# Wanted: A method to find all paths from V1 to V2 using digraph module

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## Wanted: A method to find all paths from V1 to V2 using digraph module

 Greetings, The digraph module has get_path/3 to find one path from V1 to V2. Is there a way to find all paths? I considered removing the found path and trying again, but that does not work when paths overlap. Best Wishes, bengt _______________________________________________ erlang-questions mailing list [hidden email] http://erlang.org/mailman/listinfo/erlang-questions
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## Re: Wanted: A method to find all paths from V1 to V2 using digraph module

 Hi Bengt,The solution is to do a search starting from one of the vertices and keep track of the found paths (saving a stack of already traversed vertices and watching out for cycles), but in the worst case it is an O(n!) algorithm. Even in non-pathological cases, it is easy to get an untractable number of solutions as the complexity is exponential. Someone asked the same thing before at https://stackoverflow.com/questions/7834702/find-all-possible-paths-from-one-vertex-in-a-directed-cyclic-graph-in-erlangbest regards,VladOn Sun, Apr 22, 2018 at 10:33 PM, bengt wrote:Greetings, The digraph module has get_path/3 to find one path from V1 to V2. Is there a way to find all paths? I considered removing the found path and trying again, but that does not work when paths overlap. Best Wishes, bengt _______________________________________________ erlang-questions mailing list [hidden email] http://erlang.org/mailman/listinfo/erlang-questions _______________________________________________ erlang-questions mailing list [hidden email] http://erlang.org/mailman/listinfo/erlang-questions
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## Re: Wanted: A method to find all paths from V1 to V2 using digraph module

 Hi Bengt,Can you check digraph.erl source code for function get_short_path/1, which might give you some ideas of retrieving list of paths between vertices:-Vasu-spec get_short_path(G, V1, V2) -> Vertices | 'false' when G :: graph(), V1 :: vertex(), V2 :: vertex(), Vertices :: [vertex(),...].get_short_path(G, V1, V2) -> T = new(), add_vertex(T, V1), Q = queue:new(), Q1 = queue_out_neighbours(V1, G, Q), L = spath(Q1, G, V2, T), delete(T), L. Vasu Dasari On Sun, Apr 22, 2018 at 5:44 PM, Vlad Dumitrescu wrote:Hi Bengt,The solution is to do a search starting from one of the vertices and keep track of the found paths (saving a stack of already traversed vertices and watching out for cycles), but in the worst case it is an O(n!) algorithm. Even in non-pathological cases, it is easy to get an untractable number of solutions as the complexity is exponential. Someone asked the same thing before at https://stackoverflow.com/questions/7834702/find-all-possible-paths-from-one-vertex-in-a-directed-cyclic-graph-in-erlangbest regards,VladOn Sun, Apr 22, 2018 at 10:33 PM, bengt wrote:Greetings, The digraph module has get_path/3 to find one path from V1 to V2. Is there a way to find all paths? I considered removing the found path and trying again, but that does not work when paths overlap. Best Wishes, bengt _______________________________________________ erlang-questions mailing list [hidden email] http://erlang.org/mailman/listinfo/erlang-questions _______________________________________________ erlang-questions mailing list [hidden email] http://erlang.org/mailman/listinfo/erlang-questions _______________________________________________ erlang-questions mailing list [hidden email] http://erlang.org/mailman/listinfo/erlang-questions
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## Re: Wanted: A method to find all paths from V1 to V2 using digraph module

 In reply to this post by Vlad Dumitrescu-2 On Sun, Apr 22, 2018 at 11:45 PM Vlad Dumitrescu <[hidden email]> wrote:Hi Bengt,The solution is to do a search starting from one of the vertices and keep track of the found paths (saving a stack of already traversed vertices and watching out for cycles), but in the worst case it is an O(n!) algorithm. Even in non-pathological cases, it is easy to get an untractable number of solutions as the complexity is exponential. The obvious algorithm is a breadth-first-search keeping track of the possible paths in each vertex. But if the number of edges are high, then this has to visit all the edges.It might be possible, given assumptions about cycles, to use a variant of (Floyd-)Warshall's algorithm. Build an "ascendancy matrix", but rather than processing boolean bits in each matrix cell, track the (number of) paths. If you can pull this off, then we are closer to something like O(n^3), though there are obvious flaws given cycles. So it may be you would need to analyze the incoming data and make sure the graph has a certain structure.Is the graph directed or undirected? Are all the paths simple (i.e., they are not allowed to cycle?). I'd also look into graph cuts where you can divide the graph into two halves, one containing S and one containing T. It could be the solution count can be based on that number. _______________________________________________ erlang-questions mailing list [hidden email] http://erlang.org/mailman/listinfo/erlang-questions