diff --git a/flex/engines/graph_db/runtime/codegen/builders/builders.h b/flex/engines/graph_db/runtime/codegen/builders/builders.h
index 5f7beefeeb9e..4da1c11276ce 100644
--- a/flex/engines/graph_db/runtime/codegen/builders/builders.h
+++ b/flex/engines/graph_db/runtime/codegen/builders/builders.h
@@ -20,6 +20,7 @@ limitations under the License.
 
 #include "flex/engines/graph_db/runtime/codegen/building_context.h"
 #include "flex/engines/graph_db/runtime/codegen/exprs/expr_builder.h"
+#include "flex/engines/graph_db/runtime/codegen/utils/utils.h"
 #include "flex/engines/graph_db/runtime/common/utils.h"
 #include "flex/proto_generated_gie/algebra.pb.h"
 #include "flex/proto_generated_gie/common.pb.h"
@@ -37,6 +38,12 @@ std::string build_limit(BuildingContext& context, const algebra::Limit& opr);
 
 std::string build_get_v(BuildingContext& context, const physical::GetV& opr);
 
+std::string build_edge_expand(BuildingContext& context,
+                              const physical::EdgeExpand& opr,
+                              const physical::PhysicalOpr_MetaData& meta);
+
+std::string build_select(BuildingContext& context, const algebra::Select& opr);
+
 }  // namespace runtime
 }  // namespace gs
 #endif  // RUNTIME_CODEGEN_BUILDERS_BUILDERS_H_
\ No newline at end of file
diff --git a/flex/engines/graph_db/runtime/codegen/builders/edge_expand_builder.cc b/flex/engines/graph_db/runtime/codegen/builders/edge_expand_builder.cc
new file mode 100644
index 000000000000..7dde14698ec3
--- /dev/null
+++ b/flex/engines/graph_db/runtime/codegen/builders/edge_expand_builder.cc
@@ -0,0 +1,90 @@
+#include "flex/engines/graph_db/runtime/codegen/builders/builders.h"
+
+namespace gs {
+namespace runtime {
+class EdgeExpandBuilder {
+ public:
+  EdgeExpandBuilder(BuildingContext& context) : context_(context) {};
+
+  std::string Build(const physical::EdgeExpand& opr,
+                    const physical::PhysicalOpr_MetaData& meta) {
+    int tag = -1;
+    if (opr.has_v_tag()) {
+      tag = opr.v_tag().value();
+    }
+    Direction dir = parse_direction(opr.direction());
+    CHECK(!opr.is_optional());
+
+    CHECK(opr.has_params());
+    const auto& params = opr.params();
+    int alias = -1;
+    if (opr.has_alias()) {
+      alias = opr.alias().value();
+    }
+
+    if (opr.expand_opt() ==
+        physical::EdgeExpand_ExpandOpt::EdgeExpand_ExpandOpt_VERTEX) {
+      context_.set_alias(alias, ContextColumnType::kVertex, RTAnyType::kVertex);
+      if (params.has_predicate()) {
+        LOG(FATAL) << "not support" << params.DebugString();
+      } else {
+        EdgeExpandParams eep;
+        eep.v_tag = tag;
+        eep.labels = parse_label_triplets(meta);
+        eep.dir = dir;
+        eep.alias = alias;
+        auto [cur_ctx, nxt_ctx] = context_.GetCurAndNextCtxName();
+        std::string ss;
+        ss += "auto ";
+        ss += nxt_ctx +
+              " = EdgeExpand::expand_vertex_without_predicate(txn, std::move(" +
+              cur_ctx + "), " + eep.to_string() + ");\n";
+        return ss;
+      }
+    } else if (opr.expand_opt() ==
+               physical::EdgeExpand_ExpandOpt::EdgeExpand_ExpandOpt_EDGE) {
+      EdgeExpandParams eep;
+      eep.v_tag = tag;
+      eep.labels = parse_label_triplets(meta);
+      eep.dir = dir;
+      eep.alias = alias;
+      context_.set_alias(alias, ContextColumnType::kEdge, RTAnyType::kEdge);
+      if (params.has_predicate()) {
+        std::string ss;
+        auto [expr_name, expr_str] =
