diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/memo/Group.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/memo/Group.java
index c816151731..4b227da3c5 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/memo/Group.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/memo/Group.java
@@ -70,6 +70,10 @@ public class Group {
 
     private Statistics statistics;
 
+    private PhysicalProperties chosenProperties;
+
+    private int chosenGroupExpressionId = -1;
+
     /**
      * Constructor for Group.
      *
@@ -198,10 +202,17 @@ public class Group {
      * @return {@link Optional} of cost and {@link GroupExpression} of physical plan pair.
      */
     public Optional<Pair<Cost, GroupExpression>> getLowestCostPlan(PhysicalProperties physicalProperties) {
+        chosenProperties = physicalProperties;
         if (physicalProperties == null || lowestCostPlans.isEmpty()) {
+            chosenGroupExpressionId = -1;
             return Optional.empty();
         }
-        return Optional.ofNullable(lowestCostPlans.get(physicalProperties));
+        Optional<Pair<Cost, GroupExpression>> costAndGroupExpression =
+                Optional.ofNullable(lowestCostPlans.get(physicalProperties));
+        if (costAndGroupExpression.isPresent()) {
+            chosenGroupExpressionId = costAndGroupExpression.get().second.getId().asInt();
+        }
+        return costAndGroupExpression;
     }
 
     public GroupExpression getBestPlan(PhysicalProperties properties) {
@@ -431,6 +442,10 @@ public class Group {
         for (GroupExpression enforcer : enforcers) {
             str.append("    ").append(enforcer).append("\n");
         }
+        if (chosenGroupExpressionId != -1) {
+            str.append("  chosen expression id: ").append(chosenGroupExpressionId).append("\n");
+            str.append("  chosen properties: ").append(chosenProperties).append("\n");
+        }
         return str.toString();
     }
 
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/memo/GroupExpression.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/memo/GroupExpression.java
index b0da8459f9..4d38176c77 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/memo/GroupExpression.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/memo/GroupExpression.java
@@ -340,4 +340,8 @@ public class GroupExpression {
         builder.append(" (plan=").append(plan.toString()).append(")");
         return builder.toString();
     }
+
+    public ObjectId getId() {
+        return id;
+    }
 }
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/processor/post/RecomputeLogicalPropertiesProcessor.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/processor/post/RecomputeLogicalPropertiesProcessor.java
index 835d1425b7..59f2ffdb2d 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/processor/post/RecomputeLogicalPropertiesProcessor.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/processor/post/RecomputeLogicalPropertiesProcessor.java
@@ -20,6 +20,7 @@ package org.apache.doris.nereids.processor.post;
 import org.apache.doris.nereids.CascadesContext;
 import org.apache.doris.nereids.trees.plans.Plan;
 import org.apache.doris.nereids.trees.plans.physical.PhysicalPlan;
+import org.apache.doris.nereids.util.MutableState;
 
 /**
  * merge consecutive projects
@@ -28,6 +29,8 @@ public class RecomputeLogicalPropertiesProcessor extends PlanPostProcessor {
     @Override
     public Plan visit(Plan plan, CascadesContext ctx) {
         PhysicalPlan physicalPlan = (PhysicalPlan) visitChildren(this, plan, ctx);
-        return physicalPlan.resetLogicalProperties();
+        physicalPlan.resetLogicalProperties();
+        physicalPlan.setMutableState(MutableState.KEY_GROUP, plan.getGroupIdAsString());
+        return physicalPlan;
     }
 }
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/AbstractPlan.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/AbstractPlan.java
index cdea20c74a..cfe4b31aaf 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/AbstractPlan.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/AbstractPlan.java
@@ -209,23 +209,6 @@ public abstract class AbstractPlan extends AbstractTreeNode<Plan> implements Pla
         this.mutableState = this.mutableState.set(key, state);
     }
 
