Using Dijkstra's Algorithm, find the shortest distance from source vertex 'A' to 'D' and 'E' in the following graph. [figure in the original paper]

Step-by-Step Application of Dijkstra’s Algorithm (Source = A)

Initialization

• Set distance to source $A$ as 0, all others as $\infty$.
• Set all vertices as unvisited.
• Initialize priority queue $Q$ with $(A,0)$.

Iteration 1: Extract A (distance = 0)

• Update neighbors of $A$:
  • $B$: $\min (\infty ,0+4)=4$
  • $C$: $\min (\infty ,0+2)=2$
• Mark $A$ as visited.

Iteration 2: Extract C (smallest distance = 2)

• Update neighbors of $C$:
  • $B$: $\min (4,2+1)=3$ (no change, since 3 > 4)
  • $D$: $\min (\infty ,2+8)=10$
  • $E$: $\min (\infty ,2+10)=12$
• Mark $C$ as visited.

Iteration 3: Extract B (distance = 3)

• Update neighbors of $B$:
  • $D$: $\min (10,3+5)=8$
• Mark $B$ as visited.

Iteration 4: Extract D (distance = 8)

• Update neighbor of $D$:
  • $E$: $\min (12,8+2)=10$
• Mark $D$ as visited.

Iteration 5: Extract E (distance = 10)

• No updates needed.
• Mark $E$ as visited.

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Final Shortest Distances

• Distance from A to D: 8 (Path: $A\to C\to D$)
• Distance from A to E: 10 (Path: $A\to C\to D\to E$)