DIJKSTRA’s Algorithm. Definition fwd search Find the shortest paths from a given SOURCE node to ALL other nodes, by developing the paths in order of increasing.

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Presentation transcript:

DIJKSTRA’s Algorithm

Definition fwd search Find the shortest paths from a given SOURCE node to ALL other nodes, by developing the paths in order of increasing path length. The alg. Proceeds in stages. N = set of nodes in the network; S = sourse node; M set of nodes so far incorporated by the alg l(i,j)= link cost from node i to j;l(i,i)=0; l(i,j)=  if the two nodes are not directly connected; l(i,j)>0 if they are directly connected; C1(n) = least-cost paths from S to n

FWD. Search Algorithm 1.Set M={S}; for each node n  N-S, set C1(n)=l(S,n); 2. Find W  N-M so that C1(w) in minimum, add W to M. Set C1(n)= MIN  C1(n) and C1(w)+l(w,n) 3. Repeat 2. until M=N

Definition bwd search Find the shortest paths from a given DESTINATION node from ALL other nodes. N = set of nodes in the network; D = destination node; M set of nodes so far incorporated by the alg l(i,j)= link cost from node i to j;l(i,i)=0; l(i,j)=  if the two nodes are not directly connected; l(i,j)>0 if they are directly connected; C2(n) = least-cost paths from D to n

BWD. Search Algorithm 1.Set C2(D)=0; for each node n  N-D set C2(n)=  ; 2. For each node n  N-D set C2(n)= MIN  C2(n) and C2(w)+l(n,w) (w  N) 3. Repeat 2. until no changes in C2