L24_ShortestPath_SpanningTree

L24_ShortestPath_SpanningTree - Shortest-Paths in a Graph...

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Shortest-Paths in a Graph What are the shortest paths from node c to all nodes? 2 10 e d f g a 1 2 5 3 1 6 2 4 8 4 b c Page 1 of 38
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We first investigate a simpler case: an unweighted graph. What are the shortest paths from node c to all nodes, in the following unweighted graph? e d f a b g c Page 2 of 38
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Note: in an unweighted graph, the weights of all arcs are all 1. 0 0 S S T T A A R R R T T T STA b g f e a d c Page 3 of 38
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Note: in an unweighted graph, the weights of all arcs are all 1. 0 0 S S T T A A R R R T T T STA b g 1 1 f e 1 1 a d c Page 4 of 38
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Note: in an unweighted graph, the weights of all arcs are all 1. 0 0 S S T T A A R R R T T T STA 2 2 b g 1 1 f e 2 2 1 1 a d c Page 5 of 38
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Note: in an unweighted graph, the weights of all arcs are all 1. 0 0 S S T T A A R R R T T T STA 2 2 b 3 3 g 1 1 f 3 3 e 2 2 1 1 a d c Page 6 of 38
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But what are the paths? Page 7 of 38
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Note: in an unweighted graph, the weights of all arcs are all 1. 0 0 S S T T A A R R R T T T STA 2 2 b 3 3 g 1 1 f 3 3 e 2 2 1 1 a d c Page 8 of 38
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all 1. 0 0 S
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This note was uploaded on 12/28/2010 for the course CSC CSC1110 taught by Professor Cjyuan during the Fall '06 term at CUHK.

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L24_ShortestPath_SpanningTree - Shortest-Paths in a Graph...

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