Question

I am dealing with undirected graph. I need to find all possible acyclic paths within a graph:

with G(V,E)
find all subsets of V that are acyclic paths

I am using either python scipy or matlab – whichever would be appropriate.
Is there any clever solution for this?

I’m trying to achieve it with a breadth-first search (see wiki)

I also have this toolbox in matlab: http://www.mathworks.com/matlabcentral/fileexchange/4266-grtheory-graph-theory-toolbox but it seems there’s no straightforward solution for my problem.

PS. The problem practically is stated as: Transit Network Design Problem: Find such a transport network that minimizes cost of passangers and operators (i.e. optimal subway network for urban area)

Thanks in advance
Rafal

Answer 1

I think the problem as stated in your PS may be a NP problem. If so, there are straightforward solutions only for graphs with very limited numbers of nodes (N ~ <= 20). Other solutions will be approximate, giving rise to only local optimums. The solution to your problem as stated in the question will simply be to calculate all the permutations of the node orders. Again this will become computationally infeasible with comparatively low numbers of nodes (possibly higher than 20 but not much).