diff --git a/doc/fluid/design/ir/draft.md b/doc/fluid/design/ir/draft.md
index a141dcbca584c6064c8da863410692a8be911d12..a33b5a9c9312c93247a1e1f3431061a5aad6c884 100644
--- a/doc/fluid/design/ir/draft.md
+++ b/doc/fluid/design/ir/draft.md
@@ -1,16 +1,16 @@
 ## Motivation
 
-There is a ```gap``` between the ```Program``` defined by
-user and the ```Executable``` that can be scheduled
+There is a `gap` between the `Program` defined by
+user and the `Executable` that can be scheduled
 efficiently on heterogeneous hardware, either locally
 or distributedly.
 
-Usually, the ```gap``` is bridged by
+Usually, the `gap` is bridged by
 
 * A serious transformations with defined order.
 
 * These transformations usually involve
-```insert, delete, clustering, split, dependency analysis```.
+`insert, delete, clustering, split, dependency analysis`.
 
 * Has a simple way to verify and debug each transformation.
 
@@ -38,44 +38,44 @@ design below.
 
 #### Node
 
-```Node``` represents an operation that performs some computation or
+`Node` represents an operation that performs some computation or
 a variable that is input or output of operation.
 
-```Node```s are connected to other ```Node```s via inputs and outputs.
+`Node`s are connected to other `Node`s via inputs and outputs.
 
 Other properties (maybe device placement information) can be added
-to ```Node``` in the future if it's a
-common requirement of many other ```Pass```es. Otherwise, it should live
-in a ```Node``` wrapper class that is private to some ```Pass``` or be
-a local member of a ```Pass```.
+to `Node` in the future if it's a
+common requirement of many other `Pass`es. Otherwise, it should live
+in a `Node` wrapper class that is private to some `Pass` or be
+a local member of a `Pass`.
 
 #### Graph
 
-```Graph``` contains a list of ```Node```s, which are connected to
+`Graph` contains a list of `Node`s, which are connected to
 each other via inputs and outputs.
 
 TODO: Better definitions for the graph.
 
-```Graph``` can also contain ```Attribute```s. ```Attribute```s
-can be ``any`` thing. For example, it can be a list of "wraper"
-nodes. The ```wrapper``` nodes compose ```Node```s and provide
-helper method for execution or transformation. ```Attribute```
+`Graph` can also contain `Attribute`s. `Attribute`s
+can be `any` thing. For example, it can be a list of "wraper"
+nodes. The `wrapper` nodes compose `Node`s and provide
+helper method for execution or transformation. `Attribute`
 can also contain other things that describe some properties of
-the ```Graph``` or ```Graph``` nodes. ```Attribute``` can be passed
-across ```Pass```. However, it should be used with care.
+the `Graph` or `Graph` nodes. `Attribute` can be passed
+across `Pass`. However, it should be used with care.
 
 #### Pass
 
-```Pass``` represents a transformation of ```Graph```. Its input
-is a ```Graph``` and its output is also a ```Graph```. For example,
-a ```Pass``` can simply print out the ```Graph```. A ```Pass```
-can also fuse some ```Graph```'s ```Node```s.
+`Pass` represents a transformation of `Graph`. Its input
+is a `Graph` and its output is also a `Graph`. For example,
+a `Pass` can simply print out the `Graph`. A `Pass`
+can also fuse some `Graph`'s `Node`s.
 
 #### Optimize
 
-```Optimize``` contains a series of ```Pass``` with defined order.
-```Optimize``` transforms a ```Graph``` that only contains raw
-modeling logic to a ```Graph``` that can be run efficiently while
+`Optimize` contains a series of `Pass` with defined order.
+`Optimize` transforms a `Graph` that only contains raw
+modeling logic to a `Graph` that can be run efficiently while
 maintaining the original modeling logic.
 
 
diff --git a/paddle/fluid/framework/details/CMakeLists.txt b/paddle/fluid/framework/details/CMakeLists.txt
index df55b3d05402f1aeecfd8d4218a637a81d58ed87..9df7df1f42886d40210b16aa2ae5823e3310bfe7 100644
--- a/paddle/fluid/framework/details/CMakeLists.txt
+++ b/paddle/fluid/framework/details/CMakeLists.txt
@@ -1,11 +1,11 @@
-cc_library(var_handle SRCS var_handle.cc DEPS place framework_proto)
+cc_library(var_handle SRCS var_handle.cc DEPS place framework_proto node)
 cc_library(op_handle_base SRCS op_handle_base.cc DEPS var_handle device_context lod_tensor)
 cc_library(scale_loss_grad_op_handle SRCS scale_loss_grad_op_handle.cc DEPS op_handle_base scope lod_tensor ddim memory)
 cc_library(fetch_op_handle SRCS fetch_op_handle.cc DEPS op_handle_base scope lod_tensor ddim memory)
 cc_library(computation_op_handle SRCS computation_op_handle.cc DEPS framework_proto scope place operator op_registry)
 cc_library(rpc_op_handle SRCS rpc_op_handle.cc DEPS framework_proto scope place operator op_registry)
 
-cc_library(ssa_graph_builder SRCS ssa_graph_builder.cc DEPS graph)
+cc_library(ssa_graph_builder SRCS ssa_graph_builder.cc DEPS graph graph_helper)
 cc_library(ssa_graph_printer SRCS ssa_graph_printer.cc DEPS ssa_graph_builder)
 cc_library(ssa_graph_checker SRCS ssa_graph_checker.cc DEPS ssa_graph_builder)
 
diff --git a/paddle/fluid/framework/details/multi_devices_graph_builder.cc b/paddle/fluid/framework/details/multi_devices_graph_builder.cc
index f1f8674caf663ce38df5a2eecbcf690b5ca87dc4..22f0cb20d01cc5b40325ec37a8c7cd44105bc6c6 100644
--- a/paddle/fluid/framework/details/multi_devices_graph_builder.cc
+++ b/paddle/fluid/framework/details/multi_devices_graph_builder.cc
@@ -25,6 +25,7 @@
 #include "paddle/fluid/framework/details/reduce_op_handle.h"
 #include "paddle/fluid/framework/details/rpc_op_handle.h"
 #include "paddle/fluid/framework/details/scale_loss_grad_op_handle.h"
+#include "paddle/fluid/framework/ir/graph_helper.h"
 #include "paddle/fluid/framework/ir/node.h"
 #include "paddle/fluid/framework/op_info.h"
 #include "paddle/fluid/framework/scope.h"
@@ -67,7 +68,8 @@ MultiDevSSAGraphBuilder::MultiDevSSAGraphBuilder(
   }
 }
 
-void MultiDevSSAGraphBuilder::CreateOpHandleIOs(Graph *result, ir::Node *node,
+void MultiDevSSAGraphBuilder::CreateOpHandleIOs(ir::Graph *result,
+                                                ir::Node *node,
                                                 size_t place_id) const {
   auto p = places_[place_id];
   auto *op_handle = result->Get<GraphOps>("ops").back().get();
@@ -92,12 +94,11 @@ void MultiDevSSAGraphBuilder::CreateOpHandleIOs(Graph *result, ir::Node *node,
 }
 
 std::vector<std::string> MultiDevSSAGraphBuilder::FindDistTrainSendVars(
-    const std::vector<std::unique_ptr<ir::Node>> &nodes) const {
+    const std::vector<ir::Node *> &nodes) const {
   std::vector<std::string> send_vars;
   // since parameters are all in block 0,
   // it's enough to only scan send ops in block 0
   for (auto &node : nodes) {
-    if (node->NodeType() != ir::Node::Type::kOperation) continue;
     OpDesc *op = node->Op();
     // TODO(Yancey1989): use a graceful method to find send op,
     // instead of the the hard code string
@@ -112,10 +113,9 @@ std::vector<std::string> MultiDevSSAGraphBuilder::FindDistTrainSendVars(
 }
 
 std::vector<std::string> MultiDevSSAGraphBuilder::FindDistTrainRecvVars(
-    const std::vector<std::unique_ptr<ir::Node>> &nodes) const {
+    const std::vector<ir::Node *> &nodes) const {
   std::vector<std::string> recv_vars;
   for (auto &node : nodes) {
-    if (node->NodeType() != ir::Node::Type::kOperation) continue;
     OpDesc *op = node->Op();
     // TODO(Yancey1989): use a graceful method to find recv op,
     // instead of the hard code string
@@ -170,6 +170,7 @@ size_t MultiDevSSAGraphBuilder::GetAppropriateDeviceID(
     const std::vector<std::string> &var_names) const {
   int64_t numel_sum = 0;
   for (auto var_name : var_names) {
+    if (all_vars_.find(var_name) == all_vars_.end()) continue;
     auto var_desc = all_vars_.at(var_name);
     PADDLE_ENFORCE_NOT_NULL(var_desc);
     auto dim = framework::make_ddim(var_desc->GetShape());
@@ -186,19 +187,70 @@ size_t MultiDevSSAGraphBuilder::GetAppropriateDeviceID(
   return dev_id;
 }
 
