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15.082 and 6.855J

15.082 and 6.855J. Dijkstra’s Algorithm. 1. An Example. . . 4. 2. 4. 2. 2. 0. 2. 1. 3. . 1. 6. 4. 2. 3. 3. 5. . . Initialize. Select the node with the minimum temporary distance label. Update Step. 2. . . 4. 2. 4. 2. 2. 0. 2. 1. 3. . 1. 6.

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15.082 and 6.855J

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  1. 15.082 and 6.855J Dijkstra’s Algorithm

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

  3. Update Step 2   4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5   4

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

  5. Update Step 6 2  4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5  4 4 3 The predecessor of node 3 is now node 2

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

  7. Update 2 6 4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5 3 4 d(5) is not changed.

  8. Choose Minimum Temporary Label 2 6 4 2 4 2 2 0 2 1 3  1 6 4 2 3 3 5 3 4

  9. Update 2 6 4 2 4 2 2 0 6 2 1 3  1 6 4 2 3 3 5 3 4 d(4) is not changed

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

  11. Update 2 6 4 2 4 2 2 0 2 1 3 6 1 6 4 2 3 3 5 3 4 d(6) is not updated

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

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