L19-sssp

v 1 4 5 5 short 1x i 1y do for each e x y

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Unformatted text preview: . , V 1 4 5 5 short 1,x i 1,y do for each e = (x, y ) ⌅ E ⇤ ⌅ shorti,y do shorti,y ⌥ shorti 1,y = min ⌥ shorti,y w (x, y ) + shorti 1,x do shorti,y = min ⇧ ⌃ w(x, y ) + shorti 1,x bellman-ford(G, s) 1 ds ⇥ 0 2 ⇧v ⌅ V {s}, dv ⇥ ⇤ 3 for i = 1, . . . , V 1 4 do for each e = (x, y ) ⌅ E ⇥ 5 do dy ⇥ min dy , w(x, y ) + dx ⌃ ⌦ 5 do shorti,y = min shorti,y ⌥ w(x, y ) + shorti running time bellman-ford(G, s) 1 ds ⇥ 0 2 ⇧v ⌅ V {s}, dv ⇥ ⇤ 3 for i = 1, . . . , V 1 4 do for each e = (x, y ) ⌅ E ⇥ 5 do dy ⇥ min dy , w(x, y ) + dx 1,x negative cycles? s 2 3 1 -5 t negative cycles? s 2 3 1 -5 s a b t 0 t negative cycles? s 2 3 1 -5 s 0 0 0 0 a 2 2 2 1 5 5 5 6 6 b t t applications of bf image: cheswick et al b 8 g 3 -12 c 2 9 e -4 what happens when B changes... 5 7 10 a d i 5 -4 -3 1 f 6 h a b c d0 e f g h i 0 1 8 0 7 5 5 2 bf(G,d) 3 4 5 6 7 distance vector image: hurricane electric all-pairs shortest path a b 1 2 h 2 5 7 -4 10 -1 k 3 i j -8 ashorti,j,k = ashorti,j,k = j i k ashorti,j,k = ashorti,j,k = 8 < wi,j : min ashorti,j,k-1 ashorti,k,k-1 + ashortk,j,k-1 9 k=0 = k 1; floyd-warshall(G,W) int graph[128][128], n; // a weighted graph and its size void floydWarshall() { for( int k = 0; k < n; k++ ) for( int i = 0; i < n; i++ ) for( int j = 0; j < n; j++ ) graph[i][j] = min( graph[i][j], graph[i][k] + graph[k][j] ); } int main { // initialize the graph adjacency matrix and n //...
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