The data structure commonly used in algorithms for efficient searching and sorting is the binary search tree (BST). In a BST, each node contains a key greater than all keys in its left subtree and less than those in its right subtree. This property facilitates efficient searching, as the tree can be navigated logarithmically, significantly reducing search times compared to linear data structures. Likewise, BSTs are used in various algorithms, including in-order traversal, to produce sorted data outputs, making them invaluable in many applications.