-    /**
-     * used in treeString()
-     *
-     * @return "" if groupExpression is empty, o.w. string format of group id
-     */
-    public String getGroupIdAsString() {
-        String groupId;
-        if (getGroupExpression().isPresent()) {
-            groupId = "@" + groupExpression.get().getOwnerGroup().getGroupId().asInt();
-        } else if (getMutableState("group").isPresent()) {
-            groupId = "@" + getMutableState("group").get();
-        } else {
-            groupId = "";
-        }
-        return groupId;
-    }
-
     @Override
     public boolean deepEquals(TreeNode o) {
         AbstractPlan that = (AbstractPlan) o;
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/Plan.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/Plan.java
index abefbce492..cf390be1fe 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/Plan.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/Plan.java
@@ -26,6 +26,7 @@ import org.apache.doris.nereids.trees.expressions.Expression;
 import org.apache.doris.nereids.trees.expressions.NamedExpression;
 import org.apache.doris.nereids.trees.expressions.Slot;
 import org.apache.doris.nereids.trees.plans.visitor.PlanVisitor;
+import org.apache.doris.nereids.util.MutableState;
 
 import com.google.common.collect.ImmutableList;
 import com.google.common.collect.ImmutableSet;
@@ -40,7 +41,6 @@ import java.util.stream.Collectors;
  * Abstract class for all plan node.
  */
 public interface Plan extends TreeNode<Plan> {
-
     PlanType getType();
 
     // cache GroupExpression for fast exit from Memo.copyIn.
@@ -165,4 +165,25 @@ public interface Plan extends TreeNode<Plan> {
     default String shapeInfo() {
         return this.getClass().getSimpleName();
     }
+
+    /**
+     * used in treeString()
+     *
+     * @return "" if groupExpression is empty, o.w. string format of group id
+     */
+    default String getGroupIdAsString() {
+        String groupId;
+        if (getGroupExpression().isPresent()) {
+            groupId = getGroupExpression().get().getOwnerGroup().getGroupId().asInt() + "";
+        } else if (getMutableState(MutableState.KEY_GROUP).isPresent()) {
+            groupId = getMutableState(MutableState.KEY_GROUP).get().toString();
+        } else {
+            groupId = "";
+        }
+        return groupId;
+    }
+
+    default String getGroupIdWithPrefix() {
+        return "@" + getGroupIdAsString();
+    }
 }
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalAssertNumRows.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalAssertNumRows.java
index 88fb5394cb..0ebc1426fc 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalAssertNumRows.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalAssertNumRows.java
@@ -70,7 +70,7 @@ public class PhysicalAssertNumRows<CHILD_TYPE extends Plan> extends PhysicalUnar
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalAssertNumRows" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalAssertNumRows" + getGroupIdWithPrefix(),
                 "assertNumRowsElement", assertNumRowsElement);
     }
 
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalDistribute.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalDistribute.java
index a3e9da5bf8..66b663ed62 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalDistribute.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalDistribute.java
@@ -72,7 +72,7 @@ public class PhysicalDistribute<CHILD_TYPE extends Plan> extends PhysicalUnary<C
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalDistribute[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalDistribute[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "distributionSpec", distributionSpec,
                 "stats", statistics
         );
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalFilter.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalFilter.java
index 9d14eed149..99a40baba5 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalFilter.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalFilter.java
@@ -74,7 +74,7 @@ public class PhysicalFilter<CHILD_TYPE extends Plan> extends PhysicalUnary<CHILD
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalFilter[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalFilter[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "predicates", getPredicate(),
                 "stats", statistics
         );
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalHashAggregate.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalHashAggregate.java
index e8486fc2b0..d470d0180e 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalHashAggregate.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalHashAggregate.java
@@ -196,7 +196,7 @@ public class PhysicalHashAggregate<CHILD_TYPE extends Plan> extends PhysicalUnar
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalHashAggregate[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalHashAggregate[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "aggPhase", aggregateParam.aggPhase,
                 "aggMode", aggregateParam.aggMode,
                 "maybeUseStreaming", maybeUsingStream,
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalHashJoin.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalHashJoin.java
index 22f5cbd6ff..94e49a6889 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalHashJoin.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalHashJoin.java
@@ -36,6 +36,7 @@ import org.apache.doris.nereids.trees.plans.JoinType;
 import org.apache.doris.nereids.trees.plans.Plan;
 import org.apache.doris.nereids.trees.plans.PlanType;
 import org.apache.doris.nereids.trees.plans.visitor.PlanVisitor;
+import org.apache.doris.nereids.util.MutableState;
 import org.apache.doris.nereids.util.Utils;
 import org.apache.doris.planner.RuntimeFilterId;
 import org.apache.doris.statistics.Statistics;
@@ -161,7 +162,7 @@ public class PhysicalHashJoin<
             args.add("runtimeFilters");
             args.add(runtimeFilters.stream().map(rf -> rf.toString() + " ").collect(Collectors.toList()));
         }
-        return Utils.toSqlString("PhysicalHashJoin[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalHashJoin[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 args.toArray());
     }
 
