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dialsalgorithm

# dialsalgorithm - right till there is a non-empty bucket 7...

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15.082 and 6.855J Dijkstra’s Algorithm with simple buckets (also known as Dial’s algorithm)

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2 An Example 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 2 3 4 5 6 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 2 3 4 5 6 2 3

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

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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 6 3 4 5 Find Min by starting at the leftmost bucket and scanning right till there is a non-empty bucket.

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Unformatted text preview: 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 ∞ 6 3 4 5 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 ∞ 6 4 5 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 ∞ 6 4 5 6 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 4 6 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 4 6 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...
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