Final answer:
BFS requires a significant amount of memory because it maintains a queue that stores all the visited or explored nodes, and in broad or dense graphs, this queue can grow very large.
Step-by-step explanation:
The reason Breadth-First Search (BFS) requires a large amount of memory is that it maintains a queue to store all visited or explored nodes. In BFS, each node is visited and immediately added to the queue. As the algorithm progresses, it continually adds newly discovered nodes that are adjacent to those already visited. In contrast to Depth-First Search (DFS), which uses a stack and tends to go deep into a path before backtracking, BFS works level-by-level, visiting all neighbors before moving to the next level. This means in dense or broad graphs, BFS could hold a vast number of nodes in the queue, especially if the graph gets broader at each level or has many levels.
When a node is visited, all of its immediate neighbors are added to the queue, and this process continues until all nodes have been visited or the desired node is found. Consequently, BFS can potentially require space proportional to the number of vertices in the graph if many of them need to be in the queue at the same time. This is particularly true for wide graphs, where the number of child nodes at each level can grow exponentially.
BFS algorithm executes by exploring all neighboring nodes at the present depth, prior to moving on to nodes at the next level, thus maintaining a queue of all explored nodes. This can become memory-intensive if the breadth of the graph is large at any level.