# lect08 - Lecture 8 Dijkstras Algorithm for the Shortest...

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Lecture 8 Dijkstra’s Algorithm for the Shortest Path Problem

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s t j). (i, arc of cost the is ij c
Dynamic Programming } ) ( * { min ) ( * Then . node to node origin from path shortest of length the denote ) ( * Let ) ( vu u N v c v d u d u s u d + = - Dijkstra’s Algorithm is a way to implement this dynamic programming.

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Dijkstra’s Algorithm
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.

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Update Step 2 3 4 5 6 4 2 1 3 4 2 3 2 2 4 0 1
Choose Minimum Temporary Label 1 3 4 5 6 2 4 2 1 3 4 2 3 2 2 4 0 2

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Update Step 1 2 3 4 5 6 2 4 1 3 4 2 3 2 2 4 6 4 3 0 The predecessor of node 3 is now node 2
Choose Minimum Temporary Label 1 2 4 5 6 2 4 1 3 4 2 3 2 2 3 6 4 0 3

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Update 1 2 4 5 6 2 4 1 3 4 2 3 2 0 d(5) is not changed. 3 2 3 6 4
Choose Minimum Temporary Label 1 2 4 6 2 4 1 3 4 2 3 2 0 3 2 3 6 4 5

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Update 1 2 4 6 2 4 1 3 4 2 3 2 0 3 2 3 6 4 5 d(4) is not changed 6
Choose Minimum Temporary Label 1 2 6 2 4 1 3 4 2 3 2 0 3 2 3 6 4 5 6 4

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Update 1 2 6 2 4 1 3 4 2 3 2 0 3 2 3 6 4 5 6 4 d(6) is not updated
Choose Minimum Temporary Label 1 2 2 4 1 3 4 2 3 2 0 3 2 3 6 4 5 6 4 6 There is nothing to update

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## This note was uploaded on 11/03/2010 for the course COMPUTER S CS 6363 taught by Professor Dingzhudu during the Fall '10 term at University of Texas at Dallas, Richardson.

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lect08 - Lecture 8 Dijkstras Algorithm for the Shortest...

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