Matroid parity problem

The Matroid Parity problem is a combinatorial optimization problem that deals with finding a maximal subset of edges in a given graph where the edges have certain properties related to a matroid structure. More specifically, it focuses on maximizing the size of a subset of edges such that the edges selected maintain a "parity" constraint, which requires that they can be paired off in such a way that only an even number of edges from each independent set contributes to the total.