Final answer:
In unweighted, undirected connected graphs, the shortest path from a node S to other nodes is most efficiently computed by performing a BFS starting from S. The correct option is D. Performing a BFS starting from S.
Step-by-step explanation:
In an unweighted, undirected connected graph, the most efficient algorithm in terms of time complexity for computing the shortest path from a node S to every other node is performing a Breadth-First Search (BFS) starting from S.
Unlike Warshall's algorithm which is used for finding shortest paths in a weighted graph, BFS is suited for unweighted graphs and can provide the shortest path without the need for edge weights.
Depth-First Search (DFS) is not guaranteed to find the shortest path in an unweighted graph as it may travel deeper into the graph along one branch before exploring neighbours closer to the start node. Dijkstra's algorithm, while effective for weighted graphs, is more complex than necessary for an unweighted graph where BFS suffices.
The most efficient algorithm for computing the shortest path from a node S to every other node in an unweighted, undirected connected graph is Dijkstra's algorithm starting from S.
Dijkstra's algorithm follows a greedy approach, considering the shortest path to each node one by one. It maintains priority queue to keep track of the nodes with the shortest path from the start node, and updates their distances as it explores the graph.
This algorithm has a time complexity of O((V+E)logV), where V is the number of vertices and E is the number of edges in the graph.
The correct option is D. Performing a BFS starting from S.