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In breadth-first search algorithms, queues are used to keep track of the nodes to be processed next.

Breadth-first search (BFS) is a strategy for searching in a graph when search is limited to essentially two operations: (a) visit and inspect a node of a graph; (b) gain access to visit the nodes that neighbour the currently inspected node. The BFS begins at a root node and inspects all the neighbouring nodes. Then for each of those neighbour nodes in turn, it inspects their neighbour nodes which are unvisited, and so on. This is where a queue comes in handy.

A queue is a data structure that follows the First-In-First-Out (FIFO) principle. In the context of BFS, we initialise a queue with a starting node. Then we enter a loop where we dequeue a node from the front of the queue, visit that node, and enqueue all its unvisited neighbours at the back of the queue. This process continues until the queue is empty, which means all nodes reachable from the starting node have been visited.

The use of a queue ensures that nodes are visited in the order of their distance from the start node, i.e., all nodes at distance d from the start node are visited before any nodes at distance d+1. This is because when we visit a node and enqueue its neighbours, those neighbours are at a greater distance from the start node than the current node. Since the queue is a FIFO structure, we will visit all other nodes at the current distance before we start visiting nodes at the next distance.

In summary, the queue in a BFS algorithm is used to manage the order in which nodes are visited. By using a queue, we can ensure that we first visit all nodes one step away, then all nodes two steps away, and so on. This is the essence of the breadth-first search algorithm.

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