I am looking for an algorithm mentioned in the title. The graph is complete, i.e. every two nodes have two edges in between with different directions.
I tried Traveling salesman method, but it gives a cycle path, however I don't need the path to return to the starting node. I also tried Hamilton path, but it mainly solves shortest path for undirected graph. Are there any methods to solve such issue?
Thanks!
The transformation (adding a dummy node with zero distance to and from every original node) described by @AnilCh in a comment works if you have a solver for the asymmetric traveling salesman problem (ATSP). If not, there is an additional transformation from ATSP to TSP. See Kumar, R., and Li, H. (1994). “On Asymmetric TSP: Transformation to Symmetric TSP and Performance Bound.” http://home.engineering.iastate.edu/~rkumar/PUBS/atsp.pdf.