The Optimal Path-Matching Problem

We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we establish common generalizations of the main results on those two problems|polynomial-time solvability, min-max theorems, and totally dual integral polyhedral descriptions. New applications of these results include a strongly polynomial separation algorithm for the convex hull of matchable sets of a graph, and a polynomial-time algorithm to compute the rank of a certain matrix of indeterminates.