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dijkstrasalgorithm

dijkstrasalgorithm - 2 4 6 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4...

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15.082 and 6.855J Dijkstra’s Algorithm

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

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

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

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8 Choose Minimum Temporary Label 1

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Unformatted text preview: 2 4 6 2 4 2 1 3 4 2 3 2 0 3 2 3 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 d(4) is not changed 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 11 Update 1 2 6 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 5 6 4 d(6) is not updated 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 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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