An Example ∞ 2

0

∞ 4

4

2

2 1

1

2

3

4

6



2 3



3

5



Initialize Select the node with the minimum temporary distance label. 2

Update Step 2 ∞ 2

0

∞ 4

4

2

2 1

1

2

3

4

6



2 3

∞ 4

3

5



3

Choose Minimum Temporary Label ∞

2 2

0

4

4

2

2 1

1

2

3

4

6



2 3

4

3

5



4

Update Step 6 ∞

2 2

0

4

4

2

2 1

1

2

3

4

6



2 3

4 3

3

5

∞ 4

The predecessor of node 3 is now node 2 5

Choose Minimum Temporary Label 2 2

0

6 4

4

2

2 1

1

2

3

4

6



2 3

3

3

5

4

6

Update 2 2

0

6 4

4

2

2 1

1

2

3

4

6



2 3

3

3

5

4

d(5) is not changed.

7

Choose Minimum Temporary Label 2 2

0

6 4

4

2

2 1

1

2

3

4

6



2 3

3

3

5

4

8

Update 2 2

0

6 4

4

2

2 1

1

2

3

4

6

6 ∞

2 3

3

3

5

4

d(4) is not changed

9

Choose Minimum Temporary Label 2 2

0

6 4

4

2

2 1

1

2

3

4

6

6

2 3

3

3

5

4

10

Update 2 2

0

6 4

4

2

2 1

1

2

3

4

6

6

2 3

3

3

5

4

d(6) is not updated

11

Choose Minimum Temporary Label 2 2

0

6 4

4

2

2 1

1

2

3

4

6

6

2 3

3

3

5

4

There is nothing to update 12

End of Algorithm 2 2

0

6 4

4

2

2 1

1

2

3

4

6

6

2 3

3

3

5

4

All nodes are now permanent The predecessors form a tree The shortest path from node 1 to node 6 can be found by tracing back predecessors

13

03_3 - Shortest Path Problems - Dijkstra's Algorithm - An Example ...

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