Breadth-First Search (BFS) is an algorithm used to traverse a graph or tree data structure. It begins at a given node or root node and explores all of its connected nodes before proceeding to the next level of nodes in the tree. By doing so, it visits all nodes in the graph in a level-by-level fashion, thus is referred to as a “breadth-first” search. This algorithm can be used to solve many problems such as finding the shortest path in a graph or determining if two nodes are connected.
The basic idea behind the Breadth-First Search algorithm is to start from a given node and explore all its neighbors before moving onto the next level of nodes. To do this, the algorithm maintains a queue of nodes to be explored and a set of nodes that have already been visited. As it visits each node, it adds its neighbors to the queue and marks them as visited. Once the queue is empty, the algorithm terminates.
The time complexity of Breadth-First Search is O(V + E), where V is the number of vertices in the graph and E is the number of edges. This makes it an efficient algorithm compared to other graph traversal algorithms such as Depth-First Search, which has a time complexity of O(V2).
Breadth-First Search has numerous applications in Computer Science, such as finding the shortest path between two nodes in a graph, determining a network’s connectivity, as well as solving puzzles such as Rubik’s cube.
In conclusion, Breadth-First Search is an efficient algorithm for traversing a graph or tree data structure. It is widely used in Computer Science to solve various problems, such as finding the shortest path between two nodes and determining a network’s connectivity.
References
Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to algorithms (3rd ed.). Cambridge, MA: MIT Press.
Kleinberg, J., & Tardos, E. (2006). Algorithm design (1st ed.). Upper Saddle River, NJ: Pearson/Addison-Wesley.
Kruskal, J. B. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society, 7(1), 48-50. doi:10.2307/2033241.