## shortest paths network

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nicoletsg
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Posts: 15
Joined: Sat Dec 20, 2008 8:10 pm

### shortest paths network

In a network i want to find the number of alternate shortes paths from a start node to all other nodes. Normally Dijkstra can be used.
But because there are no weights BFS should also working.
I can modify BFS algorithm so that pred (n) doesn't only store one predecessor
but a list of possible predecessors. So i have now the PATHs
But is there any way to calculate the Number of shortest paths from a start node to rest of nodes ?

maxdiver
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Location: Russia, Saratov
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### Re: shortest paths network

You don't even need in pred[], only distances dist[] from vertex s to the others.
After that, calculate for each vertex dynamics: d[v] is the number of shortest paths to v.
Set d[s] = 1.
For each other vertex d[v] = SUM d[p] over all p such that dist[p] + g[p][v] == dist[v].

nicoletsg
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Posts: 15
Joined: Sat Dec 20, 2008 8:10 pm

### Re: shortest paths network

Thank's for ideas