-std::unique_ptr<Graph> MultiDevSSAGraphBuilder::Apply(
-    std::unique_ptr<Graph> graph) const {
-  // Rebuild the graph structure.
-  auto nodes = std::move(graph->nodes);
-  graph->nodes.clear();
+// Topology sort the graph nodes from inputs to outputs.
+// Since SSAGraphBuilder depends on forward/backward nodes to assign devices
+// to parameter/gradients before optimizer ops, topo sort is insufficient. (
+// some optimizer ops might not depend on any nodes), we manually move all
+// optimizer nodes after last backward nodes.
+// However, the assumption by SSAGraphBuilder should be relaxed in the future.
+std::vector<ir::Node *> SortOpsAndDelayOptimizeOp(const ir::Graph &graph) {
+  std::vector<ir::Node *> ret = ir::TopologySortOperations(graph);
+  size_t last_backward = 0;
+  for (size_t i = 0; i < ret.size(); ++i) {
+    if (boost::get<int>(
+            ret[i]->Op()->GetAttr(OpProtoAndCheckerMaker::OpRoleAttrName())) ==
+        static_cast<int>(OpRole::kBackward)) {
+      last_backward = i;
+    }
+  }
+
+  std::vector<ir::Node *> optimize_ops;
+  std::vector<ir::Node *> sorted_ret;
+  for (size_t i = 0; i < ret.size(); ++i) {
+    if (i < last_backward) {
+      if (boost::get<int>(ret[i]->Op()->GetAttr(
+              OpProtoAndCheckerMaker::OpRoleAttrName())) ==
+          static_cast<int>(OpRole::kOptimize)) {
+        optimize_ops.push_back(ret[i]);
+      } else {
+        sorted_ret.push_back(ret[i]);
+      }
+    } else if (i == last_backward) {
+      sorted_ret.push_back(ret[i]);
+      // Verify that no operations before optimize ops depends on optimize ops.
+      std::unordered_set<ir::Node *> optimize_set(optimize_ops.begin(),
+                                                  optimize_ops.end());
+      for (ir::Node *n : sorted_ret) {
+        for (ir::Node *in : n->inputs) {
+          for (ir::Node *pre_n : in->inputs) {
+            PADDLE_ENFORCE(optimize_set.find(pre_n) == optimize_set.end(),
+                           "optimize operations cannot be depended by forward "
+                           "or backward node %s -> %s",
+                           pre_n->Name(), n->Name());
+          }
+        }
+      }
+      sorted_ret.insert(sorted_ret.end(), optimize_ops.begin(),
+                        optimize_ops.end());
+    } else {
+      sorted_ret.push_back(ret[i]);
+    }
+  }
+  return sorted_ret;
+}
+
+std::unique_ptr<ir::Graph> MultiDevSSAGraphBuilder::Apply(
+    std::unique_ptr<ir::Graph> graph) const {
+  // Give the topology sort order and rebuild the graph structure.
+  std::vector<ir::Node *> sorted_ops = SortOpsAndDelayOptimizeOp(*graph);
+  auto nodes = graph->ReleaseNodes();
+  ir::Graph &result = *graph;
 
   for (auto &node : nodes) {
-    if (node->NodeType() == ir::Node::Type::kVariable) {
+    if (node->NodeType() == ir::Node::Type::kVariable && node->Var()) {
       all_vars_.emplace(node->Name(), node->Var());
     }
   }
-
-  Graph &result = *graph;
   std::unordered_set<std::string> og_has_been_broadcast;
 
   // We cannot invoke resize. It is a bug of GCC 4.8
@@ -208,8 +260,8 @@ std::unique_ptr<Graph> MultiDevSSAGraphBuilder::Apply(
 
   // find send/recv vars so that we can place the distributed training
   // realted op in the place 0
-  auto send_vars = FindDistTrainSendVars(nodes);
-  auto recv_vars = FindDistTrainRecvVars(nodes);
+  auto send_vars = FindDistTrainSendVars(sorted_ops);
+  auto recv_vars = FindDistTrainRecvVars(sorted_ops);
 
   std::vector<std::unordered_set<std::string>> bcast_var_name_set;
   bcast_var_name_set.resize(places_.size());
@@ -217,22 +269,18 @@ std::unique_ptr<Graph> MultiDevSSAGraphBuilder::Apply(
   size_t cur_device_id = 0;
   bool is_forwarding = true;
 
-  // NOTE: Currently, passes before SSAGraphBuilder cannot reorder
-  // forward, backward nodes. E.g. you can't append an forward node
-  // at the end of the node list.
-  // TODO(panyx0718): FIXME: Needs to sort by forward->backward order.
-  for (auto &node : nodes) {
-    if (node->NodeType() != ir::Node::Type::kOperation) continue;
+  for (ir::Node *node : sorted_ops) {
     if (boost::get<int>(
             node->Op()->GetAttr(OpProtoAndCheckerMaker::OpRoleAttrName())) ==
         static_cast<int>(OpRole::kRPC)) {
-      CreateRPCOp(&result, node.get());
-    } else if (IsDistTrainOp(node.get(), send_vars, recv_vars)) {
-      CreateDistTrainOp(&result, node.get());
-    } else if (IsScaleLossOp(node.get())) {
+      CreateRPCOp(&result, node);
+    } else if (IsDistTrainOp(node, send_vars, recv_vars)) {
+      CreateDistTrainOp(&result, node);
+    } else if (IsScaleLossOp(node)) {
       // user can customize loss@grad if not use_default_grad_scale_
       if (strategy_.gradient_scale_ !=
           BuildStrategy::GradientScaleStrategy::kCustomized) {
+        // TODO(paddle-dev): Why is there no input for this op_handle?
         CreateScaleLossGradOp(&result);
       }
       // This assumes the backward generating code will ensure IsScaleLossOp
@@ -241,24 +289,23 @@ std::unique_ptr<Graph> MultiDevSSAGraphBuilder::Apply(
       // the block.
       is_forwarding = false;
     } else {
-      int op_dev_id = GetOpDeviceID(node.get());
+      int op_dev_id = GetOpDeviceID(node);
       if (op_dev_id != -1) {  // This op only runs on one specific device.
-        CreateComputationalOp(&result, node.get(), op_dev_id);
+        CreateComputationalOp(&result, node, op_dev_id);
         for (ir::Node *n : node->outputs) {
           var_name_on_devices_.emplace(n->Name(), op_dev_id);
         }
       } else {
         // This op runs on all devices, and its output may have parameter's
         // gradients.
+        // TODO(paddle-dev): Why is so special about "read" op?
         if (node->Op()->Type() == "read" && strategy_.enable_data_balance_) {
           node->Op()->SetAttr("throw_eof_exp", false);
-          CreateComputationalOps(&result, node.get(), places_.size());
-          // TODO(paddle-dev): builder shouldn't depend on the out logic of
-          // a specific op.
+          CreateComputationalOps(&result, node, places_.size());
           const auto &data_var_names = node->Op()->Output("Out");
           InsertDataBalanceOp(&result, data_var_names);
         } else {
-          CreateComputationalOps(&result, node.get(), places_.size());
+          CreateComputationalOps(&result, node, places_.size());
         }
 
         if (!is_forwarding && places_.size() > 1) {
@@ -322,17 +369,17 @@ std::unique_ptr<Graph> MultiDevSSAGraphBuilder::Apply(
       }
     }
   }
-
   /*
-    Dependency graph has been constructed. However, there are still data
-    hazards need to be handled.
-   */
+  Dependency graph has been constructed. However, there are still data
+  hazards need to be handled.
+ */
   PolishGraphToSupportDataHazards(&result);
 
   /*
    * Only variables should be the leaves of graph.
    */
   AddOutputToLeafOps(&result);
+  PADDLE_ENFORCE(!ir::HasCircle(result));
   return graph;
 }
 
@@ -357,7 +404,7 @@ void MultiDevSSAGraphBuilder::SetCommunicationContext(
 #endif
 }
 
-void MultiDevSSAGraphBuilder::CreateBroadcastOp(Graph *result,
+void MultiDevSSAGraphBuilder::CreateBroadcastOp(ir::Graph *result,
                                                 const std::string &p_name,
                                                 size_t src_dev_id) const {
 #ifdef PADDLE_WITH_CUDA
@@ -387,7 +434,7 @@ void MultiDevSSAGraphBuilder::CreateBroadcastOp(Graph *result,
   }
 }
 
-void MultiDevSSAGraphBuilder::CreateComputationalOp(Graph *result,
+void MultiDevSSAGraphBuilder::CreateComputationalOp(ir::Graph *result,
                                                     ir::Node *node,
                                                     int dev_id) const {
   result->Get<GraphOps>("ops").emplace_back(
@@ -396,7 +443,7 @@ void MultiDevSSAGraphBuilder::CreateComputationalOp(Graph *result,
   CreateOpHandleIOs(result, node, dev_id);
 }
 
