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

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

An Example ∞ 2

0

∞ 4

4

2

2 1

1

2

3

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∞

2 3

∞

3

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∞

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

Update Step 2 ∞ 2

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∞ 4

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2 1

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2

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∞

2 3

∞ 4

3

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∞

3

Choose Minimum Temporary Label ∞

2 2

0

4

4

2

2 1

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6

∞

2 3

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3

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∞

4

Update Step 6 ∞

2 2

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4

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2 1

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∞

2 3

4 3

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∞ 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

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∞

2 3

3

3

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Update 2 2

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6 4

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2 1

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2

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∞

2 3

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d(5) is not changed.

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Choose Minimum Temporary Label 2 2

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6 4

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2 1

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∞

2 3

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Update 2 2

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6 4

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2 1

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6 ∞

2 3

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d(4) is not changed

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Choose Minimum Temporary Label 2 2

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6 4

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2 1

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2 3

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Update 2 2

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6 4

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2 1

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d(6) is not updated

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Choose Minimum Temporary Label 2 2

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6 4

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2 1

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2 3

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There is nothing to update 12

End of Algorithm 2 2

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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

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