Final answer:
The database facilities that find the shortest route to information are called search algorithms. Examples include binary search and hashing.
Step-by-step explanation:
The database facilities that can find the shortest route to the information needed are known as search algorithms. These algorithms are used to efficiently locate the desired information within a database. One example of a search algorithm is binary search, which can quickly find the desired information in a sorted database by repeatedly dividing the search space in half. Another example is hashing, which uses a hash function to map the information to a specific location in the database, making it faster to retrieve.