diff --git a/include/opt/confgraph.h b/include/opt/confgraph.h
index e748033..d509587 100644
--- a/include/opt/confgraph.h
+++ b/include/opt/confgraph.h
@@ -1,4 +1,5 @@
 #pragma once
+#include <cstddef>
 #include "IR/IR_basic.h"
 #include "cfg.h"
 class ConfGraphNode {
@@ -9,8 +10,17 @@ class ConfGraphNode {
   size_t degree;
   bool is_binded_with_physical_reg;
   std::list<ConfGraphNode *> neighbors;
-  std::list<opt::MoveInstruct *> move_neighbors;
-  ConfGraphNode() = default;
+  std::list<std::pair<ConfGraphNode *, opt::MoveInstruct *>> move_neighbors;
+
+  // the following are for graph maintenance
+  ConfGraphNode *is_merged_into;
+  static ConfGraphNode *FindFather(ConfGraphNode *x) {
+    if (x->is_merged_into == x) return x;
+    return x->is_merged_into = FindFather(x->is_merged_into);
+  }
+  bool is_temporarily_removed;
+  std::list<ConfGraphNode *> neighbors_half_available;
+  std::list<ConfGraphNode *> neighbors_not_available;
 };
 class ConfGraph {
  public:
@@ -27,6 +37,7 @@ class ConfGraph {
   std::unordered_set<ConfGraphNode *> low_degree_and_move_related;
   std::unordered_set<ConfGraphNode *> high_degree_nodes;
   std::unordered_set<opt::MoveInstruct *> pending_moves;
+
   std::unordered_set<opt::MoveInstruct *> potential_moves;
 };
 
diff --git a/src/opt/confgraph.cpp b/src/opt/confgraph.cpp
index 5ea502d..966e732 100644
--- a/src/opt/confgraph.cpp
+++ b/src/opt/confgraph.cpp
@@ -14,6 +14,8 @@ ConfGraph BuildConfGraph(CFGType &cfg) {
     res.id_to_node[id] = node.get();
     res.nodes.push_back(node);
     node->is_binded_with_physical_reg = false;
+    node->is_merged_into = node.get();  // the same as `fa` in DSU
+    node->is_temporarily_removed = false;
   }
   for (auto cfg_node : cfg.nodes) {
     for (const auto &[act, out_active] : cfg_node->action_out_active_vars) {
@@ -42,10 +44,22 @@ ConfGraph BuildConfGraph(CFGType &cfg) {
     res.id_to_node[reg_id]->color = std::stoi(reg.substr(1));
     res.id_to_node[reg_id]->degree = ConfGraphNode::kInf;
   }
+  for (auto cfg_node : cfg.nodes) {
+    auto block = cfg_node->corresponding_block;
+    for (auto act : block->actions) {
+      if (auto move_act = std::dynamic_pointer_cast<opt::MoveInstruct>(act)) {
+        size_t src_id = cfg.var_to_id[move_act->src_full];
+        size_t dest_id = cfg.var_to_id[move_act->dest_full];
+        res.id_to_node[src_id]->move_neighbors.push_back({res.id_to_node[dest_id], move_act.get()});
+        res.id_to_node[dest_id]->move_neighbors.push_back({res.id_to_node[src_id], move_act.get()});
+      }
+    }
+  }
   return res;
 }
 const static size_t kMaxRegs = allocating_regs.size();
-void InitializeBeforeColoring(std::shared_ptr<FunctionDefItem> src, CFGType &cfg, ConfGraph &confgraph) {
+void InitializeBeforeColoring([[maybe_unused]] std::shared_ptr<FunctionDefItem> src, [[maybe_unused]] CFGType &cfg,
+                              ConfGraph &confgraph) {
   confgraph.stack.clear();
   confgraph.actual_spills.clear();
 
@@ -55,18 +69,137 @@ void InitializeBeforeColoring(std::shared_ptr<FunctionDefItem> src, CFGType &cfg
 
