diff --git a/daggy/include/daggy/DAG.hpp b/daggy/include/daggy/DAG.hpp
index beace9b..365b303 100644
--- a/daggy/include/daggy/DAG.hpp
+++ b/daggy/include/daggy/DAG.hpp
@@ -20,13 +20,13 @@
 
 namespace daggy {
 
-  template <typename K, typename V>
+  template <typename T>
   struct Vertex
   {
     RunState state    = RunState::QUEUED;
     uint32_t depCount = 0;
-    V data;
-    std::unordered_set<K> children;
+    T data;
+    std::unordered_set<size_t> children;
   };
 
   template <typename K, typename V>
@@ -42,7 +42,7 @@ namespace daggy {
     void addEdge(const K &from, const K &to);
 
     void addEdgeIf(const K &src,
-                   std::function<bool(const Vertex<K, V> &v)> predicate);
+                   std::function<bool(const Vertex<V> &v)> predicate);
 
     [[nodiscard]] bool isValid() const;
 
@@ -61,19 +61,21 @@ namespace daggy {
 
     void setVertexState(const K &id, RunState state);
 
-    void forEach(
-        std::function<void(const std::pair<K, Vertex<K, V>> &)> fun) const;
+    void forEach(std::function<void(const Vertex<V> &)> fun) const;
 
     [[nodiscard]] bool allVisited() const;
 
     std::optional<std::pair<K, V>> visitNext();
 
-    Vertex<K, V> &getVertex(const K &id);
+    // WARNING: reference potentially invalidated on insertions.
+    Vertex<V> &getVertex(const K &id);
 
     void completeVisit(const K &id);
 
   private:
-    std::unordered_map<K, Vertex<K, V>> vertices_;
+    std::unordered_map<K, size_t> keyMap_;
+    std::vector<K> vertexName_;
+    std::vector<Vertex<V>> vertices_;
   };
 }  // namespace daggy
 
diff --git a/daggy/include/daggy/DAG.impl.hxx b/daggy/include/daggy/DAG.impl.hxx
index f347143..2a9e33c 100644
--- a/daggy/include/daggy/DAG.impl.hxx
+++ b/daggy/include/daggy/DAG.impl.hxx
@@ -14,20 +14,20 @@ namespace daggy {
   template <typename K, typename V>
   bool DAG<K, V>::hasVertex(const K &id)
   {
-    return vertices_.count(id) != 0;
+    return keyMap_.count(id) != 0;
   }
 
   template <typename K, typename V>
-  Vertex<K, V> &DAG<K, V>::getVertex(const K &id)
+  Vertex<V> &DAG<K, V>::getVertex(const K &id)
   {
-    return vertices_.at(id);
+    return vertices_[keyMap_.at(id)];
   }
 
   template <typename K, typename V>
   std::unordered_set<K> DAG<K, V>::getVertices() const
   {
     std::unordered_set<K> keys;
-    for (const auto it : vertices_) {
+    for (const auto it : keyMap_) {
       keys.insert(it.first);
     }
     return keys;
@@ -36,58 +36,59 @@ namespace daggy {
   template <typename K, typename V>
   void DAG<K, V>::addVertex(K id, V data)
   {
-    if (vertices_.count(id) != 0) {
+    if (keyMap_.count(id) != 0) {
       std::stringstream ss;
       ss << "A vertex with ID " << id << " already exists in the DAG";
       throw std::runtime_error(ss.str());
     }
-    vertices_.emplace(
-        id,
-        Vertex<K, V>{.state = RunState::QUEUED, .depCount = 0, .data = data});
+    size_t idx = vertices_.size();
+    vertexName_.emplace_back(id);
+    vertices_.emplace_back(
+        Vertex<V>{.state = RunState::QUEUED, .depCount = 0, .data = data});
+    keyMap_.emplace(id, idx);
   }
 
   template <typename K, typename V>
   void DAG<K, V>::addEdge(const K &from, const K &to)
   {
-    if (vertices_.find(from) == vertices_.end())
-      throw std::runtime_error("No such vertex");
-    if (vertices_.find(to) == vertices_.end())
-      throw std::runtime_error("No such vertex");
-    vertices_.at(from).children.insert(to);
-    vertices_.at(to).depCount++;
+    size_t src = keyMap_.at(from);
+    size_t dst = keyMap_.at(to);
+    vertices_[src].children.insert(dst);
+    vertices_[dst].depCount++;
   }
 
   template <typename K, typename V>
-  void DAG<K, V>::addEdgeIf(
-      const K &src, std::function<bool(const Vertex<K, V> &v)> predicate)
+  void DAG<K, V>::addEdgeIf(const K &src,
+                            std::function<bool(const Vertex<V> &v)> predicate)
   {
-    auto &parent = vertices_.at(src);
-    for (auto &[name, vertex] : vertices_) {
-      if (!predicate(vertex))
+    size_t parentIdx = keyMap_.at(src);
+    auto &parent     = vertices_[parentIdx];
+    for (size_t i = 0; i < vertices_.size(); ++i) {
+      if (!predicate(vertices_[i]))
         continue;
-      if (name == src)
+      if (i == parentIdx)
         continue;
-      parent.children.insert(name);
-      vertex.depCount++;
+      parent.children.insert(i);
+      vertices_[i].depCount++;
     }
   }
 
   template <typename K, typename V>
   bool DAG<K, V>::isValid() const
   {
-    std::unordered_map<K, size_t> depCounts;
-    std::queue<K> ready;
+    std::vector<size_t> depCounts(vertices_.size(), 0);
+    std::queue<size_t> ready;
     size_t processed = 0;
 