-void MultiDevSSAGraphBuilder::InsertAllReduceOp(Graph *result,
+void MultiDevSSAGraphBuilder::InsertAllReduceOp(ir::Graph *result,
                                                 const std::string &og) const {
 #ifdef PADDLE_WITH_CUDA
   result->Get<GraphOps>("ops").emplace_back(new AllReduceOpHandle(
@@ -426,7 +473,7 @@ void MultiDevSSAGraphBuilder::InsertAllReduceOp(Graph *result,
 }
 
 void MultiDevSSAGraphBuilder::InsertDataBalanceOp(
-    Graph *result, const std::vector<std::string> &datas) const {
+    ir::Graph *result, const std::vector<std::string> &datas) const {
 #ifdef PADDLE_WITH_CUDA
   result->Get<GraphOps>("ops").emplace_back(new DataBalanceOpHandle(
       result->CreateEmptyNode("data_balance", ir::Node::Type::kOperation),
@@ -479,8 +526,8 @@ int MultiDevSSAGraphBuilder::GetOpDeviceID(ir::Node *node) const {
 
   PADDLE_ENFORCE_EQ(param_grad.size(), 2U);
   int dev_id = GetVarDeviceID(param_grad[1]);
-  PADDLE_ENFORCE_NE(dev_id, -1, "dev_id should not be -1.[%s, %s]",
-                    node->Op()->Type(), param_grad[0]);
+  PADDLE_ENFORCE_NE(dev_id, -1, "dev_id should not be -1.[%s, %s, %s]",
+                    node->Op()->Type(), param_grad[0], param_grad[1]);
   return dev_id;
 }
 
@@ -489,7 +536,7 @@ int MultiDevSSAGraphBuilder::GetVarDeviceID(const std::string &varname) const {
   return got == var_name_on_devices_.end() ? -1 : got->second;
 }
 
-void MultiDevSSAGraphBuilder::CreateScaleLossGradOp(Graph *result) const {
+void MultiDevSSAGraphBuilder::CreateScaleLossGradOp(ir::Graph *result) const {
   for (size_t i = 0; i < places_.size(); ++i) {
 // Insert ScaleCost OpHandle
 #ifdef PADDLE_WITH_CUDA
@@ -519,7 +566,7 @@ void MultiDevSSAGraphBuilder::CreateScaleLossGradOp(Graph *result) const {
   }
 }
 
-void MultiDevSSAGraphBuilder::CreateComputationalOps(Graph *result,
+void MultiDevSSAGraphBuilder::CreateComputationalOps(ir::Graph *result,
                                                      ir::Node *node,
                                                      size_t num_places) const {
   for (size_t scope_idx = 0; scope_idx < num_places; ++scope_idx) {
@@ -531,7 +578,7 @@ void MultiDevSSAGraphBuilder::CreateComputationalOps(Graph *result,
   }
 }
 
-VarHandle *MultiDevSSAGraphBuilder::CreateReduceOp(Graph *result,
+VarHandle *MultiDevSSAGraphBuilder::CreateReduceOp(ir::Graph *result,
                                                    const std::string &og,
                                                    int dst_dev_id) const {
 #ifdef PADDLE_WITH_CUDA
@@ -564,12 +611,11 @@ VarHandle *MultiDevSSAGraphBuilder::CreateReduceOp(Graph *result,
 
 // Find the first occurence of `prev_op_name` and make current `op` depend
 // on it.
-void MultiDevSSAGraphBuilder::ConnectOp(Graph *result, OpHandleBase *op,
+void MultiDevSSAGraphBuilder::ConnectOp(ir::Graph *result, OpHandleBase *op,
                                         const std::string &prev_op_name) const {
   for (auto &prev_op : result->Get<GraphOps>("ops")) {
     if (prev_op->Name() == prev_op_name) {
-      auto *dep_var = new DummyVarHandle(
-          result->CreateEmptyNode("dummy", ir::Node::Type::kVariable));
+      auto *dep_var = new DummyVarHandle(result->CreateControlDepVar());
       prev_op->AddOutput(dep_var);
       result->Get<GraphDepVars>("dep_vars").emplace(dep_var);
       op->AddInput(dep_var);
@@ -577,7 +623,7 @@ void MultiDevSSAGraphBuilder::ConnectOp(Graph *result, OpHandleBase *op,
   }
 }
 
-void MultiDevSSAGraphBuilder::CreateDistTrainOp(Graph *result,
+void MultiDevSSAGraphBuilder::CreateDistTrainOp(ir::Graph *result,
                                                 ir::Node *node) const {
   int op_dev_id = -1;
   std::vector<std::string> input_var_names;
@@ -591,6 +637,7 @@ void MultiDevSSAGraphBuilder::CreateDistTrainOp(Graph *result,
 
   if (node->Op()->Type() == "split_byref" ||
       node->Op()->Type() == "split_selected_rows") {
+    // TODO(paddle-dev): getting the first var is not safe.
     op_dev_id = GetVarDeviceID(input_var_names[0]);
     if (strategy_.reduce_ == BuildStrategy::ReduceStrategy::kAllReduce) {
       op_dev_id = GetAppropriateDeviceID(input_var_names);
@@ -624,10 +671,14 @@ void MultiDevSSAGraphBuilder::CreateDistTrainOp(Graph *result,
 }
 
 // Create RPC related op handles that connects its in ops and out ops.
-void MultiDevSSAGraphBuilder::CreateRPCOp(Graph *result, ir::Node *node) const {
+void MultiDevSSAGraphBuilder::CreateRPCOp(ir::Graph *result,
+                                          ir::Node *node) const {
   int op_dev_id = -1;
   if (node->Op()->Type() == "send") {
+    // TODO(paddle-dev): getting the first var is not safe.
     op_dev_id = GetVarDeviceID(node->inputs[0]->Name());
+    PADDLE_ENFORCE(!ir::IsControlDepVar(*node->inputs[0]),
+                   "This hack no longer holds, please fix.");
     // the variable name which contains .block means it was splited by
     // split_byref op
     // so that we can balance the variable blocks to all the pserver
diff --git a/paddle/fluid/framework/details/multi_devices_graph_builder.h b/paddle/fluid/framework/details/multi_devices_graph_builder.h
index 2b7f4f586b4e750fde9245286c977258a9db6086..55076f227b5ab56d66b5053173c9e915da23b15f 100644
--- a/paddle/fluid/framework/details/multi_devices_graph_builder.h
+++ b/paddle/fluid/framework/details/multi_devices_graph_builder.h
@@ -46,11 +46,13 @@ class MultiDevSSAGraphBuilder : public SSAGraphBuilder {
                           const std::vector<Scope *> &local_scopes,
                           const BuildStrategy &strategy);
 #endif
-  std::unique_ptr<Graph> Apply(std::unique_ptr<Graph> graph) const override;
+  std::unique_ptr<ir::Graph> Apply(
+      std::unique_ptr<ir::Graph> graph) const override;
   int GetVarDeviceID(const std::string &varname) const override;
 
  private:
-  void CreateOpHandleIOs(Graph *result, ir::Node *node, size_t device_id) const;
+  void CreateOpHandleIOs(ir::Graph *result, ir::Node *node,
+                         size_t device_id) const;
 
  private:
   std::string loss_var_name_;
@@ -64,8 +66,8 @@ class MultiDevSSAGraphBuilder : public SSAGraphBuilder {
 
   bool IsScaleLossOp(ir::Node *node) const;
 
-  void CreateRPCOp(Graph *result, ir::Node *node) const;
-  void CreateDistTrainOp(Graph *result, ir::Node *node) const;
+  void CreateRPCOp(ir::Graph *result, ir::Node *node) const;
+  void CreateDistTrainOp(ir::Graph *result, ir::Node *node) const;
 
   /**
    * Is this operator as the end-point operator before/after send operator.
@@ -74,21 +76,22 @@ class MultiDevSSAGraphBuilder : public SSAGraphBuilder {
                      const std::vector<std::string> &recv_vars) const;
 
   std::vector<std::string> FindDistTrainSendVars(
-      const std::vector<std::unique_ptr<ir::Node>> &nodes) const;
+      const std::vector<ir::Node *> &nodes) const;
 
   std::vector<std::string> FindDistTrainRecvVars(
-      const std::vector<std::unique_ptr<ir::Node>> &nodes) const;
+      const std::vector<ir::Node *> &nodes) const;
 
-  void ConnectOp(Graph *result, OpHandleBase *op,
+  void ConnectOp(ir::Graph *result, OpHandleBase *op,
                  const std::string &prev_op_name) const;
 
-  void CreateComputationalOps(Graph *result, ir::Node *node,
+  void CreateComputationalOps(ir::Graph *result, ir::Node *node,
                               size_t num_places) const;
 
-  void CreateScaleLossGradOp(Graph *result) const;
-  VarHandle *CreateReduceOp(Graph *result, const std::string &og,
+  void CreateScaleLossGradOp(ir::Graph *result) const;
+  VarHandle *CreateReduceOp(ir::Graph *result, const std::string &og,
                             int dst_dev_id) const;
-  void CreateComputationalOp(Graph *result, ir::Node *node, int dev_id) const;
+  void CreateComputationalOp(ir::Graph *result, ir::Node *node,
+                             int dev_id) const;
 
   bool IsParameterGradientOnce(
       const std::string &og,
@@ -96,12 +99,12 @@ class MultiDevSSAGraphBuilder : public SSAGraphBuilder {
 
   int GetOpDeviceID(ir::Node *node) const;
 
-  void InsertAllReduceOp(Graph *result, const std::string &og) const;
+  void InsertAllReduceOp(ir::Graph *result, const std::string &og) const;
 
-  void InsertDataBalanceOp(Graph *result,
+  void InsertDataBalanceOp(ir::Graph *result,
                            const std::vector<std::string> &datas) const;
 
-  void CreateBroadcastOp(Graph *result, const std::string &p_name,
+  void CreateBroadcastOp(ir::Graph *result, const std::string &p_name,
                          size_t src_dev_id) const;
 
   bool IsSparseGradient(const std::string &og) const;
diff --git a/paddle/fluid/framework/details/rpc_op_handle.cc b/paddle/fluid/framework/details/rpc_op_handle.cc
index 924ff4d118a192a43e5828a38fd1abbaac1a8526..f44b374edb29228dff5a8bf003d945291f166d49 100644
--- a/paddle/fluid/framework/details/rpc_op_handle.cc
+++ b/paddle/fluid/framework/details/rpc_op_handle.cc
@@ -13,6 +13,7 @@
 // limitations under the License.
 
