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diff --git a/‎paddle/cinn/common/CMakeLists.txt
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+1Lines changed: 1 addition & 0 deletions b/‎paddle/cinn/common/CMakeLists.txt
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+1Lines changed: 1 addition & 0 deletions
diff --git a/‎paddle/cinn/common/dfs_topo_walker.h
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+112Lines changed: 112 additions & 0 deletions b/‎paddle/cinn/common/dfs_topo_walker.h
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+112Lines changed: 112 additions & 0 deletions
diff --git a/‎paddle/cinn/common/dfs_topo_walker_test.cc
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+54Lines changed: 54 additions & 0 deletions b/‎paddle/cinn/common/dfs_topo_walker_test.cc
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+54Lines changed: 54 additions & 0 deletions
diff --git a/‎paddle/cinn/ir/CMakeLists.txt
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+2-1Lines changed: 2 additions & 1 deletion b/‎paddle/cinn/ir/CMakeLists.txt
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+2-1Lines changed: 2 additions & 1 deletion
diff --git a/‎paddle/cinn/ir/schedule/ir_schedule_util.cc
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+24-3Lines changed: 24 additions & 3 deletions b/‎paddle/cinn/ir/schedule/ir_schedule_util.cc
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+24-3Lines changed: 24 additions & 3 deletions
@@ -24,6 +24,7 @@ gather_srcs(
 message(STATUS "srcs: ${cinnapi_src}")
 
 cinn_cc_test(test_dfs_walker SRCS dfs_walker_test.cc DEPS gtest glog)
+cinn_cc_test(test_dfs_topo_walker SRCS dfs_topo_walker_test.cc DEPS gtest glog)
 cinn_cc_test(test_is_reachable_predicator SRCS is_reachable_predicator_test.cc
              DEPS gtest glog)
 cinn_cc_test(test_topo_walker SRCS topo_walker_test.cc DEPS gtest glog)
 
@@ -0,0 +1,112 @@
+// Copyright (c) 2023 CINN 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
+//
+//     https://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 <array>
+#include <functional>
+#include <stack>
+#include <unordered_set>
+
+namespace cinn {
+namespace common {
+
+// DFS Topological order walker.
+// Try to walk in a depth first manner while ensuring topological order.
+// For example:
+//   Graph:
+//     0 -> 1
+//     2 -> 3
+//     0 -> 3
+//     1 -> 3
+//     3 -> 4
+//   Start nodes: 0, 2
+//   Walking order: 0 -> 1 -> 2 -> 3 -> 4
+template <typename NodeType,
+          typename NodeHash = std::hash<NodeType>,
+          typename NodeEqual = std::equal_to<NodeType>>
+class DfsTopoWalker final {
+ public:
+  DfsTopoWalker(const DfsTopoWalker&) = delete;
+  DfsTopoWalker(DfsTopoWalker&&) = delete;
+
+  using NodeHandlerType = std::function<void(NodeType)>;
+  using NodesVisitorType =
+      std::function<void(NodeType, const NodeHandlerType&)>;
+
+  DfsTopoWalker(const NodesVisitorType& VisitPreNodes,
+                const NodesVisitorType& VisitNextNodes)
+      : VisitPreNodes_(VisitPreNodes), VisitNextNodes_(VisitNextNodes) {}
+
+  // Start walking from 1 node and make every effort to access all nodes that
+  // meet the walking rules.
+  // If there are more than 1 nodes with a degree of 0 in a graph,
+  // only one part will be accessed.
+  // If you want to access the entire graph,
+  // you need to provide all starting nodes.
+  void operator()(NodeType node, const NodeHandlerType& NodeHandler) const {
+    std::array<NodeType, 1> nodes{node};
+    (*this)(nodes.begin(), nodes.end(), NodeHandler);
+  }
+
+  // Start walking from a collection of node and make every effort to access all
+  // nodes that meet the walking rules.
+  // If there are other start nodes in a graph,
+  // some nodes on the graph will not be accessed.
+  // If you want to access the entire graph,
+  // you need to provide all starting nodes.
+  template <typename NodeIt>
+  void operator()(NodeIt begin,
+                  NodeIt end,
+                  const NodeHandlerType& NodeHandler) const {
+    std::stack<NodeType> node_stack;
+    std::unordered_set<NodeType, NodeHash, NodeEqual> visited;
+    std::unordered_map<NodeType, int, NodeHash, NodeEqual> in_degree;
+    const auto& InitInDegree = [&](NodeType node) {
+      if (in_degree.count(node) == 0) {
+        in_degree[node] = 0;
+        VisitPreNodes_(node, [&](NodeType in_node) { ++in_degree[node]; });
+      }
+    };
+    const auto& UpdateInDegree = [&](NodeType node) {
+      InitInDegree(node);
+      --in_degree[node];
+    };
+    const auto& TryPush = [&](NodeType node) {
+      InitInDegree(node);
+      if (visited.count(node) == 0 && in_degree[node] == 0) {
+        node_stack.push(node);
+        visited.insert(node);
+      }
+    };
+
+    for (NodeIt iter = begin; iter != end; ++iter) {
+      TryPush(*iter);
+      while (!node_stack.empty()) {
+        NodeType cur = node_stack.top();
+        node_stack.pop();
+        NodeHandler(cur);
+        VisitNextNodes_(cur, UpdateInDegree);
+        VisitNextNodes_(cur, TryPush);
+      }
+    }
+  }
+
+ private:
+  NodesVisitorType VisitNextNodes_;
+  NodesVisitorType VisitPreNodes_;
+};
+
+}  // namespace common
+}  // namespace cinn
@@ -0,0 +1,54 @@
+// Copyright (c) 2023 CINN 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
+//
+//     https://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 <glog/logging.h>
+#include <gtest/gtest.h>
+
+#include "paddle/cinn/common/dfs_topo_walker.h"
+
+namespace cinn {
+namespace common {
+
+TEST(DfsTopoWalker, simple) {
+  std::vector<std::pair<int, int>> edges{
+      {0, 1}, {2, 3}, {1, 3}, {0, 3}, {3, 4}};
+  DfsTopoWalker<int> walker(
+      [&](int node, const std::function<void(int)>& NodeHandler) {
+        for (const auto& pair : edges) {
+          if (pair.second == node) {
+            NodeHandler(pair.first);
+          }
+        }
+      },
+      [&](int node, const std::function<void(int)>& NodeHandler) {
+        for (const auto& pair : edges) {
+          if (pair.first == node) {
+            NodeHandler(pair.second);
+          }
+        }
+      });
+  std::vector<int> sources{0, 2};
+  std::vector<int> outputs;
+  walker(sources.begin(), sources.end(), [&](int node) {
+    outputs.push_back(node);
+  });
+  for (auto output : outputs) {
+    LOG(INFO) << output;
+  }
+  std::vector<int> expected{0, 1, 2, 3, 4};
+  EXPECT_TRUE((outputs == expected));
+}
+
+}  // namespace common
+}  // namespace cinn
@@ -14,7 +14,8 @@ gather_srcs(
   module.cc
   lowered_func.cc
   intrinsic_ops.cc
-  layout.cc)
+  layout.cc
+  schedule_block_graph.cc)
 