@@ -173,7 +174,7 @@ public class PhysicalHashJoin<
                 Optional.empty(), getLogicalProperties(), physicalProperties, statistics,
                 children.get(0), children.get(1));
         if (groupExpression.isPresent()) {
-            newJoin.setMutableState("group", groupExpression.get().getOwnerGroup().getGroupId().asInt());
+            newJoin.setMutableState(MutableState.KEY_GROUP, groupExpression.get().getOwnerGroup().getGroupId().asInt());
         }
         return newJoin;
     }
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalLimit.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalLimit.java
index e218d3b235..b6cc19f81b 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalLimit.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalLimit.java
@@ -156,7 +156,7 @@ public class PhysicalLimit<CHILD_TYPE extends Plan> extends PhysicalUnary<CHILD_
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalLimit[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalLimit[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "limit", limit,
                 "offset", offset,
                 "phase", phase,
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalNestedLoopJoin.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalNestedLoopJoin.java
index b18dd22746..d6b08d02c5 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalNestedLoopJoin.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalNestedLoopJoin.java
@@ -27,6 +27,7 @@ import org.apache.doris.nereids.trees.plans.JoinType;
 import org.apache.doris.nereids.trees.plans.Plan;
 import org.apache.doris.nereids.trees.plans.PlanType;
 import org.apache.doris.nereids.trees.plans.visitor.PlanVisitor;
+import org.apache.doris.nereids.util.MutableState;
 import org.apache.doris.nereids.util.Utils;
 import org.apache.doris.statistics.Statistics;
 