+            build_expr(context_, params.predicate(), VarType::kEdgeVar);
+        auto [cur_ctx, nxt_ctx] = context_.GetCurAndNextCtxName();
+        ss += expr_str;
+        ss += "auto ";
+        ss += nxt_ctx + " = EdgeExpand::expand_edge(txn, std::move(" + cur_ctx +
+              "), " + eep.to_string() + ", EdgePredicate(";
+        ss += expr_name;
+        ss += "));\n";
+        return ss;
+      } else {
+        auto [cur_ctx, nxt_ctx] = context_.GetCurAndNextCtxName();
+        std::string ss;
+        ss += "auto ";
+        ss += nxt_ctx +
+              " = EdgeExpand::expand_edge_without_predicate(txn, std::move(" +
+              cur_ctx + "), " + eep.to_string() + ");\n";
+        return ss;
+      }
+    }
+
+    LOG(FATAL) << "not support" << opr.DebugString();
+
+    return "";
+  }
+
+  BuildingContext& context_;
+};
+
+std::string build_edge_expand(BuildingContext& context,
+                              const physical::EdgeExpand& opr,
+                              const physical::PhysicalOpr_MetaData& meta) {
+  EdgeExpandBuilder builder(context);
+  return builder.Build(opr, meta);
+}
+}  // namespace runtime
+}  // namespace gs
\ No newline at end of file
diff --git a/flex/engines/graph_db/runtime/codegen/builders/get_v_builder.cc b/flex/engines/graph_db/runtime/codegen/builders/get_v_builder.cc
index 74ba27b78205..a07af92a7fe4 100644
--- a/flex/engines/graph_db/runtime/codegen/builders/get_v_builder.cc
+++ b/flex/engines/graph_db/runtime/codegen/builders/get_v_builder.cc
@@ -32,14 +32,14 @@ class GetVBuilder {
           auto [cur_ctx, nxt_ctx] = context_.GetCurAndNextCtxName();
           ss += "auto ";
           ss += (cur_ctx + " = GetV::get_vertex_from_vertices(txn, std::move(" +
-                 cur_ctx + "), " + get_v_params.toString() + ", " + expr_name +
-                 ");\n");
+                 cur_ctx + "), " + get_v_params.to_string() +
+                 ", VertexPredicate(" + expr_name + "));\n");
           return ss;
         } else if (opt == VOpt::kEnd || opt == VOpt::kStart) {
           auto [cur_ctx, nxt_ctx] = context_.GetCurAndNextCtxName();
           ss += "auto ";
           ss += (nxt_ctx + " = GetV::get_vertex_from_edges(txn, std::move(" +
-                 cur_ctx + "), " + get_v_params.toString() + ", " + expr_name +
+                 cur_ctx + "), " + get_v_params.to_string() + ", " + expr_name +
                  ");\n");
           return ss;
         }
@@ -50,7 +50,7 @@ class GetVBuilder {
           auto [cur_ctx, nxt_ctx] = context_.GetCurAndNextCtxName();
           ss += "auto ";
           ss += (nxt_ctx + " = GetV::get_vertex_from_edges(txn, std::move(" +
-                 cur_ctx + "), " + get_v_params.toString() +
+                 cur_ctx + "), " + get_v_params.to_string() +
                  ", [](size_t){\nreturn true;});\n ");
           return ss;
         }
diff --git a/flex/engines/graph_db/runtime/codegen/builders/scan_builder.cc b/flex/engines/graph_db/runtime/codegen/builders/scan_builder.cc
index 75459a8b8d01..79ea1aa571b2 100644
--- a/flex/engines/graph_db/runtime/codegen/builders/scan_builder.cc
+++ b/flex/engines/graph_db/runtime/codegen/builders/scan_builder.cc
@@ -1,7 +1,4 @@
 #include "flex/engines/graph_db/runtime/codegen/builders/builders.h"
-#include "flex/engines/graph_db/runtime/codegen/exprs/expr_utils.h"
-#include "flex/engines/graph_db/runtime/codegen/utils/utils.h"
-#include "flex/engines/graph_db/runtime/common/utils.h"
 
