Unformatted text preview: a s, w, u, v A . 2 43 1 s w u v 2 43 1 s w u v 4 1 3 The proof of Dijkstra’s algorithm does not go through when negative edge weights are allowed, for the following reason. Recall that in case 2 of the proof, y lies on the shortest path from s to u and y n = u . In the proof given in class, we claim that since y lies midway on the shortest path from s to u , δ ( s, y ) < δ ( s, u ). This crucial fact is true if the edge weights are all positive; however, it breaks down if negative edge weights are allowed! 1...
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 Spring '10
 may
 English, Graph Theory, Shortest path problem, 4 W, negative edge weights, 3 4 w

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