Tuesday, April 6, 2010

Dijkstra's Shortest Path Algorithm - Cannot be used if negative edge weight is present.

Dijkstra's Shortest Path Algorithm

Let the node at which we are starting be called the initial node. Let the distance of node Y be the distance from the initial node to Y. Dijkstra's algorithm will assign some initial distance values and will try to improve them step-by-step.

  1. Assign to every node a distance value. Set it to zero for our initial node and to infinity for all other nodes.
  2. Mark all nodes as unvisited. Set initial node as current.
  3. For current node, consider all its unvisited neighbors and calculate their distance (from the initial node). For example, if current node (A) has distance of 6, and an edge connecting it with another node (B) is 2, the distance to B through A will be 6+2=8. If this distance is less than the previously recorded distance (infinity in the beginning, zero for the initial node), overwrite the distance.
  4. When we are done considering all neighbors of the current node, mark it as visited. A visited node will not be checked ever again; its distance recorded now is final and minimal.
  5. Set the unvisited node with the smallest distance (from the initial node) as the next "current node" and continue from step 3.

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