Longest Simple Path

This attempts to find a long simple path (without repeated vertices) in a weighted digraph. It uses heuristics to find good paths.

Quick preview:

    DiGraph D(10000); // creates a digraph on 10000 vertices named 0, 1, ... , 9999
    D.add_edge(1,27,3); // adds an edge to the digraph from node 1 to node 27 with weight 3
    Path P = D.FindLongestSimplePath(); // Uses 5 seconds to find a long simple path

prints out the path.

Vertices can be named too:

    DiGraph G({"A","B","C","D","E","F","G","H"});
    
    G.add_edge("A","B",5);
    G.add_edge("B","C",2);
    G.add_edge("C","A",3);
    G.add_edge("C","D",4);
    G.add_edge("D","E",1);
    G.add_edge("B","F",3);
    G.add_edge("F","G",2);
    
    cout << G << endl;
    Path PG = G.FindLongestSimplePath();
    
    cout << "The best path I found has value " << 
PG.Value() << endl;

Of course, this program is not optimized at all for small graphs, but for large (~10,000 vertices) graphs. It will consume the time it has trying to improve something that can't be improved...

Note 1

Graph D gets modified when calling FindLongestSimplePath, so beware. The problem is that we erase nodes in "small" connected components. If possible, make sure D is (weakly) connected. Else, the program will only focus on the largest (weakly) connected component. For example, is you have two components: A->B->C and D->E, but weight of D->E is 1000 and weight of A->B and B->C are both 1, it will ignore the D->E, since it's a small component. For most graphs this doesn't matter, since the longest path will likely be in the largest connected component.

Improving your results

It's very likely you can improve your results. Many choices were made in order to improve stability of the algorithm (i.e. repeat some searches a few times, and so on) that can be removed and in most cases work better, but are easier to "trick". See class SearchOptions for a bunch of options.

The method

The method it uses will be described in an upcoming research paper (in process), but it does a lot of things. You can also invite me to give a talk on this.

Acknowledgements

Research supported in part by PAPIIT IA106316, UNAM.

mraggi / LongestSimplePath