Readd terminal arcs heuristic

src/adiar/internal/algorithms/quantify.h

@@ -1306,28 +1306,47 @@ namespace adiar::internal
                                  const predicate<typename Policy::label_type>& pred)
   {
     // Extract meta data constants about the DAG
-    const size_t size  = dd.size();
-    const size_t width = dd.width();
+    const size_t size            = dd.size();
+    const size_t width           = dd.width();
+    const size_t false_terminals = dd.number_of_terminals(false);
+    const size_t true_terminals  = dd.number_of_terminals(true);
+
+    // ---------------------------------------------------------------------------------------------
+    // Terminal Count Heuristics
+
+    const size_t false_weight =
+      1 + Policy::collapse_to_terminal(typename Policy::pointer_type(false));
+
+    const size_t true_weight =
+      1 + Policy::collapse_to_terminal(typename Policy::pointer_type(true));
+
+    const double total_arcs         = 2.0 * size;
+    const double weighted_terminals = false_weight * false_terminals + true_weight * true_terminals;
+    const size_t exponent           = 16.0 * (weighted_terminals / total_arcs) + 0.5;
+
+    const typename Policy::label_type terminal_threshold =
+      (1u << std::min<size_t>(exponent, log2(2*Policy::max_label))) - 1u;
+
+    // ---------------------------------------------------------------------------------------------
+    // Shallow Variables Heuristic
 
     // Keep track of the number of nodes on the top-most levels in relation to the total size
     size_t seen_nodes = 0u;
 
     // Threshold to stop after the first n/3 nodes.
     const size_t max_nodes = size / 3;
 
-    // Final result
-    //
-    // TODO: Turn `result` into a double and decrease the weight of to-be quantified variables
-    //       depending on `seen_nodes`, the number of levels of width `width`, and/or in general a
-    //       (quadratic?) decay in the weight.
-    typename Policy::label_type result = 0u;
+    // TODO: Turn `shallow_variables` into a double and decrease the weight of to-be quantified
+    //       variables depending on `seen_nodes`, the number of levels of width `width`, and/or in
+    //       general using a (quadratic?) decay.
+    typename Policy::label_type shallow_variables = 0u;
 
     level_info_stream<false /*top-down*/> lis(dd);
 
     while (lis.can_pull()) {
       const level_info li = lis.pull();
 
-      if (pred(li.label()) == Policy::quantify_onset) { result++; }
+      if (pred(li.label()) == Policy::quantify_onset) { shallow_variables++; }
 
       // Stop at the (first) widest level
       if (li.width() == width) { break; }
@@ -1337,8 +1356,10 @@ namespace adiar::internal
       if (max_nodes < seen_nodes) { break; }
     }
 
-    adiar_assert(result < Policy::max_label);
-    return result;
+    adiar_assert(shallow_variables <= Policy::max_label);
+
+    // ---------------------------------------------------------------------------------------------
+    return std::min<size_t>(terminal_threshold, shallow_variables);
   }
 
   //////////////////////////////////////////////////////////////////////////////////////////////////