Minimizing number of crossings in a bipartite graph

Question

The following algorithm problem occurred to me while drawing a graph for something unrelated:

Answer 1

Peter de Rivaz pointed that it is NP-Hard, but still if you are fine with some approximation you can go with the following solution.

My initial thought was to use some force-based algorithm for graph layouting, but it can be bit tedious to implement. But hey, there is this wonderful program graphviz.org, that can make the whole work for you.

So after installing just prepare a file with your graph:

graph G{
   {rank=same A B C D E}
   {rank=same F G H K I J}

    A -- F;
    A -- G;
    A -- K;
    A -- I;
    A -- H;
    A -- J;

    B -- G;

    C -- G;
    C -- J;

    D -- K;
    D -- I;
}

Run: dot -Tpng yourgraph -o yourgraph.png

and get something like that for free :-):