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# Nowitlookslike15

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Unformatted text preview: twork. – Directed graph G = (V, E). – Source s, destination t. – Length we = length of edge e. s Applications: • GIS routing • Google Maps, Mapquest • Routing in communication networks Shortest path problem: find shortest directed path from s to t. cost of path = sum of edge costs in path 23 2 9 3 18 14 5 30 11 5 5 16 20 7 6 2 6 44 19 4 6 t Cost of path s­2­3­5­t = 9 + 23 + 2 + 16 = 48. Greedy Approach Greedy Approach 100 A B 1 10 C F 1 1 5 s 10 E 1 D 6 100 G Fails Miserably t 1 Let’s be careful… Let 1 A 1 0 s t 10 C The shortest path to s has weight 0. The shortest path to A must have weight 1 (why)? The shortest path to C must have weight 10 ?? NO! could have A­­>C of cost 1 Let’s be careful… Let 1 A 100 101 B 1 0 s t 10 C 10 NOW LOOK AT EDGES COMING OUT OF {s, A} CONCLUDE: shortest path to C must be 10 Let’s be careful… Let 1 100 A 101 15 B 1 0 5 s 10 C 10 t 1 D 11 NOW LOOK AT EDGES COMING OUT OF {s, A, C} A moment ago we thought path to B cost 101. Now it looks like 15… But ­ is that the smallest?? Might not be. Note “15”, but don’t circle B yet Let’s be careful… Let 1 100 A 15 B 1 0 5 s 10 C 10 t 1 D 11 If all edges coming out of {s, A, C } are shown, can we write down the shortest distance to S...
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