title: finding the total number of distinct shortest paths between 2 nodes in undirected weighted graph in linear time?
body: <p>I was wondering, that if there is a weighted graph G(V,E), and I need to find a single shortest path between any two vertices S and T in it then I could have used the Dijkstras algorithm. but I am not sure how this can be done when we need to find all the distinct shortest paths from S to T. Is it solvable on O(n) time? I had one more question like if we assume that the weights of the edges in the graph can assume values only in certain range lets say 1 &lt;=w(e)&lt;=2 will this effect the time complexity?</p>