Directed maximum weighted bipartite matching allowing sharing of start/end vertices

Question

Let G (U u V, E) be a weighted directed bipartite graph (i.e. U and V are the two sets of nodes of the bipartite graph and E contains directed weighted edges from U to V or from

Answer 1

This problem can be solved in polynomial time using the Hungarian Algorithm. The "proof" by Vor above is wrong.

The method of structuring the problem for the above example is as follows:

   D E F
A  # 7 9  
B  1 # #
C  # 3 #

where "#" means negative infinity. You then resolve the matrix using the Hungarian algorithm to determine the maximum matching. You can multiply the numbers by -1 if you want to find a minimum matching.