 namespace gs {
 namespace runtime {
@@ -172,12 +169,12 @@ class ScanBuilder {
         ss += str + "\n auto ";
         if (scan_oid) {
           ss += ctx_name + " = Scan::filter_oids(txn, " +
-                scan_params.toString() + ", [" + name +
+                scan_params.to_string() + ", [" + name +
                 "](label_t label, vid_t vid){\n return " + name +
                 ".typed_eval_vertex(label, vid, 0);\n" + "}, ";
         } else {
           ss += ctx_name + " = Scan::filter_gids(txn, " +
-                scan_params.toString() + ", [" + name +
+                scan_params.to_string() + ", [" + name +
                 "](label_t label, vid_t vid){\n return " + name +
                 ".typed_eval_vertex(label, vid, 0);\n" + "}, ";
         }
@@ -186,8 +183,9 @@ class ScanBuilder {
       } else {
         std::string ss;
         ss += str + "\n auto ";
-        ss += ctx_name + " = Scan::scan_vertex(txn, " + scan_params.toString() +
-              ", [" + name + "](label_t label, vid_t vid){\n return " + name +
+        ss += ctx_name + " = Scan::scan_vertex(txn, " +
+              scan_params.to_string() + ", [" + name +
+              "](label_t label, vid_t vid){\n return " + name +
               ".typed_eval_vertex(label, vid, 0);\n" + "});\n";
         return ss;
       }
@@ -201,13 +199,14 @@ class ScanBuilder {
       if (scan_oid) {
         std::string ss{"auto "};
 
-        ss += ctx_name + " = Scan::filter_oids(txn, " + scan_params.toString() +
-              "[](label_t label, vid_t vid){\n" + "return true;\n" + "}, " +
-              vec_2_str(oids) + ");\n";
+        ss += ctx_name + " = Scan::filter_oids(txn, " +
+              scan_params.to_string() + "[](label_t label, vid_t vid){\n" +
+              "return true;\n" + "}, " + vec_2_str(oids) + ");\n";
         return ss;
       } else {
         std::string ss{"auto "};
-        ss += ctx_name + " = Scan::filter_gids(txn, " + scan_params.toString() +
+        ss += ctx_name + " = Scan::filter_gids(txn, " +
+              scan_params.to_string() +
               "[](label_t label, vid_t vid){\n    return true;\n" + "}, " +
               vec_2_str(oids) + ");\n";
         return ss;
@@ -215,7 +214,7 @@ class ScanBuilder {
 
     } else {
       std::string ss{"auto "};
-      ss += ctx_name + " = Scan::scan_vertex(txn, " + scan_params.toString() +
+      ss += ctx_name + " = Scan::scan_vertex(txn, " + scan_params.to_string() +
             "[](label_t label, vid_t vid){\n    return true;\n});\n";
       return ss;
     }
diff --git a/flex/engines/graph_db/runtime/codegen/builders/select_builder.cc b/flex/engines/graph_db/runtime/codegen/builders/select_builder.cc
new file mode 100644
index 000000000000..57953d5c48fe
--- /dev/null
+++ b/flex/engines/graph_db/runtime/codegen/builders/select_builder.cc
@@ -0,0 +1,24 @@
+#include "flex/engines/graph_db/runtime/codegen/builders/builders.h"
+namespace gs {
+namespace runtime {
+class SelectBuilder {
+ public:
+  SelectBuilder(BuildingContext& context) : context_(context) {};
+  std::string Build(const algebra::Select& opr) {
+    auto [expr_name, expr_str] =
+        build_expr(context_, opr.predicate(), VarType::kPathVar);
+    std::string ss;
+    auto [cur_ctx, nxt_ctx] = context_.GetCurAndNextCtxName();
+    ss += "auto ";
+    ss += (nxt_ctx + " = Select::select(" + cur_ctx + ", PathPredicate(" +
+           expr_name + "));\n");
+    return ss;
+  }
+  BuildingContext& context_;
+};
+std::string build_select(BuildingContext& context, const algebra::Select& opr) {
+  SelectBuilder builder(context);
+  return builder.Build(opr);
+}
+}  // namespace runtime
+}  // namespace gs
\ No newline at end of file
diff --git a/flex/engines/graph_db/runtime/codegen/codegen.cc b/flex/engines/graph_db/runtime/codegen/codegen.cc
index 26d1943f6003..715dfacb58f1 100644
--- a/flex/engines/graph_db/runtime/codegen/codegen.cc
+++ b/flex/engines/graph_db/runtime/codegen/codegen.cc
@@ -31,6 +31,14 @@ class Codegen {
         ss += build_get_v(context, opr.opr().vertex());
         LOG(INFO) << ss;
         break;
+      case physical::PhysicalOpr_Operator::OpKindCase::kEdge:
+        ss += build_edge_expand(context, opr.opr().edge(), opr.meta_data(0));
+        LOG(INFO) << ss;
+        break;
+
+      case physical::PhysicalOpr_Operator::OpKindCase::kSelect:
+        ss += build_select(context, opr.opr().select());
+        break;
 