 #include "paddle/fluid/framework/details/rpc_op_handle.h"
+#include "paddle/fluid/framework/ir/graph.h"
 
 namespace paddle {
 namespace framework {
@@ -33,7 +34,7 @@ void RPCOpHandle::RunImpl() {
   for (auto *in : inputs_) {
     auto &p = static_cast<VarHandle *>(in)->place_;
     // FIXME(Yancey1989): need a better solution instead of use DebugString()
-    if (in->DebugString() == "dummy") {  // HACK
+    if (ir::IsControlDepVar(*in->Node())) {  // HACK
       continue;
     }
     if (in->GeneratedOp()) {
diff --git a/paddle/fluid/framework/details/ssa_graph_builder.cc b/paddle/fluid/framework/details/ssa_graph_builder.cc
index 7bc130ef6e8d2e0caf6e445d12950b87e6dd4dbd..506e7eb35cd977869424223cb863dd64dbaa9d30 100644
--- a/paddle/fluid/framework/details/ssa_graph_builder.cc
+++ b/paddle/fluid/framework/details/ssa_graph_builder.cc
@@ -17,7 +17,7 @@
 namespace paddle {
 namespace framework {
 namespace details {
-void SSAGraphBuilder::PolishGraphToSupportDataHazards(Graph *graph) {
+void SSAGraphBuilder::PolishGraphToSupportDataHazards(ir::Graph *graph) {
   for (auto &var_map : graph->Get<GraphVars>("vars")) {
     for (auto &name_pair : var_map) {
       if (name_pair.second.size() <= 1) {
@@ -36,9 +36,18 @@ void SSAGraphBuilder::PolishGraphToSupportDataHazards(Graph *graph) {
             // Read Write is the same op.
             continue;
           }
+          bool has_dep = false;
+          for (auto *r_out : read_op->Outputs()) {
+            for (auto *w_in : write_op->Inputs()) {
+              if (r_out->Node() == w_in->Node()) {
+                has_dep = true;
+                break;
+              }
+            }
+          }
+          if (has_dep) continue;
 
-          auto *dep_var = new DummyVarHandle(
-              graph->CreateEmptyNode("dummy", ir::Node::Type::kVariable));
+          auto *dep_var = new DummyVarHandle(graph->CreateControlDepVar());
           read_op->AddOutput(dep_var);
           write_op->AddInput(dep_var);
           graph->Get<GraphDepVars>("dep_vars").emplace(dep_var);
@@ -49,7 +58,7 @@ void SSAGraphBuilder::PolishGraphToSupportDataHazards(Graph *graph) {
 }
 
 VarHandle *SSAGraphBuilder::CreateOrGetLatestVarHandle(
-    Graph *graph, ir::Node *node, const platform::Place &place,
+    ir::Graph *graph, ir::Node *node, const platform::Place &place,
     size_t place_offset) {
   auto &var_holders = graph->Get<GraphVars>("vars")[place_offset];
   auto &var_holder = var_holders[node->Name()];
@@ -70,7 +79,7 @@ VarHandle *SSAGraphBuilder::CreateOrGetLatestVarHandle(
   return var;
 }
 
-void SSAGraphBuilder::CreateOpOutput(Graph *graph, OpHandleBase *op_handle,
+void SSAGraphBuilder::CreateOpOutput(ir::Graph *graph, OpHandleBase *op_handle,
                                      ir::Node *new_node,
                                      const platform::Place &place,
                                      size_t place_offset) {
@@ -82,13 +91,12 @@ void SSAGraphBuilder::CreateOpOutput(Graph *graph, OpHandleBase *op_handle,
   op_handle->AddOutput(var);
 }
 
-void SSAGraphBuilder::AddOutputToLeafOps(Graph *graph) {
+void SSAGraphBuilder::AddOutputToLeafOps(ir::Graph *graph) {
   for (auto &op : graph->Get<GraphOps>("ops")) {
     if (!op->Outputs().empty()) {
       continue;
     }
-    auto *dummy_leaf = new DummyVarHandle(
-        graph->CreateEmptyNode("dummy", ir::Node::Type::kVariable));
+    auto *dummy_leaf = new DummyVarHandle(graph->CreateControlDepVar());
     graph->Get<GraphDepVars>("dep_vars").emplace(dummy_leaf);
     op->AddOutput(dummy_leaf);
   }
diff --git a/paddle/fluid/framework/details/ssa_graph_builder.h b/paddle/fluid/framework/details/ssa_graph_builder.h
index e8e8acdb38f893302fb92c47d6f1cb2d38453e0f..2b4f31f2ff3444f909e3be5eb810ae6737e237b2 100644
--- a/paddle/fluid/framework/details/ssa_graph_builder.h
+++ b/paddle/fluid/framework/details/ssa_graph_builder.h
@@ -57,26 +57,23 @@ class SSAGraphBuilder : public ir::Pass {
   DISABLE_COPY_AND_ASSIGN(SSAGraphBuilder);
 
  protected:
-  /**
-   * We only handle write after read(WAR), since it should not have a write
-   * after write in program. If there are write after write operators, we need
-   * prune them.
-   *
-   * https://en.wikipedia.org/wiki/Hazard_(computer_architecture)#Write_after_read_(WAR)
-   */
-  static void PolishGraphToSupportDataHazards(Graph *graph);
-
-  static VarHandle *CreateOrGetLatestVarHandle(Graph *graph, ir::Node *node,
+  /*
+    Dependency graph has been constructed. However, there are still data
+    hazards need to be handled.
+  */
+  static void PolishGraphToSupportDataHazards(ir::Graph *graph);
+
+  static VarHandle *CreateOrGetLatestVarHandle(ir::Graph *graph, ir::Node *node,
                                                const platform::Place &place,
                                                size_t place_offset);
 
   // Add an output variable (each_var_name, place, place_offset) to op_handle,
   // which belongs to graph
-  static void CreateOpOutput(Graph *graph, OpHandleBase *op_handle,
+  static void CreateOpOutput(ir::Graph *graph, OpHandleBase *op_handle,
                              ir::Node *new_node, const platform::Place &place,
                              size_t place_offset);
 
-  static void AddOutputToLeafOps(Graph *graph);
+  static void AddOutputToLeafOps(ir::Graph *graph);
 };
 }  // namespace details
 }  // namespace framework
diff --git a/paddle/fluid/framework/details/ssa_graph_checker.cc b/paddle/fluid/framework/details/ssa_graph_checker.cc
index 7c79d7f1e881c67514634d56caa715c41927dbce..0438b096109a287366610d06ef2bd14c765a8f43 100644
--- a/paddle/fluid/framework/details/ssa_graph_checker.cc
+++ b/paddle/fluid/framework/details/ssa_graph_checker.cc
@@ -20,7 +20,7 @@ namespace paddle {
 namespace framework {
 namespace details {
 
-bool SSAGraghBuilderWithChecker::IsValidGraph(const Graph *graph) const {
+bool SSAGraghBuilderWithChecker::IsValidGraph(const ir::Graph *graph) const {
   std::unordered_map<OpHandleBase *, size_t> pending_ops;
   std::unordered_set<VarHandleBase *> pending_vars;
   std::unordered_set<VarHandleBase *> ready_vars;
diff --git a/paddle/fluid/framework/details/ssa_graph_checker.h b/paddle/fluid/framework/details/ssa_graph_checker.h
index 2e397e86825a41765a360d31fa8595d17027f3ec..51ce6e5ecad755613551aa6525b5cfbe4a8933ef 100644
--- a/paddle/fluid/framework/details/ssa_graph_checker.h
+++ b/paddle/fluid/framework/details/ssa_graph_checker.h
@@ -28,7 +28,8 @@ class SSAGraghBuilderWithChecker : public SSAGraphBuilder {
       std::unique_ptr<SSAGraphBuilder>&& builder)
       : builder_(std::move(builder)) {}
 
