Tree rotation is an essential process in computer science used to maintain the balance of binary search trees, thereby enhancing their efficiency.

To elaborate, tree rotation is a fundamental operation that helps keep binary search trees balanced. A binary search tree is a specific type of data structure that organizes items in memory, enabling efficient searching, insertion, and deletion operations. However, as items are added or removed, the tree can become unbalanced, which in turn can degrade performance. This is where tree rotation plays a vital role.

Tree rotation modifies the structure of the tree while preserving the in-order traversal of its elements. This operation focuses on altering the parent-child relationships between nodes. There are two primary types of tree rotations: right rotation and left rotation. In a right rotation, the root node becomes the right child of its left child, effectively adjusting the tree structure downward. Conversely, in a left rotation, the root node becomes the left child of its right child.

Tree rotations are integral to various self-balancing binary search trees, such as AVL trees and red-black trees. These types of trees employ rotations to maintain approximate balance, which ensures that search, insert, and delete operations can be performed in logarithmic time, denoted as $O(\log n)$.

For instance, in an AVL tree, after each insertion or deletion, the tree evaluates the balance factor of each node. The balance factor is defined as the difference in height between the left and right subtrees. If the balance factor of any node falls outside the range of $-1$, $0$, or $1$, the tree executes a rotation to restore balance.

In summary, tree rotation is a critical operation in computer science that helps maintain the efficiency of binary search trees. Understanding this concept is fundamental to grasping how data is organized and manipulated within computer systems.