-    for (const auto &[k, v] : vertices_) {
-      depCounts[k] = v.depCount;
-      if (v.depCount == 0)
-        ready.push(k);
+    for (size_t i = 0; i < vertices_.size(); ++i) {
+      depCounts[i] = vertices_[i].depCount;
+      if (depCounts[i] == 0)
+        ready.push(i);
     }
 
     while (!ready.empty()) {
       const auto &k = ready.front();
-      for (const auto &child : vertices_.at(k).children) {
+      for (const auto &child : vertices_[k].children) {
         auto dc = --depCounts[child];
         if (dc == 0)
           ready.push(child);
@@ -103,15 +104,15 @@ namespace daggy {
   void DAG<K, V>::reset()
   {
     // Reset the state of all vertices
-    for (auto &[_, v] : vertices_) {
+    for (auto &v : vertices_) {
       v.state    = RunState::QUEUED;
       v.depCount = 0;
     }
 
     // Calculate the upstream count
-    for (auto &[_, v] : vertices_) {
+    for (auto &v : vertices_) {
       for (auto c : v.children) {
-        vertices_.at(c).depCount++;
+        vertices_[c].depCount++;
       }
     }
   }
@@ -119,7 +120,7 @@ namespace daggy {
   template <typename K, typename V>
   void DAG<K, V>::resetRunning()
   {
-    for (auto &[k, v] : vertices_) {
+    for (auto &v : vertices_) {
       if (v.state != +RunState::RUNNING)
         continue;
       v.state = RunState::QUEUED;
@@ -129,29 +130,28 @@ namespace daggy {
   template <typename K, typename V>
   void DAG<K, V>::setVertexState(const K &id, RunState state)
   {
-    vertices_.at(id).state = state;
+    vertices_[keyMap_.at(id)].state = state;
   }
 
   template <typename K, typename V>
   bool DAG<K, V>::allVisited() const
   {
-    for (const auto &[_, v] : vertices_) {
-      if (v.state != +RunState::COMPLETED)
-        return false;
-    }
-    return true;
+    return not std::any_of(
+        vertices_.begin(), vertices_.end(),
+        [](const auto &v) { return v.state != +RunState::COMPLETED; });
   }
 
   template <typename K, typename V>
   std::optional<std::pair<K, V>> DAG<K, V>::visitNext()
   {
-    for (auto &[k, v] : vertices_) {
+    for (size_t i = 0; i < vertices_.size(); ++i) {
+      auto &v = vertices_[i];
       if (v.state != +RunState::QUEUED)
         continue;
       if (v.depCount != 0)
         continue;
       v.state = RunState::RUNNING;
-      return std::make_pair(k, v.data);
+      return std::make_pair(vertexName_[i], v.data);
     }
     return {};
   }
@@ -159,16 +159,15 @@ namespace daggy {
   template <typename K, typename V>
   void DAG<K, V>::completeVisit(const K &id)
   {
-    auto &v = vertices_.at(id);
+    auto &v = vertices_[keyMap_.at(id)];
     v.state = RunState::COMPLETED;
     for (auto c : v.children) {
-      --vertices_.at(c).depCount;
+      --vertices_[c].depCount;
     }
   }
 
   template <typename K, typename V>
-  void DAG<K, V>::forEach(
-      std::function<void(const std::pair<K, Vertex<K, V>> &)> fun) const
+  void DAG<K, V>::forEach(std::function<void(const Vertex<V> &)> fun) const
   {
     for (auto it = vertices_.begin(); it != vertices_.end(); ++it) {
       fun(*it);
diff --git a/daggy/src/Utilities.cpp b/daggy/src/Utilities.cpp
index 12c6b0d..29ecfff 100644
--- a/daggy/src/Utilities.cpp
+++ b/daggy/src/Utilities.cpp
@@ -146,22 +146,36 @@ namespace daggy {
         if (fut.valid()) {
           auto attempt = fut.get();
           logger.logTaskAttempt(runID, taskName, attempt);
-          auto &vert = dag.getVertex(taskName);
+
+          // Not a reference, since adding tasks will invalidate references
+          auto vert  = dag.getVertex(taskName);
           auto &task = vert.data;
           if (attempt.rc == 0) {
             logger.updateTaskState(runID, taskName, RunState::COMPLETED);
             if (task.isGenerator) {
               // Parse the output and update the DAGs
               try {
-                auto newTasks = expandTaskSet(tasksFromJSON(attempt.outputLog),
-                                              executor, parameters);
+                auto parsedTasks = tasksFromJSON(attempt.outputLog);
+                auto newTasks =
+                    expandTaskSet(parsedTasks, executor, parameters);
                 updateDAGFromTasks(dag, newTasks);
 
