Matroids

Algorithms

• A matroid intersection of two or more matroids on the same ground set is the family of sets that are simultaneously independent in each of the matroids. The problem of finding the largest set, or the maximum weighted set, in the intersection of two matroids can be found in polynomial time, and provides a solution to many other important combinatorial optimization problems. For instance, maximum matching in bipartite graphs can be expressed as a problem of intersecting two partition matroids. However, finding the largest set in an intersection of three or more matroids is NP-complete.