In graph theory, we use the Hungarian Algorithm to compute a weighted bipartite graph's minimum edge cover (a set of edges that is incident to every vertices, the one with the minimum total weight.)
I find that in new version 8 of Mathematica, there is a whole new package of functions for Graph Theory, (begin with
Graph.) But I've not found any function that do this job. I do find a function called
FindEdgeCover that can only find a edge cover, not the minimum one.