       default:
         break;
diff --git a/flex/engines/graph_db/runtime/codegen/exprs/static_expr.h b/flex/engines/graph_db/runtime/codegen/exprs/static_expr.h
index d50df4609715..3094c59a6fe3 100644
--- a/flex/engines/graph_db/runtime/codegen/exprs/static_expr.h
+++ b/flex/engines/graph_db/runtime/codegen/exprs/static_expr.h
@@ -20,6 +20,20 @@ namespace gs {
 
 namespace runtime {
 
+template <typename T>
+class is_optional_test {
+ private:
+  template <typename U>
+  static auto test(int) -> decltype(std::declval<U>().is_optional(),
+                                    std::true_type());
+
+  template <typename U>
+  static std::false_type test(...);
+
+ public:
+  static constexpr bool value = decltype(test<T>(0))::value;
+};
+
 template <typename EXPR, typename OP>
 struct UnaryOpExpr {
   UnaryOpExpr(const EXPR& expr, OP&& op) : expr_(expr), op_(op) {}
@@ -300,6 +314,19 @@ struct PathPredicate {
     return expr_.typed_eval_path(path_idx);
   }
 
+  bool is_optional() const {
+    return is_optional_test<EXPR>::value && expr_.is_optional();
+  }
+
+  bool operator()(size_t path_idx, int) const {
+    // typed_eval_path(idx, 0) return std::optional<bool>
+    auto val = expr_.typed_eval_path(path_idx, 0);
+    if (val.has_value()) {
+      return val.value();
+    }
+    return false;
+  }
+
   const EXPR& expr_;
 };
 
diff --git a/flex/engines/graph_db/runtime/common/operators/edge_expand.h b/flex/engines/graph_db/runtime/common/operators/edge_expand.h
index ed1e8bb7feeb..cfb12e08150b 100644
--- a/flex/engines/graph_db/runtime/common/operators/edge_expand.h
+++ b/flex/engines/graph_db/runtime/common/operators/edge_expand.h
@@ -22,19 +22,13 @@
 #include "flex/engines/graph_db/runtime/common/columns/edge_columns.h"
 #include "flex/engines/graph_db/runtime/common/columns/vertex_columns.h"
 #include "flex/engines/graph_db/runtime/common/context.h"
+#include "flex/engines/graph_db/runtime/common/utils.h"
 
