diff --git a/optd-core/src/cascades/memo.rs b/optd-core/src/cascades/memo.rs
index 62ad52b7..c4bbfb0a 100644
--- a/optd-core/src/cascades/memo.rs
+++ b/optd-core/src/cascades/memo.rs
@@ -6,7 +6,10 @@ use std::{
 };
 
 use anyhow::{bail, Result};
-use disjoint_group::set::{DisjointSet, UnionFind};
+use disjoint_group::{
+    set::{DisjointSet, UnionFind},
+    DisjointGroupMap,
+};
 use itertools::Itertools;
 use std::any::Any;
 
@@ -195,6 +198,7 @@ impl<T: RelNodeTyp> Memo<T> {
         props
     }
 
+    // TODO(yuchen): make internal to disjoint group
     fn clear_exprs_in_group(&mut self, group_id: GroupId) {
         self.groups.remove(&group_id);
     }
@@ -202,6 +206,7 @@ impl<T: RelNodeTyp> Memo<T> {
     /// If group_id exists, it adds expr_id to the existing group
     /// Otherwise, it creates a new group of that group_id and insert expr_id into the new group
     fn add_expr_to_group(&mut self, expr_id: ExprId, group_id: GroupId, memo_node: RelMemoNode<T>) {
+        // TODO(yuchen): use entry API
         if let Entry::Occupied(mut entry) = self.groups.entry(group_id) {
             let group = entry.get_mut();
             group.group_exprs.insert(expr_id);
@@ -214,6 +219,7 @@ impl<T: RelNodeTyp> Memo<T> {
         };
         group.group_exprs.insert(expr_id);
         self.disjoint_group_ids.add(group_id);
+        // TODO(yuchen): use insert
         self.groups.insert(group_id, group);
     }
 
@@ -228,6 +234,7 @@ impl<T: RelNodeTyp> Memo<T> {
     ) -> bool {
         let replace_group_id = self.get_reduced_group_id(replace_group_id);
 
+        // TODO(yuchen): use disjoint group entry API
         if let Entry::Occupied(mut entry) = self.groups.entry(replace_group_id) {
             let group = entry.get_mut();
             if !group.group_exprs.contains(&expr_id) {
diff --git a/optd-core/src/cascades/memo/disjoint_group.rs b/optd-core/src/cascades/memo/disjoint_group.rs
index d7e52559..57c22567 100644
--- a/optd-core/src/cascades/memo/disjoint_group.rs
+++ b/optd-core/src/cascades/memo/disjoint_group.rs
@@ -1 +1,111 @@
+use std::{
+    collections::{hash_map, HashMap},
+    ops::Index,
+};
+
+use set::{DisjointSet, UnionFind};
+
+use crate::cascades::GroupId;
+
+use super::Group;
+
 pub mod set;
+
+const MISMATCH_ERROR: &str = "`groups` and `id_map` report unmatched group membership";
+
+pub(crate) struct DisjointGroupMap {
+    id_map: DisjointSet<GroupId>,
+    groups: HashMap<GroupId, Group>,
+}
+
+impl DisjointGroupMap {
+    /// Creates a new disjoint group instance.
+    pub fn new() -> Self {
+        DisjointGroupMap {
+            id_map: DisjointSet::new(),
+            groups: HashMap::new(),
+        }
+    }
+
+    pub fn get(&self, id: &GroupId) -> Option<&Group> {
+        self.id_map
+            .find(id)
+            .map(|rep| self.groups.get(&rep).expect(MISMATCH_ERROR))
+    }
+
+    pub fn get_mut(&mut self, id: &GroupId) -> Option<&mut Group> {
+        self.id_map
+            .find(id)
+            .map(|rep| self.groups.get_mut(&rep).expect(MISMATCH_ERROR))
+    }
+
+    unsafe fn insert_new(&mut self, id: GroupId, group: Group) {
+        self.id_map.add(id);
+        self.groups.insert(id, group);
+    }
+
+    pub fn entry(&mut self, id: GroupId) -> GroupEntry<'_> {
+        use hash_map::Entry::*;
+        let rep = self.id_map.find(&id).unwrap_or(id);
+        let id_entry = self.id_map.entry(rep);
+        let group_entry = self.groups.entry(rep);
+        match (id_entry, group_entry) {
+            (Occupied(_), Occupied(inner)) => GroupEntry::Occupied(OccupiedGroupEntry { inner }),
+            (Vacant(id), Vacant(inner)) => GroupEntry::Vacant(VacantGroupEntry { id, inner }),
+            _ => unreachable!("{MISMATCH_ERROR}"),
+        }
+    }
+}
+
+pub enum GroupEntry<'a> {
+    Occupied(OccupiedGroupEntry<'a>),
+    Vacant(VacantGroupEntry<'a>),
+}
+
+pub struct OccupiedGroupEntry<'a> {
+    inner: hash_map::OccupiedEntry<'a, GroupId, Group>,
+}
+
+pub struct VacantGroupEntry<'a> {
+    id: hash_map::VacantEntry<'a, GroupId, GroupId>,
+    inner: hash_map::VacantEntry<'a, GroupId, Group>,
+}
+
+impl<'a> OccupiedGroupEntry<'a> {
+    pub fn id(&self) -> &GroupId {
+        self.inner.key()
+    }
+
+    pub fn get(&self) -> &Group {
+        self.inner.get()
+    }
+
+    pub fn get_mut(&mut self) -> &mut Group {
+        self.inner.get_mut()
+    }
+}
+
+impl<'a> VacantGroupEntry<'a> {
+    pub fn id(&self) -> &GroupId {
+        self.inner.key()
+    }
+
+    pub fn insert(self, group: Group) -> &'a mut Group {
+        let id = *self.id();
+        self.id.insert(id);
+        self.inner.insert(group)
+    }
+}
+
+impl Index<&GroupId> for DisjointGroupMap {
+    type Output = Group;
+
+    fn index(&self, index: &GroupId) -> &Self::Output {
+        let rep = self
+            .id_map
+            .find(index)
+            .expect("no group found for group id");
+
+        self.groups.get(&rep).expect(MISMATCH_ERROR)
+    }
+}
diff --git a/optd-core/src/cascades/memo/disjoint_group/set.rs b/optd-core/src/cascades/memo/disjoint_group/set.rs
index 35cc6b81..c343e59e 100644
--- a/optd-core/src/cascades/memo/disjoint_group/set.rs
+++ b/optd-core/src/cascades/memo/disjoint_group/set.rs
@@ -1,4 +1,8 @@
-use std::{collections::HashMap, fmt::Debug, hash::Hash};
+use std::{
+    collections::{hash_map, HashMap},
+    fmt::Debug,
+    hash::Hash,
+};
 
 /// A data structure for efficiently maintaining disjoint sets of `T`.
 pub struct DisjointSet<T> {
@@ -37,7 +41,7 @@ where
 
 impl<T> DisjointSet<T>
 where
-    T: Ord + Hash + Copy,
+    T: Ord + Hash + Copy + Debug,
 {
     pub fn new() -> Self {
         DisjointSet {
@@ -99,6 +103,11 @@ where
 
         Some(parent)
     }
+
+    /// Gets the given node corresponding entry in `node_parents` map for in-place manipulation.
+    pub(super) fn entry(&mut self, node: T) -> hash_map::Entry<'_, T, T> {
+        self.node_parents.entry(node)
+    }
 }
 
 impl<T> UnionFind<T> for DisjointSet<T>