossom dual variable from modified dual.
-                    delta.blossom = &blossom;
+            WeightType blossom_dual = blossom->dual_var - 2 * delta_sum;
-                }
+            if (blossom_dual / 2 <= delta.value) {
+                delta.kind = 4;
+                delta.value = blossom_dual / 2;
+                delta.blossom = blossom;
             }
         }
 
@@ -1923,7 +1941,7 @@ public:
 
         // TODO -- check delta2_queue empty
         assert(delta3_queue.empty());
-        // TODO -- check delta4_queue empty
+        assert(delta4_queue.empty());
     }
 
     /** Run the matching algorithm. */