For a robot vision problem, I'm matching observations to known robot locations. After searching this site, I have figured out that I need to find the maximum edge set of a bipartite graph (i.e., the Hungarian Maximum Matching Algorithm; however, in my case, there are many possible maximum independent edge sets (consider a square with four vertexes and four edges, which has two maximum independent edge sets).
I want to find the one with the smallest sum of edge weights (which are distances squared). How should I go about this? How can I use the aforementioned algorithm to find ALL maximum independent edge sets?