Question

6. [14 points] Shortest Path Given the costs of edges in the following graph (note the negative-valued edges) S 5 t 7 -3 U X 6 3 5 5 -2 W V -1 (a) Use the Bellman-Ford shortest path algorithm to find the shortest paths using the node $t$ as the source. You may choose the order of iterating the edges in each pass. show the $d$ and $\pi$ values after each pass and list the final shortest paths to each node and corresponding costs. (b) If you apply Dijkstra's algorithm to find the shortest paths using the node $t$ as the source in this graph, what are the weights of the shortest paths from $t$ to every other nodes? Are the answers the same as (a) and why?

          6. [14 points] Shortest Path
Given the costs of edges in the following graph (note the negative-valued edges)
S
5
t
7
-3
U
X
6
3
5
5
-2
W
V
-1
(a) Use the Bellman-Ford shortest path algorithm to find the shortest paths using the node $t$ as the
source. You may choose the order of iterating the edges in each pass. show the $d$ and $\pi$ values
after each pass and list the final shortest paths to each node and corresponding costs.
(b) If you apply Dijkstra's algorithm to find the shortest paths using the node $t$ as the source in this
graph, what are the weights of the shortest paths from $t$ to every other nodes? Are the answers
the same as (a) and why?

6. [14 points] Shortest Path
Given the costs of edges in the following graph (note the negative-valued edges)
S
5
t
7
-3
U
X
6
3
5
5
-2
W
V
-1
(a) Use the Bellman-Ford shortest path algorithm to find the shortest paths using the node t as the
source. You may choose the order of iterating the edges in each pass. show the d and π values
after each pass and list the final shortest paths to each node and corresponding costs.
(b) If you apply Dijkstra's algorithm to find the shortest paths using the node t as the source in this
graph, what are the weights of the shortest paths from t to every other nodes? Are the answers
the same as (a) and why?

Added by Brett C.

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