Question

(a) Consider the weighted directed graph shown in Figure 1, and consider computing the single source all shortest paths. (i) Explain the main ideas behind Dijkstra's algorithm in brief. [5 marks] (ii) Show how Dijkstra's algorithm works step by step from the single source node A to all others for the graph shown in Figure 1. [20 marks] (iii) Show the shortest paths from the node A to all other nodes based on your answer of [5 marks] (ii). 10 1 B G 31 21 15 23 22 4 A E 24 H F D 3 2 21 8 15 7 25 J K C 40 Figure 2: A weighted undirected graph. (b) Show step-by-step how a minimum cost spanning tree is computed for the undirected graph as depicted in Figure 2 using the Kruskal's algorithm. [15 marks]

          (a) Consider the weighted directed graph shown in Figure 1, and consider computing the single
source all shortest paths.
(i) Explain the main ideas behind Dijkstra's algorithm in brief.
[5 marks]
(ii) Show how Dijkstra's algorithm works step by step from the single source node A to all
others for the graph shown in Figure 1.
[20 marks]
(iii) Show the shortest paths from the node A to all other nodes based on your answer of
[5 marks]
(ii).
10
1
B
G
31
21
15
23
22
4
A
E
24
H
F
D
3
2
21
8
15
7
25
J
K
C
40
Figure 2: A weighted undirected graph.
(b) Show step-by-step how a minimum cost spanning tree is computed for the undirected graph
as depicted in Figure 2 using the Kruskal's algorithm.
[15 marks]

(a) Consider the weighted directed graph shown in Figure 1, and consider computing the single
source all shortest paths.
(i) Explain the main ideas behind Dijkstra's algorithm in brief.
[5 marks]
(ii) Show how Dijkstra's algorithm works step by step from the single source node A to all
others for the graph shown in Figure 1.
[20 marks]
(iii) Show the shortest paths from the node A to all other nodes based on your answer of
[5 marks]
(ii).
10
1
B
G
31
21
15
23
22
4
A
E
24
H
F
D
3
2
21
8
15
7
25
J
K
C
40
Figure 2: A weighted undirected graph.
(b) Show step-by-step how a minimum cost spanning tree is computed for the undirected graph
as depicted in Figure 2 using the Kruskal's algorithm.
[15 marks]

Added by Meredith P.

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