+                // Add in dependencies from current task to new tasks
                 for (const auto &[ntName, ntTask] : newTasks) {
                   logger.addTask(runID, ntName, ntTask);
-                  dag.addEdge(taskName, ntName);
                   task.children.insert(ntName);
                 }
+
+                // Efficiently add new edges from generator task
+                // to children
+                std::unordered_set<std::string> baseNames;
+                for (const auto &[k, v] : parsedTasks) {
+                  baseNames.insert(v.definedName);
+                }
+                dag.addEdgeIf(taskName, [&](const auto &v) {
+                  return baseNames.count(v.data.definedName) > 0;
+                });
+
                 logger.updateTask(runID, taskName, task);
               }
               catch (std::exception &e) {
diff --git a/tests/unit_dag.cpp b/tests/unit_dag.cpp
index c0eb1d1..61764a7 100644
--- a/tests/unit_dag.cpp
+++ b/tests/unit_dag.cpp
@@ -63,7 +63,9 @@ TEST_CASE("dag_traversal", "[dag]")
     std::vector<size_t> visitOrder(N_VERTICES);
     size_t i = 0;
     while (!dag.allVisited()) {
-      const auto v = dag.visitNext().value();
+      auto o = dag.visitNext();
+      REQUIRE(o.has_value());
+      const auto v = o.value();
       dag.completeVisit(v.first);
       visitOrder[v.first] = i;
       ++i;
diff --git a/tests/unit_utilities.cpp b/tests/unit_utilities.cpp
index 1471f27..1c6a6f0 100644
--- a/tests/unit_utilities.cpp
+++ b/tests/unit_utilities.cpp
@@ -150,6 +150,13 @@ TEST_CASE("dag_runner", "[utilities_dag_runner]")
       REQUIRE(attempts.front().rc == 0);
     }
   }
+}
+
+TEST_CASE("runDAG_recovery", "[runDAG]")
+{
+  daggy::executors::task::ForkingTaskExecutor ex(10);
+  std::stringstream ss;
+  daggy::loggers::dag_run::OStreamLogger logger(ss);
 
   SECTION("Recovery from Error")
   {
@@ -198,6 +205,13 @@ TEST_CASE("dag_runner", "[utilities_dag_runner]")
 
     cleanup();
   }
+}
+
+TEST_CASE("runDAG_generator", "[runDAG_generator]")
+{
+  daggy::executors::task::ForkingTaskExecutor ex(10);
+  std::stringstream ss;
+  daggy::loggers::dag_run::OStreamLogger logger(ss);
 
   SECTION("Generator tasks")
   {
@@ -211,8 +225,8 @@ TEST_CASE("dag_runner", "[utilities_dag_runner]")
     ofh << generatorOutput << std::endl;
     ofh.close();
 
+    daggy::TimePoint globalStartTime = daggy::Clock::now();
     std::stringstream jsonTasks;
-
     jsonTasks
         << R"({ "A": { "job": {"command": [ "/usr/bin/cat", )"
         << std::quoted(ofn.string())
@@ -221,8 +235,10 @@ TEST_CASE("dag_runner", "[utilities_dag_runner]")
 
     auto baseTasks = daggy::tasksFromJSON(jsonTasks.str());
     REQUIRE(baseTasks.size() == 2);
+    REQUIRE(baseTasks["A"].children == std::unordered_set<std::string>{"C"});
     auto tasks = daggy::expandTaskSet(baseTasks, ex, params);
     REQUIRE(tasks.size() == 2);
+    REQUIRE(tasks["A_0"].children == std::unordered_set<std::string>{"C"});
     auto dag = daggy::buildDAGFromTasks(tasks);
     REQUIRE(dag.size() == 2);
 
@@ -250,5 +266,27 @@ TEST_CASE("dag_runner", "[utilities_dag_runner]")
     REQUIRE(record.tasks["B_1"].children ==
             std::unordered_set<std::string>{"C"});
     REQUIRE(record.tasks["C_0"].children.empty());
+
+    // Ensure they were run in the right order
+    // All A's get run before B's, which run before C's
+    daggy::TimePoint globalStopTime = daggy::Clock::now();
+    std::array<daggy::TimePoint, 3> minTimes;
+    minTimes.fill(globalStartTime);
+    std::array<daggy::TimePoint, 3> maxTimes;
+    maxTimes.fill(globalStopTime);
+
+    for (const auto &[k, v] : record.taskAttempts) {
+      size_t idx      = k[0] - 65;
+      auto &startTime = minTimes[idx];
+      auto &stopTime  = maxTimes[idx];
+      startTime       = std::max(startTime, v.front().startTime);
+      stopTime        = std::min(stopTime, v.back().stopTime);
+    }
+
+    for (size_t i = 0; i < 3; ++i) {
+      for (size_t j = i + 1; j < 2; ++j) {
+        REQUIRE(maxTimes[i] < minTimes[j]);
+      }
+    }
   }
 }