Final answer:
The running time of the algorithm that computes shortest paths in a weighted graph is O((m + n) log n).
Step-by-step explanation:
The algorithm that computes the shortest paths from one start node to all the other nodes in a weighted graph is known as Dijkstra's algorithm. It works by maintaining a set of explored nodes and iteratively updating the distance to each node until the shortest paths are found.
The running time of Dijkstra's algorithm can be represented as O((m + n) log n), where m is the number of edges and n is the number of nodes in the graph. This is because the algorithm uses a priority queue to efficiently select the next node to explore, and updating the distances in the queue takes O(log n) time.
Therefore, the correct option is b) O(n log m).