-  std::unique_ptr<Graph> Apply(std::unique_ptr<Graph> graph) const override {
+  std::unique_ptr<ir::Graph> Apply(
+      std::unique_ptr<ir::Graph> graph) const override {
     auto new_graph = builder_->Apply(std::move(graph));
     PADDLE_ENFORCE(IsValidGraph(new_graph.get()));
     return new_graph;
@@ -38,7 +39,7 @@ class SSAGraghBuilderWithChecker : public SSAGraphBuilder {
     return builder_->GetVarDeviceID(var_name);
   }
 
-  bool IsValidGraph(const Graph* graph) const;
+  bool IsValidGraph(const ir::Graph* graph) const;
 
  private:
   std::unique_ptr<SSAGraphBuilder> builder_;
diff --git a/paddle/fluid/framework/details/ssa_graph_printer.cc b/paddle/fluid/framework/details/ssa_graph_printer.cc
index 6dd6fd262e35a192ba85eb3aa16660526d2ebca2..20aab1464400aa9bb1bd6af11c06269c688a8308 100644
--- a/paddle/fluid/framework/details/ssa_graph_printer.cc
+++ b/paddle/fluid/framework/details/ssa_graph_printer.cc
@@ -21,7 +21,7 @@ namespace framework {
 namespace details {
 
 template <typename Callback>
-static inline void IterAllVar(const Graph &graph, Callback callback) {
+static inline void IterAllVar(const ir::Graph &graph, Callback callback) {
   for (auto &each : graph.Get<GraphVars>("vars")) {
     for (auto &pair1 : each) {
       for (auto &pair2 : pair1.second) {
@@ -35,7 +35,7 @@ static inline void IterAllVar(const Graph &graph, Callback callback) {
   }
 }
 
-void GraphvizSSAGraphPrinter::Print(const Graph &graph,
+void GraphvizSSAGraphPrinter::Print(const ir::Graph &graph,
                                     std::ostream &sout) const {
   size_t var_id = 0;
   std::unordered_map<const VarHandleBase *, size_t> vars;
diff --git a/paddle/fluid/framework/details/ssa_graph_printer.h b/paddle/fluid/framework/details/ssa_graph_printer.h
index cd72162f44ca76aa6340606cf79a73601eae89af..a77c1bad3f15bca9064ded860696eb68b033b090 100644
--- a/paddle/fluid/framework/details/ssa_graph_printer.h
+++ b/paddle/fluid/framework/details/ssa_graph_printer.h
@@ -25,12 +25,12 @@ namespace details {
 class SSAGraphPrinter {
  public:
   virtual ~SSAGraphPrinter() {}
-  virtual void Print(const Graph& graph, std::ostream& sout) const = 0;
+  virtual void Print(const ir::Graph& graph, std::ostream& sout) const = 0;
 };
 
 class GraphvizSSAGraphPrinter : public SSAGraphPrinter {
  public:
-  void Print(const Graph& graph, std::ostream& sout) const override;
+  void Print(const ir::Graph& graph, std::ostream& sout) const override;
 };
 
 class SSAGraghBuilderWithPrinter : public SSAGraphBuilder {
@@ -50,7 +50,8 @@ class SSAGraghBuilderWithPrinter : public SSAGraphBuilder {
         stream_ptr_(std::move(sout)),
         stream_ref_(*stream_ptr_) {}
 
-  std::unique_ptr<Graph> Apply(std::unique_ptr<Graph> graph) const override {
+  std::unique_ptr<ir::Graph> Apply(
+      std::unique_ptr<ir::Graph> graph) const override {
     auto new_graph = builder_->Apply(std::move(graph));
     printer_->Print(*new_graph, stream_ref_);
     return new_graph;
diff --git a/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc b/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
index f85c62dd6c4a8033a037b1e001ece6a9cc90ca98..c19f74476f9a1498a7d61f5faf204e9966aea155 100644
--- a/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
+++ b/paddle/fluid/framework/details/threaded_ssa_graph_executor.cc
@@ -21,7 +21,8 @@ namespace framework {
 namespace details {
 ThreadedSSAGraphExecutor::ThreadedSSAGraphExecutor(
     const ExecutionStrategy &strategy, const std::vector<Scope *> &local_scopes,
-    const std::vector<platform::Place> &places, std::unique_ptr<Graph> &&graph)
+    const std::vector<platform::Place> &places,
+    std::unique_ptr<ir::Graph> &&graph)
     : graph_(std::move(graph)),
       pool_(strategy.num_threads_ >= 2 ? new ::ThreadPool(strategy.num_threads_)
                                        : nullptr),
diff --git a/paddle/fluid/framework/details/threaded_ssa_graph_executor.h b/paddle/fluid/framework/details/threaded_ssa_graph_executor.h
index bf7c0a367a19ff4ac9462334516f1577672faa68..3d67daa45e20fdea52689684397ad01f2f4cd783 100644
--- a/paddle/fluid/framework/details/threaded_ssa_graph_executor.h
+++ b/paddle/fluid/framework/details/threaded_ssa_graph_executor.h
@@ -40,7 +40,7 @@ class ThreadedSSAGraphExecutor : public SSAGraphExecutor {
   ThreadedSSAGraphExecutor(const ExecutionStrategy &strategy,
                            const std::vector<Scope *> &local_scopes,
                            const std::vector<platform::Place> &places,
-                           std::unique_ptr<Graph> &&graph);
+                           std::unique_ptr<ir::Graph> &&graph);
 
   // Run a SSAGraph by a thread pool
   // Use topological sort algorithm
@@ -53,7 +53,7 @@ class ThreadedSSAGraphExecutor : public SSAGraphExecutor {
              details::OpHandleBase *op);
 
  private:
-  std::unique_ptr<Graph> graph_;
+  std::unique_ptr<ir::Graph> graph_;
   std::unique_ptr<::ThreadPool> pool_;
   std::vector<Scope *> local_scopes_;
   std::vector<platform::Place> places_;
diff --git a/paddle/fluid/framework/details/var_handle.cc b/paddle/fluid/framework/details/var_handle.cc
index 6f00abd9473a84a77ed1a39015e2ae079e00be79..5457870e9ff5d7cf67c9c7076b9aae94eeada779 100644
--- a/paddle/fluid/framework/details/var_handle.cc
+++ b/paddle/fluid/framework/details/var_handle.cc
@@ -26,7 +26,7 @@ std::string VarHandle::DebugString() const {
   return ss.str();
 }
 
-std::string DummyVarHandle::DebugString() const { return "dummy"; }
+std::string DummyVarHandle::DebugString() const { return node_->Name(); }
 }  // namespace details
 }  // namespace framework
 }  // namespace paddle
diff --git a/paddle/fluid/framework/ir/CMakeLists.txt b/paddle/fluid/framework/ir/CMakeLists.txt
index ee0604383ec9df826fa2abaef1f643ba0da6a096..6447452ae58344273fe569c91168c7c95a901c8d 100644
--- a/paddle/fluid/framework/ir/CMakeLists.txt
+++ b/paddle/fluid/framework/ir/CMakeLists.txt
@@ -1,5 +1,6 @@
 cc_library(node SRCS node.cc DEPS proto_desc)
 cc_library(graph SRCS graph.cc DEPS node)
+cc_library(graph_helper SRCS graph_helper.cc DEPS graph)
 cc_library(pass SRCS pass.cc DEPS graph node)
-
-cc_test(graph_test SRCS graph_test.cc DEPS graph proto_desc op_registry)
+cc_test(graph_test SRCS graph_test.cc DEPS graph op_registry)
+cc_test(graph_helper_test SRCS graph_helper_test.cc DEPS graph_helper op_registry)
diff --git a/paddle/fluid/framework/ir/graph.cc b/paddle/fluid/framework/ir/graph.cc
index e4021aa92b6da2343b604fb7bc01d31edb97d842..740acfafb7594d8d9f3ca5439323ce76c5ed271a 100644
--- a/paddle/fluid/framework/ir/graph.cc
+++ b/paddle/fluid/framework/ir/graph.cc
@@ -12,14 +12,18 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License. */
 
+#include <algorithm>
+#include <unordered_set>
+
 #include "paddle/fluid/framework/ir/graph.h"
+#include "paddle/fluid/framework/op_proto_maker.h"
 #include "paddle/fluid/framework/program_desc.h"
 #include "paddle/fluid/framework/var_desc.h"
 
 namespace paddle {
 namespace framework {
+namespace ir {
 
-// NOTE(paddle-dev): This graph contains circle.
 Graph::Graph(const ProgramDesc &program) : program_(program) {
   VLOG(3) << "block in program:" << program_.Size();
   std::unordered_map<std::string, VarDesc *> all_vars;
@@ -27,40 +31,87 @@ Graph::Graph(const ProgramDesc &program) : program_(program) {
     all_vars.emplace(var->Name(), var);
   }
 
