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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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