Suppose we have a connected undirected graph with a positive integer cost assigned to each edge.
Given two verticies, how do we find the set of minimal cost paths between those two nodes? Does this problem have a name? What algorithm should we use?
Suppose we have a connected undirected graph with a positive integer cost assigned to each edge.
Given two verticies, how do we find the set of minimal cost paths between those two nodes? Does this problem have a name? What algorithm should we use?
If you looking for algorithm for all possible shortest paths between two vertices, I'd say that unfortunately this problem has exponential output size, assume graph with $n$ distinct cycles: $C_1,C_2,...C_n$, such that each cycle has $4$ vertices, $\forall i\in [1,n-1]$ $C_i$ is connected to $C_{i+1}$ by one edge $e_i$. internal edges in each cycles are:$v_{i_1}v_{i_2},v_{i_2}v_{i_3},v_{i_3}v_{i_4},v_{i_4}v_{i_1}$ and $e_i = v_{i_3}v_{i+1_1}$. number of shortest path between $v_{1_1}$ and $v_{n_3}$ is $O(2^{n \over 2})$. and because size of graph is $4n$, this causes to exponential number of paths.