-  std::map<std::string, ir::Node *> var_nodes;
+  std::map<std::string, std::vector<ir::Node *>> var_nodes;
   for (auto *op : program.Block(0).AllOps()) {
     ir::Node *node = CreateOpNode(op);
-
+    // For input args, reuse the same var name if it was created before.
+    // Otherwise, create a new one.
     for (auto &each_var_name : op->InputArgumentNames()) {
       ir::Node *var = nullptr;
       if (var_nodes.find(each_var_name) != var_nodes.end()) {
-        var = var_nodes.at(each_var_name);
+        var = var_nodes.at(each_var_name).back();
       } else if (all_vars.count(each_var_name) != 0) {
         var = CreateVarNode(all_vars.at(each_var_name));
-        var_nodes[each_var_name] = var;
+        var_nodes[each_var_name].push_back(var);
       } else {
-        // TODO(paddle-dev): Seems some assumption doesn't hold?
-        VLOG(3) << op->Type()
-                << " input var not in all_var list: " << each_var_name;
+        // Operation input var can be optional (dispensable). Which means
+        // the operation doesn't really need the var at runtime. In this
+        // case, the no-existed var is ready at the beginning.
         var = CreateEmptyNode(each_var_name, ir::Node::Type::kVariable);
-        var_nodes[each_var_name] = var;
+        var_nodes[each_var_name].push_back(var);
       }
       node->inputs.push_back(var);
       var->outputs.push_back(node);
     }
-
+    // For output args, always create a new var.
     for (auto &each_var_name : op->OutputArgumentNames()) {
-      ir::Node *var = nullptr;
-      if (var_nodes.find(each_var_name) != var_nodes.end()) {
-        var = var_nodes.at(each_var_name);
-      } else {
-        var = CreateVarNode(all_vars.at(each_var_name));
-        var_nodes[each_var_name] = var;
-      }
+      ir::Node *var = CreateVarNode(all_vars.at(each_var_name));
+      var_nodes[each_var_name].push_back(var);
       node->outputs.push_back(var);
       var->inputs.push_back(node);
     }
   }
+  /**
+   * We only handle write after read(WAR), since it should not have a write
+   * after write in program. If there are write after write operators, we need
+   * prune them.
+   *
+   * https://en.wikipedia.org/wiki/Hazard_(computer_architecture)#Write_after_read_(WAR)
+   */
+
+  for (auto &var : var_nodes) {
+    auto &versions = var.second;
+    if (versions.size() <= 1) continue;
+
+    auto it_new = versions.rbegin();
+    auto it_old = versions.rbegin();
+    ++it_old;
+    for (; it_old != versions.rend(); it_new = it_old, ++it_old) {
+      ir::Node *write_op =
+          (*it_new)->inputs.empty() ? nullptr : (*it_new)->inputs[0];
+      const auto &read_ops = (*it_old)->outputs;
+
+      for (auto *read_op : read_ops) {
+        // Manually add a dependency var from read_op to write_op;
+        if (read_op == write_op) {
+          // Read Write is the same op.
+          continue;
+        }
+        // 2 ops might have been connected via other vars.
+        bool has_dep = false;
+        for (ir::Node *r_out : read_op->outputs) {
+          for (ir::Node *w_in : write_op->inputs) {
+            if (r_out == w_in) {
+              has_dep = true;
+              break;
+            }
+          }
+        }
+        if (has_dep) continue;
+
+        ir::Node *dep_var = CreateControlDepVar();
+        read_op->outputs.push_back(dep_var);
+        dep_var->inputs.push_back(read_op);
+        write_op->inputs.push_back(dep_var);
+        dep_var->outputs.push_back(write_op);
+      }
+    }
+  }
+}
+
+bool IsControlDepVar(const ir::Node &var) {
+  return var.Name().find(ir::Node::kControlDepVarName) != std::string::npos;
 }
+}  // namespace ir
 }  // namespace framework
 }  // namespace paddle
diff --git a/paddle/fluid/framework/ir/graph.h b/paddle/fluid/framework/ir/graph.h
index b4ac135b029005b723abca2cb9b9a9aa175eda40..4f59ec82a7d1217621c95d9a4a433a9af43e95da 100644
--- a/paddle/fluid/framework/ir/graph.h
+++ b/paddle/fluid/framework/ir/graph.h
@@ -26,13 +26,14 @@ limitations under the License. */
 
 namespace paddle {
 namespace framework {
+namespace ir {
 
 class Graph {
  public:
-  explicit Graph(const ProgramDesc& program);
+  explicit Graph(const ProgramDesc &program);
 
   virtual ~Graph() {
-    for (auto& attr : attrs_) {
+    for (auto &attr : attrs_) {
       attr_dels_[attr.first]();
     }
     attrs_.clear();
@@ -40,12 +41,12 @@ class Graph {
   }
 
   template <typename AttrType>
-  AttrType& Get(const std::string& attr_name) const {
-    return *boost::any_cast<AttrType*>(attrs_.at(attr_name));
+  AttrType &Get(const std::string &attr_name) const {
+    return *boost::any_cast<AttrType *>(attrs_.at(attr_name));
   }
 
   template <typename AttrType>
-  void Set(const std::string& attr_name, AttrType* attr) {
+  void Set(const std::string &attr_name, AttrType *attr) {
     PADDLE_ENFORCE(attrs_.count(attr_name) == 0);
     attrs_[attr_name] = attr;
     attr_dels_[attr_name] = [attr, attr_name]() {
@@ -54,29 +55,70 @@ class Graph {
     };
   }
 
-  ir::Node* CreateVarNode(VarDesc* var_desc) {
-    nodes.emplace_back(new ir::Node(var_desc));
-    return nodes.back().get();
+  const std::unordered_set<ir::Node *> &Nodes() const { return node_set_; }
+
+  // Create a normal variable with non-null VarDesc.
+  ir::Node *CreateVarNode(VarDesc *var_desc) {
+    return AddNode(new ir::Node(var_desc));
+  }
+
+  // Create a normal runnable operator with OpDesc.
+  ir::Node *CreateOpNode(OpDesc *op_desc) {
+    return AddNode(new ir::Node(op_desc));
   }
 
-  ir::Node* CreateOpNode(OpDesc* op_desc) {
-    nodes.emplace_back(new ir::Node(op_desc));
-    return nodes.back().get();
+  // Create a control dependency var that connects 2 operations. The
+  // var doesn't hold any data. Other than that, it's no different from
+  // other var, considering dependency analysis.
+  ir::Node *CreateControlDepVar() {
+    // TODO(panyx0718): control var name should be really unique.
+    const std::string name = string::Sprintf(
+        "%s@%llu", ir::Node::kControlDepVarName, node_set_.size());
+    return AddNode(new ir::Node(name, ir::Node::Type::kVariable));
   }
 
-  ir::Node* CreateEmptyNode(const std::string& name, ir::Node::Type type) {
-    nodes.emplace_back(new ir::Node(name, type));
-    return nodes.back().get();
+  // A more free style way of creating a graph node. Mostly use for test
+  // or "copy" from another node. Avoid using it if possible.
+  ir::Node *CreateEmptyNode(const std::string &name, ir::Node::Type type) {
+    return AddNode(new ir::Node(name, type));
   }
 
-  std::vector<std::unique_ptr<ir::Node>> nodes;
+  // Clear all node information of the graph and return the ownership of the
+  // nodes.
+  std::vector<std::unique_ptr<ir::Node>> ReleaseNodes() {
+    std::vector<std::unique_ptr<ir::Node>> ret;
+    for (auto &n : nodes_) {
+      ret.emplace_back(n.second.release());
+    }
+    nodes_.clear();
+    node_set_.clear();
+    return ret;
+  }
 
  private:
+  // This method takes ownership of `node`.
+  ir::Node *AddNode(ir::Node *node) {
+    PADDLE_ENFORCE(node_set_.find(node) == node_set_.end());
+    nodes_[node].reset(node);
+    node_set_.insert(node);
+    return node;
+  }
+
+  void RemoveNode(ir::Node *node) {
+    PADDLE_ENFORCE(node_set_.find(node) != node_set_.end());
+    node_set_.erase(node);
+    nodes_.erase(node);
+  }
+
   // NOTE: program_ shouldn't be exposed to user.
-  const ProgramDesc& program_;
+  const ProgramDesc &program_;
   std::map<std::string, boost::any> attrs_;
   std::map<std::string, std::function<void(void)>> attr_dels_;
+  std::map<ir::Node *, std::unique_ptr<ir::Node>> nodes_;
+  std::unordered_set<ir::Node *> node_set_;
 };
 
