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03_4 - Shortest Path Problems - Dial's Algorithm - An Example.pdf ...

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An Example Initialize distance labels

∞

∞ 4

2 2

0

Initialize buckets.

4 2

2

1

1

3

6

4

2

1

1

2

3

3

3

Select the node with the minimum temporary distance label. 0

∞

5

∞ 4

∞

∞ 5

6

7

2 3 4 5 6 2

Update Step 2 ∞

∞ 4

2

4

2

0

2 2

1

1

3

6

4

2 3

3

5

∞ 4 0 1

1

2 2

3

∞

4 3

∞

∞ 5

6

7

2 3 4 5 6 3

Choose Minimum Temporary Label Find Min by starting at the leftmost bucket and scanning right till there is a non-empty bucket.

∞

2 4

2

4

2

0

2 2

1

1

3

4

1

3

3

2 2

3

∞

2 5

4 3

∞

∞

4 0

6

5

6

7

4 5 6

4

Update Step 6 ∞

2 4

2

4

2

0

2 2

1

1

3

6

4

2 3

3

0

1

2

3

2

3

∞

4 3 4 3 5

5

∞

∞ 4 5

6 4

7

4 5 6

5

Choose Minimum Temporary Label Find Min by starting at the leftmost bucket and scanning right till there is a non-empty bucket.

2

6 4

2

4

2

0

2 2

1

1

3

4

1

3

3

2

∞

2 5

3 0

6

3

4

3

5

∞

4 5

6 4

7 6

6

Update 2

6 4

2

4

2

0

2 2

1

1

3

6

4

2 3

3

5

3 0

1

2

∞

3

4

3

5

∞

4 5

6 4

7 6

7

Choose Minimum Temporary Label 2

6 4

2

4

2

0

2 2

1

1

3

6

4

2 3

3

5

3 0

1

2

3

∞

4 5

∞

4 5

6 4

7 6

8

Update 2

6 4

2

4

2

0

2 2

1

1

3

6

4

2 3

3

5

3 0

1

2

3

6 ∞

4 5

∞

4 5

6 4 6

7 6

9

Choose Minimum Temporary Label 2

6 4

2

4

2

0

2 2

1

1

3

6

4

2 3

3

5

3 0

1

2

3

6

4

4 5

6

7

4 6 10

Update 2

6 4

2

4

2

0

2 2

1

1

3

6

4

2 3

3

5

3 0

1

2

3

6

4

4 5

6

7

4 6 11

Choose Minimum Temporary Label 2

6 4

2

There is nothing to update

4

2

0

2 2

1

1

3

6

4

2 3

3

5

3 0

1

2

3

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4

4 5

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6 12

End of Algorithm 2 2

0

6 4

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2 1

1

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6

2 3

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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

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