Sergio Caracciolo

Spanning trees in the Assignment Problem: two theorems and two conjectures

The \emph{Minimum Matching Problem} consists of finding an independent edge set of minimum weight $M_{\star}(G)$ in a given edge-weighted graph $G$. When $G$ is bipartite, this reduces to the \emph{Assignment Problem}. We consider a variant of this problem defined by taking the union of optimal matchings across various...