diff --git a/bigframes/core/bigframe_node.py b/bigframes/core/bigframe_node.py
index 369e8f6329..96b76159b2 100644
--- a/bigframes/core/bigframe_node.py
+++ b/bigframes/core/bigframe_node.py
@@ -211,9 +211,11 @@ def explicitly_ordered(self) -> bool:
 
     @functools.cached_property
     def height(self) -> int:
-        if len(self.child_nodes) == 0:
-            return 0
-        return max(child.height for child in self.child_nodes) + 1
+        from bigframes.core import tree_properties
+
+        return tree_properties.GLOBAL_PROPERTY_SCOPE.get_property(
+            self, tree_properties.HEIGHT_PROP
+        )
 
     @functools.cached_property
     def total_variables(self) -> int:
diff --git a/bigframes/core/tree_properties.py b/bigframes/core/tree_properties.py
index 82df53af82..fd75ebb15c 100644
--- a/bigframes/core/tree_properties.py
+++ b/bigframes/core/tree_properties.py
@@ -13,13 +13,154 @@
 # limitations under the License.
 from __future__ import annotations
 
+import abc
+import dataclasses
 import functools
 import itertools
-from typing import Callable, Dict, Optional, Sequence
+from typing import (
+    Any,
+    Callable,
+    Dict,
+    Generator,
+    Generic,
+    Hashable,
+    List,
+    Optional,
+    Sequence,
+    Tuple,
+    TypeVar,
+)
+import weakref
 
 import bigframes.core.nodes as nodes
 
 
+@dataclasses.dataclass(frozen=True)
+class GetPropRequest:
+    property: Property
+    node: nodes.BigFrameNode
+
+
+T = TypeVar("T", bound=Hashable)
+
+
+@dataclasses.dataclass(frozen=True)
+class Property(abc.ABC, Generic[T]):
+    id: str
+
+    @abc.abstractmethod
+    def get(self, node: nodes.BigFrameNode) -> Generator[GetPropRequest, Any, T]:
+        ...
+
+
+@dataclasses.dataclass(frozen=True)
+class Height(Property[int]):
+    id: str = "Height"
+
+    def get(self, node: nodes.BigFrameNode) -> Generator[GetPropRequest, int, int]:
+        if len(node.child_nodes) == 0:
+            return 0
+        heights = []
+        for child in node.child_nodes:
+            child_height = yield GetPropRequest(self, child)
+            heights.append(child_height)
+        return min(heights) + 1
+
+
+class PropertyScope:
+    _memoized: weakref.WeakKeyDictionary[
+        nodes.BigFrameNode, Dict[Property, Any]
+    ] = weakref.WeakKeyDictionary()
+
+    def get_property(
+        self, node: nodes.BigFrameNode, property_instance: Property[T]
+    ) -> T:
+        """
+        Gets the value of a property for a given node, using memoization and
+        an iterative approach with an explicit stack to avoid deep Python recursion
+        in this method.
+
+        Args:
+            node: The node for which to compute the property.
+            property_instance: The specific Property object (e.g., an instance of Height).
+
+        Returns:
+            The computed value of the property for the node.
+
+        Raises:
+            RecursionError: If a cycle in property dependencies is detected.
+            TypeError: If a property's get() method yields an unexpected value type.
+            Exception: Propagates exceptions raised during property computation.
+        """
+        # Stack to manage generators that are waiting for a dependency result.
+        generator_stack: List[Tuple[Generator, nodes.BigFrameNode, Property]] = []
+
+        # Value computed by the most recent dependency, to be sent into the parent generator.
+        result_to_send: Any = None
+
+        # The current node and property being processed. Start with the initial request.
+        current_node: nodes.BigFrameNode = node
+        current_prop: Property = property_instance
+        current_gen: Optional[Generator[Any, None, None]] = None
+
+        while True:
+            if self._cache_contains(current_node, current_prop):
+                result_to_send = self._get_cache(current_node, current_prop)
+                if not generator_stack:
+                    # No generators are waiting, this is the final result.
+                    return result_to_send
+                else:
+                    current_gen, current_node, current_prop = generator_stack.pop()
+                    continue
+            elif current_gen is None:
+                current_gen = current_prop.get(current_node)
+                result_to_send = None  # Send None initially, gen.send(None) = next(gen)
+            try:
+                # Send the result from a completed dependency (or None initially).
+                request = current_gen.send(result_to_send)
+                result_to_send = None  # Consume the result after sending
+
+                # Generator yielded a request for another property.
+                assert isinstance(request, GetPropRequest)
+                # Push the current generator onto the stack, as it's now waiting.
+                generator_stack.append((current_gen, current_node, current_prop))
+                # Set the new dependency as the current task.
+                current_node, current_prop = request.node, request.property
+                current_gen = None  # Clear current generator before looping
+                continue
+
+            except StopIteration as e:
+                self._insert_cache(current_node, current_prop, e.value)
+                result_to_send = e.value
+                # Check if this completes the overall request or a dependency.
+                if not generator_stack:
+                    return result_to_send  # Final result
+                else:
+                    current_gen, current_node, current_prop = generator_stack.pop()
+                    continue
+
+    def _insert_cache(self, node, property, value):
+        if node not in self._memoized:
+            self._memoized[node] = {}
+        self._memoized[node][property] = value
+
+    def _cache_contains(self, node, property: Property[T]) -> bool:
+        node_cache = self._memoized.get(node)
+        if node_cache is not None and property in node_cache:
+            return True
+        return False
+
+    def _get_cache(self, node, property: Property[T]) -> T:
+        node_cache = self._memoized.get(node)
+        if node_cache is not None and property in node_cache:
+            return node_cache[property]  # Get cached result
+        raise ValueError("no value")
+
+
+HEIGHT_PROP = Height()
+GLOBAL_PROPERTY_SCOPE = PropertyScope()
+
+
 def is_trivially_executable(node: nodes.BigFrameNode) -> bool:
     if local_only(node):
         return True