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I was wondering if there is an algorithm which would find shortest paths in graph.
Let’s say that I have a graph where there are couples of path from one vertex to another. Two or more of these paths have the same cost. How can I mark, find etc all shortest paths between these vertices ? As far as I know Dijkstra or Bellman-Ford algorithms will find shortest path but they “choose” only one.
Dijkstra’s algorithm gives you the cost to all the possible intermediate nodes, and the cost of the shortest path to the sink. You can get all the paths from source to sink by doing a depth first search from the sink to the source (going backwards), where you traverse an edge (backwards) only if the cost of that edge is equal to the difference between cost of the shortest path from the source to the two nodes. Of course you get the paths in reverse order, but reversing them is easy.
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