 add_subdirectory(op)
 add_subdirectory(test)
 
@@ -860,11 +860,18 @@ std::vector<Expr> GetProducers(const Expr& block, const Expr& root) {
   auto compute_body = block.As<ir::ScheduleBlockRealize>()
                           ->schedule_block.As<ir::ScheduleBlock>()
                           ->body;
+  std::string block_name = block.As<ir::ScheduleBlockRealize>()
+                               ->schedule_block.As<ir::ScheduleBlock>()
+                               ->name;
   ir::CollectIRNodesWithoutTensor(
-      compute_body, [&producer_tensor_names](const Expr* x) {
+      compute_body, [&producer_tensor_names, &block_name](const Expr* x) {
         auto* load = x->As<ir::Load>();
         if (load) {
           producer_tensor_names.insert(load->tensor.as_tensor()->name);
+          if (load->tensor.as_tensor()->name == block_name) {
+            producer_tensor_names.insert(
+                GenReduceInitTensorNameOf(load->tensor.as_tensor()->name));
+          }
           return true;
         }
         return false;
@@ -896,6 +903,18 @@ std::vector<Expr> GetConsumers(const Expr& block, const Expr& root) {
   CHECK(root.As<ir::ScheduleBlockRealize>());
   std::vector<Expr> consumers;
   std::string block_tensor = GetTensor(block)->name;
+  if (IsReduceInitTensorName(block_tensor)) {
+    std::string consumer_name = GetOriginalReduceTensorName(block_tensor);
+    auto consumer = ir::CollectIRNodesWithoutTensor(root, [&](const Expr* x) {
+      return x->As<ir::ScheduleBlockRealize>() &&
+             x->As<ir::ScheduleBlockRealize>()
+                     ->schedule_block.As<ir::ScheduleBlock>()
+                     ->name == consumer_name;
+    });
+    CHECK_EQ(consumer.size(), 1);
+    return {*consumer.begin()};
+  }
+
   auto find_block = ir::CollectIRNodesWithoutTensor(root, [&](const Expr* x) {
     return x->As<ir::ScheduleBlockRealize>() && *x != block && *x != root;
   });
@@ -997,10 +1016,12 @@ std::vector<IterRange> CalculateRequiredRegions(
   // deduce accessed regions of the provided tensor in block by itering each
   // required block
   for (const Expr& pro_node : provided_nodes) {
-    const std::string& provided_tensor_name =
+    std::string provided_tensor_name =
         is_store_provided ? pro_node.As<ir::Store>()->tensor.as_tensor()->name
                           : pro_node.As<ir::Load>()->tensor.as_tensor()->name;
-
+    if (IsReduceInitTensorName(provided_tensor_name)) {
+      provided_tensor_name = GetOriginalReduceTensorName(provided_tensor_name);
+    }
     for (const Expr& req_block : required_blocks) {
       CHECK(req_block.As<ir::ScheduleBlockRealize>());
       Expr block_body =