15.082J & 6.855J & ESD.78J
Visualizations
Dijkstra’s Algorithm

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

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

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

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

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

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

Update
0
1
2
4
3
3
2
2
1
4
3
2
5
4
6
4
3
2
2
6
∞ d(5) is not changed.
8

Choose Minimum Temporary Label
0
1
2
4
3
3
2
2
1
4
3
2
5
4
6
4
3
2
2
6
∞
9

Update
0
1
2
4
3
3
2
2
1
4
3
2
5
4
6
4
3
2
2
6
6
∞ d(4) is not changed
10

Choose Minimum Temporary Label
0
1
2
4
3
3
2
2
1
4
3
2
5
4
6
4
3
2
2
6 6
11

Update
0
1
2
4
3
3
2
2
1
4
3
2
5
4
6
4
3
2
2
6 6 d(6) is not updated
12

Choose Minimum Temporary Label
0
1
2
4
3
3
2
2
1
4
3
2
5
4
6
4
3
2
2
6 6
There is nothing to update
13

End of Algorithm
0
1
2
4
3
3
2
2
1
4
3
2
5
4
6
4
3
2
2
6 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
14

MIT OpenCourseWare http://ocw.mit.edu
15.082J / 6.855J / ESD.78J Network Optimization
Fall 2010
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