15.082J & 6.855J & ESD.78J
Visualizations
Dijkstra’s Algorithm
An Example
∞
2
0
∞
4
4
2
2
1
1
2
3
4
6
∞
2
3
∞
3
5
∞
Initialize
Select the node with
the minimum temporary
distance label.
2
An Example
∞
2
0
∞
4
4
2
2
1
1
2
3
4
6
∞
2
3
∞
3
5
∞
Initialize
Select the node with
the minimum temporary
distance label.
3
Update Step
2
∞
2
0
∞
4
4
2
2
1
1
2
3
4
6
∞
2
3
∞
4
3
5
∞
4
Choose Minimum Temporary Label
∞
2
2
0
4
4
2
2
1
1
2
3
4
6
∞
2
3
4
3
5
∞
5
Update Step
6
∞
2
2
0
4
4
2
2
1
1
2
3
4
6
∞
2
3
4
3
3
5
∞
4
The predecessor
of node 3 is now
node 2
6
Choose Minimum Temporary Label
2
2
0
6
4
4
2
2
1
1
2
3
4
6
∞
2
3
3
3
5
4
7
Update
2
2
0
6
4
4
2
2
1
1
2
3
4
6
∞
2
3
3
3
5
4
d(5) is not changed.
8
Choose Minimum Temporary Label
2
2
0
6
4
4
2
2
1
1
2
3
4
6
∞
2
3
3
3
5
4
9
Update
2
2
0
6
4
4
2
2
1
1
2
3
4
6
6
∞
2
3
3
3
5
4
d(4) is not changed
10
Choose Minimum Temporary Label
2
2
0
6
4
4
2
2
1
1
2
3
4
6
6
2
3
3
3
5
4
11
Update
2
2
0
6
4
4
2
2
1
1
2
3
4
6
6
2
3
3
3
5
4
d(6) is not updated
12
Choose Minimum Temporary Label
2
2
0
6
4
4
2
2
1
1
2
3
4
6
6
2
3
3
3
5
4
There is nothing to update
13
End of Algorithm
2
2
0
6
4
4
2
2
1
1
2
3
4
6
6
2
3
3
3
5
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
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