I'm looking for a computationally efficient algorithm for solving the following type of assignment problem:
I have two sets of points. Set A has N points and set B has M points. I'd like to establish one-to-many assignments from A to B, where each element in A can have at most two and at least zero matches in B. Obviously, in this bipartite graph the edges have non-zero costs. Also, the matchings are unique - two elements from A cannot be assigned to the same element in B.
I first thought of using the Hungarian algorithm, but it always finds one-to-one matches, which renders it not directly applicable in my case. The sought algorithm should be able to account 1-to-0 and 1-to-2 assignments as well.
Do you know any such algorithm from the literature?