   confgraph.pending_moves.clear();
   confgraph.potential_moves.clear();
+  for (auto confg_node : confgraph.nodes) {
+    for (auto [move_neighbor, move] : confg_node->move_neighbors) {
+      if (confgraph.adj_table[confg_node.get()].find(move_neighbor) == confgraph.adj_table[confg_node.get()].end()) {
+        if (confg_node->degree < kMaxRegs && move_neighbor->degree < kMaxRegs) {
+          confgraph.pending_moves.insert(move);
+        } else if (confg_node->is_binded_with_physical_reg || move_neighbor->is_binded_with_physical_reg) {
+          if (confg_node->is_binded_with_physical_reg && move_neighbor->is_binded_with_physical_reg)
+            throw std::runtime_error(
+                "something strange happened: at the beginning two physical registers are directly move related");
+          confgraph.pending_moves.insert(move);
+        } else {
+          confgraph.potential_moves.insert(move);
+        }
+      } else {
+        // do nothing
+      }
+    }
+    if (confg_node->degree < kMaxRegs) {
+      if (confg_node->move_neighbors.size() == 0) {
+        confgraph.low_degree_and_not_move_related.insert(confg_node.get());
+      } else {
+        confgraph.low_degree_and_move_related.insert(confg_node.get());
+      }
+    } else if (!confg_node->is_binded_with_physical_reg) {
+      confgraph.high_degree_nodes.insert(confg_node.get());
+    }
+  }
+}
+
+void DetachNode(ConfGraphNode *node, ConfGraph &confgraph, bool during_selecting = false) {
+  // this function operates on the conflict graph, temporarily remove the node from the graph, it do nothing on the move
+  // link graph although they share the same node set
+  // It is also responsible for maintaining all the changes caused by the removal of the node
+}
+
+void JoinNode(ConfGraphNode *node, ConfGraph &confgraph, bool during_selecting = false) {
+  // this function operates on the conflict graph, temporarily remove the node from the graph, it do nothing on the move
+  // link graph although they share the same node set
+  // It is also responsible for maintaining all the changes caused by the removal of the node
+}
+
+void MergeNodeInto(ConfGraphNode *node, ConfGraphNode *target, ConfGraph &confgraph) {
+  // this function operates on both the conflict graph and the move link graph, and the effect is permanent
+  // It is also responsible for maintaining all the changes caused by the merge of the node
+}
+
+void Simplify(std::shared_ptr<FunctionDefItem> src, CFGType &cfg, ConfGraph &confgraph) {
+  auto u = *(confgraph.low_degree_and_not_move_related.begin());
+  confgraph.low_degree_and_not_move_related.erase(u);
+  DetachNode(u, confgraph);
+  confgraph.stack.push_back(u);
+}
+
+void Coalesce(std::shared_ptr<FunctionDefItem> src, CFGType &cfg, ConfGraph &confgraph) {
+  auto move = *(confgraph.pending_moves.begin());
+  confgraph.pending_moves.erase(move);
+  size_t src_id = cfg.var_to_id[move->src_full];
+  size_t dest_id = cfg.var_to_id[move->dest_full];
+  auto src_node = confgraph.id_to_node[src_id];
+  auto dest_node = confgraph.id_to_node[dest_id];
+  if (confgraph.adj_table[src_node].find(dest_node) != confgraph.adj_table[src_node].end()) {
+    // no need to update low_degree_and_move_related, when confgraph.pending_moves.size()==0, nodes in
+    // low_degree_and_move_related will automatically be moved to low_degree_and_not_move_related
+    return;
+  }
+  if (src_node->is_binded_with_physical_reg && dest_node->is_binded_with_physical_reg)
+    throw std::runtime_error("something strange happened: two physical registers do not conflict");
+  if (src_node->is_binded_with_physical_reg || dest_node->is_binded_with_physical_reg) {
+    // George condition
+    if (src_node->is_binded_with_physical_reg) {
+      std::swap(src_node, dest_node);
+    }
+    bool condition_satisfied = true;
+    for (auto t : src_node->neighbors) {
+      if (t->degree >= kMaxRegs && confgraph.adj_table[t].find(dest_node) == confgraph.adj_table[t].end()) {
+        condition_satisfied = false;
+        break;
+      }
+    }
+    if (condition_satisfied) {
+      MergeNodeInto(src_node, dest_node, confgraph);
+    } else {
+      confgraph.pending_moves.insert(move);
+    }
+  } else {
+    // Briggs condition
+    std::unordered_set<ConfGraphNode *> dangerous_neighbors;
+    for (auto t : src_node->neighbors) {
+      if (t != dest_node && t->degree >= kMaxRegs) {
+        dangerous_neighbors.insert(t);
+      }
+    }
+    for (auto t : dest_node->neighbors) {
+      if (t != src_node && t->degree >= kMaxRegs) {
+        dangerous_neighbors.insert(t);
+      }
+    }
+    if (dangerous_neighbors.size() < kMaxRegs) {
+      MergeNodeInto(src_node, dest_node, confgraph);
+    } else {
+      confgraph.pending_moves.insert(move);
+    }
+  }
+}
+
+void Freeze(std::shared_ptr<FunctionDefItem> src, CFGType &cfg, ConfGraph &confgraph) {
+  auto u = *confgraph.low_degree_and_move_related.begin();
+  confgraph.low_degree_and_move_related.erase(u);
+  confgraph.low_degree_and_not_move_related.insert(u);
+  for (auto [_, ins] : u->move_neighbors) {
+    confgraph.potential_moves.erase(ins);
+  }
+}
+
+void PotentailSpill(std::shared_ptr<FunctionDefItem> src, CFGType &cfg, ConfGraph &confgraph) {
+  auto u = *confgraph.high_degree_nodes.begin();
+  confgraph.high_degree_nodes.erase(u);
+  DetachNode(u, confgraph);
+  confgraph.stack.push_back(u);
 }
 bool ConductColoring(std::shared_ptr<FunctionDefItem> src, CFGType &cfg, ConfGraph &confgraph) {
   InitializeBeforeColoring(src, cfg, confgraph);
   do {
     if (confgraph.low_degree_and_not_move_related.size() > 0) {
-      // simplify
+      Simplify(src, cfg, confgraph);
     } else if (confgraph.pending_moves.size() > 0) {
-      // coalesce
+      Coalesce(src, cfg, confgraph);
     } else if (confgraph.low_degree_and_move_related.size() > 0) {
-      // freeze
+      Freeze(src, cfg, confgraph);
     } else if (confgraph.high_degree_nodes.size() > 0) {
-      // potential spill
+      PotentailSpill(src, cfg, confgraph);
     }
   } while (confgraph.low_degree_and_not_move_related.size() > 0 || confgraph.pending_moves.size() > 0 ||
            confgraph.low_degree_and_move_related.size() > 0 || confgraph.high_degree_nodes.size() > 0);
@@ -74,6 +207,7 @@ bool ConductColoring(std::shared_ptr<FunctionDefItem> src, CFGType &cfg, ConfGra
   if (confgraph.actual_spills.size() > 0) {
     std::cerr << "spilled " << confgraph.actual_spills.size() << " nodes" << std::endl;
     // allocate memory for spilled nodes
+    // rewrite the spilled nodes
     return true;
   }
   return false;