1. 15.082 and 6.855J Dijkstras Algorithm with simple buckets (also known as Dials algorithm)

2. 2 An Example 1 2 3 4 5 6 2 4 2 1 3 4 2 3 2 Initialize distance labels 1 0 Select the node with the minimum temporary distance label. 01234567 1 2 3 4 5 6 Initialize buckets.

3. 3 Update Step 2 3 4 5 6 2 4 2 1 3 4 2 3 2 2 4 0 1 01234567 1 2 3 4 5 6 23

4. 4 Choose Minimum Temporary Label 1 3 4 5 6 2 4 2 1 3 4 2 3 2 2 4 0 2 01234567 4 5 6 23 Find Min by starting at the leftmost bucket and scanning right till there is a non-empty bucket.

5. 5 Update Step 1 2 3 4 5 6 2 4 2 1 3 4 2 3 2 2 4 6 4 3 0 01234567 4 5 6 23 3 4 5

6. 6 Choose Minimum Temporary Label 1 24 5 6 2 4 2 1 3 4 2 3 2 2 3 6 4 0 3 01234567 6 3 45 Find Min by starting at the leftmost bucket and scanning right till there is a non-empty bucket.

7. 7 Update 1 24 5 6 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 01234567 6 3 45

8. 8 Choose Minimum Temporary Label 1 24 6 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 5 01234567 6 45

9. 9 Update 1 24 6 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 5 6 01234567 6 45 6

10. 10 Choose Minimum Temporary Label 1 2 6 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 5 6 4 01234567 4 6

11. 11 Update 1 2 6 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 5 6 4 01234567 4 6

12. 12 Choose Minimum Temporary Label 1 2 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 5 6 4 6 01234567 6 There is nothing to update

13. 13 End of Algorithm 1 2 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 5 6 4 6 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