The data structure typically used to implement a queue in breadth-first search (BFS) is a common array-based or linked-list-based queue.

  In breadth-first search, the algorithm explores all the vertices of a graph in a level-by-level manner, starting from a specified source vertex. It uses a queue data structure to keep track of the vertices to be explored.

  In an array-based implementation, a queue can be implemented using a fixed-size or dynamic-size array. It maintains two pointers, one pointing to the front of the queue and the other pointing to the rear. The enqueue operation inserts an element at the rear of the queue, and the dequeue operation removes the element from the front. This allows the BFS algorithm to process the vertices in the order they are added to the queue.

  In a linked-list-based implementation, a queue can be implemented using a singly linked list or a doubly linked list. It also maintains two pointers, one pointing to the head of the queue and the other pointing to the tail. The enqueue operation adds an element at the tail of the queue, and the dequeue operation removes the element from the head.

  Both array-based and linked-list-based implementations have their own advantages and trade-offs. Array-based queue offers constant time complexity for both enqueue and dequeue operations but may require resizing the array if the number of elements exceeds the fixed size. On the other hand, linked-list-based queue allows dynamic resizing and insertion/deletion at both ends in constant time, but incurs additional memory overhead for maintaining the pointers.

  Overall, the choice of data structure for implementing a queue in BFS depends on the specific requirements of the algorithm and the constraints of the problem.