@@ -115,7 +116,7 @@ public class PhysicalNestedLoopJoin<
     @Override
     public String toString() {
         // TODO: Maybe we could pull up this to the abstract class in the future.
-        return Utils.toSqlString("PhysicalNestedLoopJoin[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalNestedLoopJoin[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "type", joinType,
                 "otherJoinCondition", otherJoinConjuncts,
                 "isMarkJoin", markJoinSlotReference.isPresent(),
@@ -131,7 +132,7 @@ public class PhysicalNestedLoopJoin<
                 hashJoinConjuncts, otherJoinConjuncts, markJoinSlotReference, Optional.empty(),
                 getLogicalProperties(), physicalProperties, statistics, children.get(0), children.get(1));
         if (groupExpression.isPresent()) {
-            newJoin.setMutableState("group", groupExpression.get().getOwnerGroup().getGroupId().asInt());
+            newJoin.setMutableState(MutableState.KEY_GROUP, groupExpression.get().getOwnerGroup().getGroupId().asInt());
         }
         return newJoin;
     }
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalOlapScan.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalOlapScan.java
index 8462705c54..02c0ece757 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalOlapScan.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalOlapScan.java
@@ -114,7 +114,7 @@ public class PhysicalOlapScan extends PhysicalCatalogRelation implements OlapSca
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalOlapScan[" + relationId.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalOlapScan[" + relationId.asInt() + "]" + getGroupIdWithPrefix(),
                 "qualified", Utils.qualifiedName(qualifier, table.getName()),
                 "stats", statistics, "fr", getMutableState(AbstractPlan.FRAGMENT_ID)
         );
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalOneRowRelation.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalOneRowRelation.java
index 8ed08a642a..e1ab09739e 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalOneRowRelation.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalOneRowRelation.java
@@ -108,7 +108,7 @@ public class PhysicalOneRowRelation extends PhysicalRelation implements OneRowRe
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalOneRowRelation[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalOneRowRelation[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "expressions", projects
         );
     }
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalPartitionTopN.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalPartitionTopN.java
index 888ca05544..ce57ad0782 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalPartitionTopN.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalPartitionTopN.java
@@ -178,7 +178,7 @@ public class PhysicalPartitionTopN<CHILD_TYPE extends Plan> extends PhysicalUnar
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalPartitionTopN[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalPartitionTopN[" + id.asInt() + "]" + getGroupIdWithPrefix(),
             "function", function,
             "partitionKeys", partitionKeys,
             "orderKeys", orderKeys,
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalProject.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalProject.java
index 6388a19457..2e3b11f526 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalProject.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalProject.java
@@ -77,7 +77,7 @@ public class PhysicalProject<CHILD_TYPE extends Plan> extends PhysicalUnary<CHIL
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalProject[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalProject[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "projects", projects,
                 "stats", statistics
         );
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalQuickSort.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalQuickSort.java
index 58875ccdc0..5981c8e538 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalQuickSort.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalQuickSort.java
@@ -101,7 +101,7 @@ public class PhysicalQuickSort<CHILD_TYPE extends Plan> extends AbstractPhysical
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalQuickSort[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalQuickSort[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "orderKeys", orderKeys,
                 "phase", phase.toString()
         );
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalRepeat.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalRepeat.java
index e9b9c4a02e..3cb6f73006 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalRepeat.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalRepeat.java
@@ -97,7 +97,7 @@ public class PhysicalRepeat<CHILD_TYPE extends Plan> extends PhysicalUnary<CHILD
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalRepeat[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalRepeat[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "groupingSets", groupingSets,
                 "outputExpressions", outputExpressions,
                 "stats", statistics
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalStorageLayerAggregate.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalStorageLayerAggregate.java
index 7a9550adc3..86a43aaabc 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalStorageLayerAggregate.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalStorageLayerAggregate.java
@@ -73,7 +73,7 @@ public class PhysicalStorageLayerAggregate extends PhysicalCatalogRelation {
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalStorageLayerAggregate[" + relationId.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalStorageLayerAggregate[" + relationId.asInt() + "]" + getGroupIdWithPrefix(),
                 "pushDownAggOp", aggOp,
                 "relation", relation,
                 "stats", statistics
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalTopN.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalTopN.java
index bccc2cad41..4c24a03b78 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalTopN.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalTopN.java
@@ -149,7 +149,7 @@ public class PhysicalTopN<CHILD_TYPE extends Plan> extends AbstractPhysicalSort<
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalTopN[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalTopN[" + id.asInt() + "]" + getGroupIdWithPrefix(),
                 "limit", limit,
                 "offset", offset,
                 "orderKeys", orderKeys,
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalUnion.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalUnion.java
index 5ff387c3ba..a983932710 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalUnion.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalUnion.java
@@ -84,7 +84,7 @@ public class PhysicalUnion extends PhysicalSetOperation implements Union {
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalUnion" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalUnion" + getGroupIdWithPrefix(),
                 "qualifier", qualifier,
                 "constantExprsList", constantExprsList,
                 "stats", statistics);
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalWindow.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalWindow.java
index 22a78ca887..5632e970a3 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalWindow.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/trees/plans/physical/PhysicalWindow.java
@@ -104,7 +104,7 @@ public class PhysicalWindow<CHILD_TYPE extends Plan> extends PhysicalUnary<CHILD
 
     @Override
     public String toString() {
-        return Utils.toSqlString("PhysicalWindow[" + id.asInt() + "]" + getGroupIdAsString(),
+        return Utils.toSqlString("PhysicalWindow[" + id.asInt() + "]" + getGroupIdWithPrefix(),
             "windowFrameGroup", windowFrameGroup,
             "requiredProperties", requireProperties
         );
diff --git a/fe/fe-core/src/main/java/org/apache/doris/nereids/util/MutableState.java b/fe/fe-core/src/main/java/org/apache/doris/nereids/util/MutableState.java
index 95ba886e3f..37234e954d 100644
--- a/fe/fe-core/src/main/java/org/apache/doris/nereids/util/MutableState.java
+++ b/fe/fe-core/src/main/java/org/apache/doris/nereids/util/MutableState.java
@@ -23,6 +23,9 @@ import java.util.Optional;
 
 /** MutableState */
 public interface MutableState {
+    String KEY_GROUP = "group";
+    String KEY_FRAGMENT = "fragment";
+
     <T> Optional<T> get(String key);
 
     MutableState set(String key, Object value);