+bool IsControlDepVar(const ir::Node &var);
+}  // namespace ir
 }  // namespace framework
 }  // namespace paddle
diff --git a/paddle/fluid/framework/ir/graph_helper.cc b/paddle/fluid/framework/ir/graph_helper.cc
new file mode 100644
index 0000000000000000000000000000000000000000..b1c19e6535150130822e9f48685241e62de5b064
--- /dev/null
+++ b/paddle/fluid/framework/ir/graph_helper.cc
@@ -0,0 +1,118 @@
+/* Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#include <algorithm>
+#include <unordered_set>
+
+#include "paddle/fluid/framework/ir/graph_helper.h"
+
+namespace paddle {
+namespace framework {
+namespace ir {
+namespace {
+void SortHelper(
+    const std::map<ir::Node *, std::unordered_set<ir::Node *>> &adj_list,
+    ir::Node *node, std::unordered_set<ir::Node *> *visited,
+    std::vector<ir::Node *> *ret) {
+  visited->insert(node);
+
+  for (auto adj : adj_list.at(node)) {
+    if (visited->find(adj) == visited->end()) {
+      SortHelper(adj_list, adj, visited, ret);
+    }
+  }
+
+  VLOG(3) << "topology sort insert: " << node->Name()
+          << reinterpret_cast<void *>(node) << " input " << node->inputs.size();
+  ret->push_back(node);
+}
+
+bool HasCircleHelper(
+    ir::Node *node,
+    const std::map<ir::Node *, std::unordered_set<ir::Node *>> &adj_list,
+    std::unordered_set<ir::Node *> *visited,
+    std::unordered_set<ir::Node *> *in_trace) {
+  if (visited->find(node) == visited->end()) {
+    visited->insert(node);
+    in_trace->insert(node);
+
+    for (ir::Node *in : adj_list.at(node)) {
+      if (visited->find(in) == visited->end() &&
+          HasCircleHelper(in, adj_list, visited, in_trace)) {
+        return true;
+      } else if (in_trace->find(in) != in_trace->end()) {
+        return true;
+      }
+    }
+  }
+  in_trace->erase(node);
+  return false;
+}
+
+bool HasCircleInternal(
+    const std::map<ir::Node *, std::unordered_set<ir::Node *>> &adj_list) {
+  std::unordered_set<ir::Node *> visited;
+  std::unordered_set<ir::Node *> in_trace;
+  for (auto &adj : adj_list) {
+    if (HasCircleHelper(adj.first, adj_list, &visited, &in_trace)) {
+      return true;
+    }
+  }
+  return false;
+}
+}  // namespace
+
+bool HasCircle(const Graph &graph) {
+  return HasCircleInternal(BuildOperationAdjList(graph));
+}
+
+std::vector<ir::Node *> TopologySortOperations(const Graph &graph) {
+  std::map<ir::Node *, std::unordered_set<ir::Node *>> adj_list =
+      BuildOperationAdjList(graph);
+  PADDLE_ENFORCE(!HasCircleInternal(adj_list));
+  std::unordered_set<ir::Node *> visited;
+  std::vector<ir::Node *> ret;
+  for (auto adj : adj_list) {
+    if (visited.find(adj.first) == visited.end()) {
+      SortHelper(adj_list, adj.first, &visited, &ret);
+    }
+  }
+  return ret;
+}
+
+std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildOperationAdjList(
+    const Graph &graph) {
+  std::map<ir::Node *, std::unordered_set<ir::Node *>> adj_list;
+
+  for (auto &n : graph.Nodes()) {
+    if (n->NodeType() != ir::Node::Type::kOperation) continue;
+    if (adj_list.find(n) == adj_list.end()) {
+      adj_list[n] = std::unordered_set<ir::Node *>();
+    }
+    for (auto &var : n->inputs) {
+      for (auto &adj_n : var->inputs) {
+        PADDLE_ENFORCE(adj_n->NodeType() == ir::Node::Type::kOperation);
+        adj_list[n].insert(adj_n);
+        VLOG(3) << "adj " << adj_n->Name() << reinterpret_cast<void *>(adj_n)
+                << " -> " << n->Name() << reinterpret_cast<void *>(n)
+                << "  via " << var->Name() << reinterpret_cast<void *>(var);
+      }
+    }
+  }
+  return adj_list;
+}
+
+}  // namespace ir
+}  // namespace framework
+}  // namespace paddle
diff --git a/paddle/fluid/framework/ir/graph_helper.h b/paddle/fluid/framework/ir/graph_helper.h
new file mode 100644
index 0000000000000000000000000000000000000000..cd6c53a07f8f56781989739d995226bd02b3d3d0
--- /dev/null
+++ b/paddle/fluid/framework/ir/graph_helper.h
@@ -0,0 +1,40 @@
+/* Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#pragma once
+
+#include <map>
+#include <memory>
+#include <vector>
+
+#include "paddle/fluid/framework/ir/graph.h"
+#include "paddle/fluid/framework/ir/node.h"
+
+namespace paddle {
+namespace framework {
+namespace ir {
+// Test if the graph contains circle.
+bool HasCircle(const Graph &graph);
+
+// Topology Sort the operations in the graph from inputs to outputs.
+// `graph` cannot contain circle.
+std::vector<ir::Node *> TopologySortOperations(const Graph &graph);
+
+// Build an adjacency list of operations for the `graph`.
+std::map<ir::Node *, std::unordered_set<ir::Node *>> BuildOperationAdjList(
+    const Graph &graph);
+
+}  // namespace ir
+}  // namespace framework
+}  // namespace paddle
diff --git a/paddle/fluid/framework/ir/graph_helper_test.cc b/paddle/fluid/framework/ir/graph_helper_test.cc
new file mode 100644
index 0000000000000000000000000000000000000000..b517442bb73f43bc1cb1d639b6c6cf004b28d4cf
--- /dev/null
+++ b/paddle/fluid/framework/ir/graph_helper_test.cc
@@ -0,0 +1,125 @@
+/* Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License. */
+
+#include "paddle/fluid/framework/ir/graph.h"
+#include <string>
+#include "gtest/gtest.h"
+#include "paddle/fluid/framework/ir/graph_helper.h"
+#include "paddle/fluid/framework/program_desc.h"
+
+namespace paddle {
+namespace framework {
+namespace ir {
+
+void BuildCircleGraph(Graph* g) {
+  ir::Node* o1 = g->CreateEmptyNode("op1", Node::Type::kOperation);
+  ir::Node* v1 = g->CreateEmptyNode("var1", Node::Type::kVariable);
+
+  o1->outputs.push_back(v1);
+  o1->inputs.push_back(v1);
+  v1->inputs.push_back(o1);
+  v1->outputs.push_back(o1);
+}
+
+void BuildCircleGraph2(Graph* g) {
+  ir::Node* o1 = g->CreateEmptyNode("op1", Node::Type::kOperation);
+  ir::Node* o2 = g->CreateEmptyNode("op2", Node::Type::kOperation);
+  ir::Node* v1 = g->CreateEmptyNode("var1", Node::Type::kVariable);
+  ir::Node* v2 = g->CreateEmptyNode("var2", Node::Type::kVariable);
+
+  o1->outputs.push_back(v1);
+  o2->inputs.push_back(v1);
+  v1->inputs.push_back(o1);
+  v1->outputs.push_back(o2);
+
+  o2->outputs.push_back(v2);
+  o1->inputs.push_back(v2);
+  v2->inputs.push_back(o2);
+  v2->outputs.push_back(o1);
+}
+
+void BuildNoCircleGraph(Graph* g) {
+  ir::Node* o1 = g->CreateEmptyNode("op1", Node::Type::kOperation);
+  ir::Node* o2 = g->CreateEmptyNode("op2", Node::Type::kOperation);
+  ir::Node* o3 = g->CreateEmptyNode("op3", Node::Type::kOperation);
+  ir::Node* o4 = g->CreateEmptyNode("op4", Node::Type::kOperation);
+  ir::Node* o5 = g->CreateEmptyNode("op5", Node::Type::kOperation);
+  ir::Node* v1 = g->CreateEmptyNode("var1", Node::Type::kVariable);
+  ir::Node* v2 = g->CreateEmptyNode("var2", Node::Type::kVariable);
+  ir::Node* v3 = g->CreateEmptyNode("var3", Node::Type::kVariable);
+  ir::Node* v4 = g->CreateEmptyNode("var4", Node::Type::kVariable);
+
+  // o1->v1->o2
+  o1->outputs.push_back(v1);
+  o2->inputs.push_back(v1);
+  v1->inputs.push_back(o1);
+  v1->outputs.push_back(o2);
+  // o2->v2->o3
+  // o2->v2->o4
+  o2->outputs.push_back(v2);
+  o3->inputs.push_back(v2);
+  o4->inputs.push_back(v2);
+  v2->inputs.push_back(o2);
+  v2->outputs.push_back(o3);
+  v2->outputs.push_back(o4);
+  // o2->v3->o5
+  o2->outputs.push_back(v3);
+  o5->inputs.push_back(v3);
+  v3->inputs.push_back(o2);
+  v3->outputs.push_back(o5);
+  // o3-v4->o5
+  o3->outputs.push_back(v4);
+  o5->inputs.push_back(v4);
+  v4->inputs.push_back(o3);
+  v4->outputs.push_back(o5);
+}
+
+TEST(GraphHelperTest, Basic) {
+  ProgramDesc prog;
+
+  Graph g(prog);
+  BuildCircleGraph(&g);
+  ASSERT_TRUE(HasCircle(g));
+
+  Graph g2(prog);
+  BuildCircleGraph2(&g2);
+  ASSERT_TRUE(HasCircle(g2));
+
+  auto adj_list = BuildOperationAdjList(g2);
+  for (auto& adj : adj_list) {
+    auto& adj_set = adj.second;
+    if (adj.first->Name() == "op1") {
+      ASSERT_EQ((*adj_set.begin())->Name(), "op2");
+    } else if (adj.first->Name() == "op2") {
+      ASSERT_EQ((*adj_set.begin())->Name(), "op1");
+    } else {
+      ASSERT_TRUE(false);
+    }
+  }
+
+  Graph g3(prog);
+  BuildNoCircleGraph(&g3);
+  ASSERT_FALSE(HasCircle(g3));
+  auto sorted = TopologySortOperations(g3);
+  std::map<std::string, size_t> node_map;
+  for (size_t i = 0; i < sorted.size(); ++i) {
+    node_map[sorted[i]->Name()] = i;
+  }
+  ASSERT_EQ(node_map.at("op1"), 0);
+  ASSERT_EQ(node_map.at("op2"), 1);
+  ASSERT_TRUE(node_map.at("op3") < node_map.at("op5"));
+}
+}  // namespace ir
+}  // namespace framework
+}  // namespace paddle
diff --git a/paddle/fluid/framework/ir/graph_test.cc b/paddle/fluid/framework/ir/graph_test.cc
index 4e23bf124f8822e25be0f6b1c7c8c5de4e4f600a..73ef55756c330bdbc3be89c436967b2a88625a43 100644
--- a/paddle/fluid/framework/ir/graph_test.cc
+++ b/paddle/fluid/framework/ir/graph_test.cc
@@ -76,6 +76,7 @@ TEST(GraphTest, Basic) {
   op->SetType("sum");
   op->SetInput("X", {"test_a", "test_b", "test_c"});
   op->SetOutput("Out", {"test_out"});
+  op->SetAttr("op_role", 1);
 
