DIJKSTRA

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DIJKSTRAs Algorithm
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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 jl(i,i)0
  l(i,j)? if the two nodes are not directly
  connected l(i,j)gt0 if they are directly
  connected
• C1(n) least-cost paths from S to n

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FWD. Search Algorithm

• 1.Set MS 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 MN

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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 jl(i,i)0
  l(i,j)? if the two nodes are not directly
  connected l(i,j)gt0 if they are directly
  connected
• C2(n) least-cost paths from D to n

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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