15.082 and 6.855j
DESCRIPTION
15.082 and 6.855J. 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. 3. 1. 6. 4. 2. 3. - PowerPoint PPT PresentationTRANSCRIPT
1
15.082 and 6.855J
Dijkstra’s Algorithm with simple buckets
(also known as Dial’s algorithm)
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.
0 1 2 3 4 5 6 7
1
23456
Initialize buckets.
3
Update Step
2
3
4
5
6
2
4
2 1
3
4
2
3
2
2
4
0
1
0 1 2 3 4 5 6 7
1
23456
2 3
4
Choose Minimum Temporary Label
1
3
4
5
6
2
4
2 1
3
4
2
3
2
2
4
0
2
0 1 2 3 4 5 6 7
4562 3
Find Min by starting at the leftmost bucket and scanning right till there is a non-empty bucket.
5
Update Step
1
2
3
4
5
6
2
4
2 1
3
4
2
3
2
2
4
6
43
0
0 1 2 3 4 5 6 7
4562 33 4
5
6
Choose Minimum Temporary Label
1
2 4
5
6
2
4
2 1
3
4
2
3
2
2
3
6
4
0
3
0 1 2 3 4 5 6 7
63 45
Find Min by starting at the leftmost bucket and scanning right till there is a non-empty bucket.
7
Update
1
2 4
5
6
2
4
2 1
3
4
2
3
2
0
3
2
3
6
4
0 1 2 3 4 5 6 7
63 45
8
Choose Minimum Temporary Label
1
2 4
6
2
4
2 1
3
4
2
3
2
0
3
2
3
6
4
5
0 1 2 3 4 5 6 7
645
9
Update
1
2 4
6
2
4
2 1
3
4
2
3
2
0
3
2
3
6
4
5
6
0 1 2 3 4 5 6 7
6456
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
0 1 2 3 4 5 6 7
46
11
Update
1
2
6
2
4
2 1
3
4
2
3
2
0
3
2
3
6
4
5
6
4
0 1 2 3 4 5 6 7
46
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
0 1 2 3 4 5 6 7
6
There is nothing to update
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