Question

1. Consider the following directed, weighted graph of 7 network routers labelled A, B, C, D, E, F, G. a) Step through Dijkstra's algorithm to calculate supposedly cheapest path from router C to every other router in the network. Clearly cross out old values and write in new ones as the algorithm proceeds. (5 marks) b) Dijkstra's algorithm found the wrong path to some of the routers. For just the routers where the wrong path was computed, indicate both the wrongly computed path and the correct path. (8 marks) c) What single edge could be removed from the graph such that Dijkstra's algorithm would happen to compute correct answers for all routers in the remaining graph? Justify your answer. (4 marks) d) What are the best- and worst-case running times of the Bellman-Ford algorithm? Explain. (8 marks)

          1. Consider the following directed, weighted graph of 7 network routers labelled A, B, C, D, E, F, G.
a) Step through Dijkstra's algorithm to calculate supposedly
cheapest path from router C to every other router in the
network. Clearly cross out old values and write in new ones
as the algorithm proceeds. (5 marks)
b) Dijkstra's algorithm found the wrong path to some of the
routers. For just the routers where the wrong path was
computed, indicate both the wrongly computed path and the
correct path. (8 marks)
c) What single edge could be removed from the graph such
that Dijkstra's algorithm would happen to compute correct
answers for all routers in the remaining graph? Justify your
answer. (4 marks)
d) What are the best- and worst-case running times of the Bellman-Ford algorithm? Explain. (8 marks)

1. Consider the following directed, weighted graph of 7 network routers labelled A, B, C, D, E, F, G.
a) Step through Dijkstra's algorithm to calculate supposedly
cheapest path from router C to every other router in the
network. Clearly cross out old values and write in new ones
as the algorithm proceeds. (5 marks)
b) Dijkstra's algorithm found the wrong path to some of the
routers. For just the routers where the wrong path was
computed, indicate both the wrongly computed path and the
correct path. (8 marks)
c) What single edge could be removed from the graph such
that Dijkstra's algorithm would happen to compute correct
answers for all routers in the remaining graph? Justify your
answer. (4 marks)
d) What are the best- and worst-case running times of the Bellman-Ford algorithm? Explain. (8 marks)

Added by Daniel J.

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