I have got two sets of elements and a pruned graph of bipartite edges with weights assigned to each edge. I need to find the minimal set of edged with the minimum cost covering all nodes from both sets. Multiple assignment is ok as long as every element is covered.
I find the Assignment Problem is the closest to the problem I am trying to solve. Again with the exception that multiple assignments in both ways are permitted.
I tried using the Hungarian Algorithm. The problem is that it tries to avoid multiple assignments. Anyone has any hints on a way for solving this problem?