1 / 14

Dijkstra’s Algorithm with simple buckets (also known as Dial’s algorithm)

15.082J & 6.855J & ESD.78J Visualizations. Dijkstra’s Algorithm with simple buckets (also known as Dial’s algorithm). ∞. ∞. 0. ∞. 1. ∞. ∞. ∞. 2. 0. 1. 2. 3. 4. 5. 6. 7. 3. 4. 5. 6. An Example. Initialize distance labels. 4. 2. 4. 2. 2. Initialize buckets. 2. 1.

caridadm
Download Presentation

Dijkstra’s Algorithm with simple buckets (also known as Dial’s algorithm)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 15.082J & 6.855J & ESD.78JVisualizations Dijkstra’s Algorithm with simple buckets (also known as Dial’s algorithm)

  2. ∞ ∞ 0 ∞ 1 ∞ ∞ ∞ 2 0 1 2 3 4 5 6 7 3 4 5 6 An Example Initialize distance labels 4 2 4 2 2 Initialize buckets. 2 1 3 1 6 4 2 3 Select the node with the minimum temporary distance label. 3 5 1

  3. 0 1 2 3 4 5 6 7 Update Step 2 ∞ ∞ 4 2 4 2 2 0 2 1 3 ∞ 1 6 4 2 3 3 5 ∞ ∞ ∞ 4 2 3 4 5 1 6

  4. 0 1 2 3 4 5 6 7 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 2 0 2 1 3 ∞ 1 6 4 2 3 3 5 ∞ ∞ 4 4 5 6 2 3

  5. 0 1 2 3 4 5 6 7 Update Step 6 2 ∞ 4 2 4 2 2 0 2 1 3 ∞ 1 6 4 2 3 3 5 ∞ ∞ 4 4 3 4 5 6 2 3

  6. 0 1 2 3 4 5 6 7 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 2 0 2 1 3 ∞ 1 6 4 2 3 3 5 ∞ 3 4 6 3 5 4

  7. 0 1 2 3 4 5 6 7 Update 2 6 4 2 4 2 2 0 2 1 3 ∞ 1 6 4 2 3 3 5 ∞ 3 4 6 3 5 4

  8. ∞ 0 1 2 3 4 5 6 7 Choose Minimum Temporary Label 2 6 4 2 4 2 2 0 2 1 3 ∞ 1 6 4 2 3 3 5 3 4 6 5 4

  9. 0 1 2 3 4 5 6 7 Update 2 6 4 2 4 2 2 0 6 2 1 3 ∞ 1 6 4 2 3 3 5 ∞ 3 4 6 5 4

  10. 0 1 2 3 4 5 6 7 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 4 6

  11. 0 1 2 3 4 5 6 7 Update 2 6 4 2 4 2 2 0 2 1 3 6 1 6 4 2 3 3 5 3 4 4 6

  12. 0 1 2 3 4 5 6 7 Choose Minimum Temporary Label 2 6 4 2 4 There is nothing to update 2 2 0 2 1 3 6 1 6 4 2 3 3 5 3 4 6

  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

  14. MITOpenCourseWare http://ocw.mit.edu 15.082J / 6.855J / ESD.78J Network Optimization Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

More Related