Question

2. (a) (2 points - Completeness) Dijkstra's Walk-through Dijkstra's algorithm to compute the shortest paths from A to every other node in the given graph Show your steps in the table below. Do this by crossing out old values and writing in new ones as the algorithm proceeds 25 9 7 (D-G) 19 14 (B-E) 4 (A-C) 2 2 (G-H) Vertex Visited Cost Previous

Answer 1

Dijkstra’s shortest-path algorithm to compute the shortest path from “A” to all network nodes is as follows

Step Vertex A)AD(B) P(B) D(C)P(C) D(D) P(D) D(E) P(E) D(F) P(F) D(G) P(G)D(H) P(H) / Node 0 1,A(min) 4,A 25,A | 25,А 6(3+3),C25,B 7(6+1),Bo0 7,B 0,A 0,A 0,A 0,A 1,A 0,A 0,A 1,A 0,A 1,A 3(2+1),B | 20(19+1),B | 15(14+1),B 1,A 1,A 11(8+3),C 11,C 9(7+2),G 2 3,B 3,B 3, B 3, В 3,B 20,B 15(9+6),E 14(7+7),G 6,C 14,G 14 14,G 18(12+6),E 18(12+6),E 18,E 18,E 18 17, В 4 G 5 6 D 6,C 7,B 7,B 7,B 1,A 9,G 9,G

Edge	A - B	A - C	A - D	A - E	A - F	A - G	A - H
Cost	1	3	14	6	18	7	9

The shortest path tree from the above routing table

7 (D-G) 2 (G-H)