 #include "glog/logging.h"
 
 namespace gs {
 namespace runtime {
 
-struct EdgeExpandParams {
-  int v_tag;
-  std::vector<LabelTriplet> labels;
-  int alias;
-  Direction dir;
-};
-
 class EdgeExpand {
  public:
   template <typename PRED_T>
diff --git a/flex/engines/graph_db/runtime/common/operators/select.h b/flex/engines/graph_db/runtime/common/operators/select.h
index 47a98a7b1eac..136c547e19d7 100644
--- a/flex/engines/graph_db/runtime/common/operators/select.h
+++ b/flex/engines/graph_db/runtime/common/operators/select.h
@@ -28,9 +28,17 @@ class Select {
   static void select(Context& ctx, const PRED_T& pred) {
     size_t row_num = ctx.row_num();
     std::vector<size_t> offsets;
-    for (size_t k = 0; k < row_num; ++k) {
-      if (pred(k)) {
-        offsets.push_back(k);
+    if (pred.is_optional()) {
+      for (size_t k = 0; k < row_num; ++k) {
+        if (pred(k, 0)) {
+          offsets.push_back(k);
+        }
+      }
+    } else {
+      for (size_t k = 0; k < row_num; ++k) {
+        if (pred(k)) {
+          offsets.push_back(k);
+        }
       }
     }
 
diff --git a/flex/engines/graph_db/runtime/common/types.h b/flex/engines/graph_db/runtime/common/types.h
index 33bd9cd0fed6..8a097925fe80 100644
--- a/flex/engines/graph_db/runtime/common/types.h
+++ b/flex/engines/graph_db/runtime/common/types.h
@@ -135,9 +135,9 @@ struct LabelTriplet {
       : src_label(src), dst_label(dst), edge_label(edge) {}
 
   std::string to_string() const {
-    return "(" + std::to_string(static_cast<int>(src_label)) + "-" +
-           std::to_string(static_cast<int>(edge_label)) + "-" +
-           std::to_string(static_cast<int>(dst_label)) + ")";
+    return "(" + std::to_string(static_cast<int>(src_label)) + "," +
+           std::to_string(static_cast<int>(dst_label)) + "," +
+           std::to_string(static_cast<int>(edge_label)) + ")";
   }
 
   bool operator==(const LabelTriplet& rhs) const {
diff --git a/flex/engines/graph_db/runtime/common/utils.h b/flex/engines/graph_db/runtime/common/utils.h
index abefee04a9a4..de64ce21f4da 100644
--- a/flex/engines/graph_db/runtime/common/utils.h
+++ b/flex/engines/graph_db/runtime/common/utils.h
@@ -25,7 +25,7 @@ struct ScanParams {
       : alias(alias), tables(tables) {}
   ScanParams() = default;
 
-  std::string toString() const {
+  std::string to_string() const {
     std::stringstream ss;
     ss << "ScanParams(" << alias << ", ";
     ss << "{";
@@ -49,7 +49,7 @@ struct GetVParams {
   GetVParams(VOpt opt, int tag, const std::vector<label_t>& tables, int alias)
       : opt(opt), tag(tag), tables(tables), alias(alias) {}
   GetVParams() = default;
-  std::string toString() const {
+  std::string to_string() const {
     std::stringstream ss;
     ss << "GetVParams(" << vopt_2_str(opt) << ", " << tag << ", ";
     ss << "{";
@@ -65,6 +65,33 @@ struct GetVParams {
   }
 };
 
+struct EdgeExpandParams {
+  int v_tag;
+  std::vector<LabelTriplet> labels;
+  int alias;
+  Direction dir;
+
+  EdgeExpandParams(int v_tag, const std::vector<LabelTriplet>& labels,
+                   int alias, Direction dir)
+      : v_tag(v_tag), labels(labels), alias(alias), dir(dir) {}
+  EdgeExpandParams() = default;
+
+  std::string to_string() const {
+    std::stringstream ss;
+    ss << "EdgeExpandParams(" << v_tag << ", ";
+    ss << "{";
+    for (size_t i = 0; i < labels.size(); ++i) {
+      if (i + 1 == labels.size()) {
+        ss << "LabelTriplet" << labels[i].to_string();
+      } else {
+        ss << "LabelTriplet" << labels[i].to_string() << ", ";
+      }
+    }
+    ss << "}, " << alias << ", " << dir_2_str(dir) << ")";
+    return ss.str();
+  }
+};
+
 }  // namespace runtime
 }  // namespace gs