   prog.MutableBlock(0)->Var("test_a")->SetType(proto::VarType::SELECTED_ROWS);
   prog.MutableBlock(0)->Var("test_b")->SetType(proto::VarType::SELECTED_ROWS);
@@ -92,21 +93,22 @@ TEST(GraphTest, Basic) {
   ASSERT_EQ(proto::VarType::LOD_TENSOR,
             prog.MutableBlock(0)->Var("test_out")->GetType());
 
-  std::unique_ptr<Graph> g(new Graph(prog));
-  ASSERT_EQ(g->nodes[0]->Name(), "sum");
-  ASSERT_EQ(g->nodes[0]->inputs[0]->Name(), "test_a");
-  ASSERT_EQ(g->nodes[0]->inputs[1]->Name(), "test_b");
-  ASSERT_EQ(g->nodes[0]->inputs[2]->Name(), "test_c");
-  ASSERT_EQ(g->nodes[0]->outputs[0]->Name(), "test_out");
-  ASSERT_EQ(g->nodes[1]->Name(), "test_a");
-  ASSERT_EQ(g->nodes[1]->outputs[0]->Name(), "sum");
-  ASSERT_EQ(g->nodes[2]->Name(), "test_b");
-  ASSERT_EQ(g->nodes[2]->outputs[0]->Name(), "sum");
-  ASSERT_EQ(g->nodes[3]->Name(), "test_c");
-  ASSERT_EQ(g->nodes[3]->outputs[0]->Name(), "sum");
-  ASSERT_EQ(g->nodes[4]->Name(), "test_out");
-  ASSERT_EQ(g->nodes[4]->inputs[0]->Name(), "sum");
-  ASSERT_EQ(g->nodes.size(), 5);
+  std::unique_ptr<ir::Graph> g(new ir::Graph(prog));
+  std::vector<ir::Node *> nodes(g->Nodes().begin(), g->Nodes().end());
+  for (ir::Node *n : nodes) {
+    if (n->Name() == "sum") {
+      ASSERT_EQ(n->inputs.size(), 3);
+      ASSERT_EQ(n->outputs.size(), 1);
+    } else if (n->Name() == "test_a" || n->Name() == "test_b" ||
+               n->Name() == "test_c") {
+      ASSERT_EQ(n->inputs.size(), 0);
+      ASSERT_EQ(n->outputs.size(), 1);
+    } else if (n->Name() == "test_out") {
+      ASSERT_EQ(n->inputs.size(), 1);
+      ASSERT_EQ(n->outputs.size(), 0);
+    }
+  }
+  ASSERT_EQ(nodes.size(), 5);
 }
 }  // namespace framework
 }  // namespace paddle
diff --git a/paddle/fluid/framework/ir/node.cc b/paddle/fluid/framework/ir/node.cc
index 86376e7e8bc8bee2ddbc18f7f24bcdd849a06cbf..aca77da8d674f29b89c023717cdcd061232d023a 100644
--- a/paddle/fluid/framework/ir/node.cc
+++ b/paddle/fluid/framework/ir/node.cc
@@ -15,5 +15,9 @@ limitations under the License. */
 #include "paddle/fluid/framework/ir/node.h"
 
 namespace paddle {
-namespace framework {}  // namespace framework
+namespace framework {
+namespace ir {
+const char Node::kControlDepVarName[] = "__control_var";
+}  // namespace ir
+}  // namespace framework
 }  // namespace paddle
diff --git a/paddle/fluid/framework/ir/node.h b/paddle/fluid/framework/ir/node.h
index b98c29b81ddc2f57553b8fe76fcfeb0936ddd837..b3138fccee86fb274abe72007961fc1c982b1e96 100644
--- a/paddle/fluid/framework/ir/node.h
+++ b/paddle/fluid/framework/ir/node.h
@@ -27,6 +27,8 @@ namespace ir {
 class Node {
  public:
   enum class Type { kOperation, kVariable };
+  static const char kControlDepVarName[];
+
   explicit Node(const std::string& name, Type type)
       : name_(name), var_desc_(nullptr), op_desc_(nullptr), type_(type) {}
 
@@ -50,6 +52,7 @@ class Node {
     PADDLE_ENFORCE(type_ == Type::kVariable);
     return var_desc_;
   }
+
   OpDesc* Op() {
     PADDLE_ENFORCE(type_ == Type::kOperation);
     return op_desc_;
diff --git a/paddle/fluid/framework/parallel_executor.cc b/paddle/fluid/framework/parallel_executor.cc
index 1e5bba62b53025dacdbf2d74b35f266cf4e422c2..02c836bea194553bb9c4bc5677cc408dd302e9ce 100644
--- a/paddle/fluid/framework/parallel_executor.cc
+++ b/paddle/fluid/framework/parallel_executor.cc
@@ -132,7 +132,7 @@ ParallelExecutor::ParallelExecutor(
 #endif
   }
   builder_ = builder_factory.Create();
-  std::unique_ptr<Graph> graph(new Graph(main_program));
+  std::unique_ptr<ir::Graph> graph(new ir::Graph(main_program));
   graph = builder_->Apply(std::move(graph));
   member_->executor_.reset(new details::ThreadedSSAGraphExecutor(
       exec_strategy, member_->local_scopes_, places, std::move(graph)));
diff --git a/paddle/fluid/operators/CMakeLists.txt b/paddle/fluid/operators/CMakeLists.txt
index 4e2002ad24415437ae4f85eba0e90a6c689e2996..9b56ad4c55e35d497aa7abe4e1da3867a2084b88 100644
--- a/paddle/fluid/operators/CMakeLists.txt
+++ b/paddle/fluid/operators/CMakeLists.txt
@@ -192,9 +192,9 @@ if(WITH_DISTRIBUTE)
     
     set(DISTRIBUTE_DEPS "")
     if(WITH_GRPC)
-        set(DISTRIBUTE_DEPS sendrecvop_grpc grpc++_unsecure grpc_unsecure gpr cares zlib protobuf)
+        set(DISTRIBUTE_DEPS sendrecvop_grpc grpc++_unsecure grpc_unsecure gpr cares zlib protobuf node)
     else()
-        set(DISTRIBUTE_DEPS sendrecvop_brpc brpc leveldb snappystream snappy protobuf ssl crypto zlib)
+        set(DISTRIBUTE_DEPS sendrecvop_brpc brpc leveldb snappystream snappy protobuf ssl crypto zlib node)
         if(WITH_BRPC_RDMA)
             find_library(IBVERBS_LIBRARY NAMES ibverbs)
             ADD_LIBRARY(ibverbs SHARED IMPORTED GLOBAL)
diff --git a/paddle/fluid/operators/send_recv_util.h b/paddle/fluid/operators/send_recv_util.h
index deab005149027caffa962783df944fad7110382f..dc26c53c64f06ce21856fb5af8f2a5eb3fc75bb7 100644
--- a/paddle/fluid/operators/send_recv_util.h
+++ b/paddle/fluid/operators/send_recv_util.h
@@ -14,6 +14,7 @@ limitations under the License. */
 
 #pragma once
 #include <string>
+#include "paddle/fluid/framework/ir/node.h"
 
 namespace paddle {
 namespace operators {
@@ -22,7 +23,10 @@ inline bool NeedSend(const framework::Scope& scope,
                      const std::string& varname) {
   // dummy variable is only used in parallel executor to represent
   // some dependency relationship, we don't need to send/recv it.
-  if (varname == "dummy") return false;
+  // TODO(paddle-dev): Why would parallel executor logic leaked into here?
+  if (varname.find(framework::ir::Node::kControlDepVarName) !=
+      std::string::npos)
+    return false;
   auto* var = scope.FindVar(varname);
   PADDLE_ENFORCE_NOT_NULL(var, "Can not find variable '%s' in the send side.",
                           varname);