MATROID

A matroid is a mathematical structure that generalizes the concept of independence, similar to how we think of linearly independent vectors in linear algebra or independent sets of edges in a network. It consists of a set and a collection of subsets called independent sets, satisfying properties like the ability to add elements without losing independence and the exchange property. This framework helps in understanding and solving optimization problems in various fields like graph theory, coding theory, and combinatorics, by capturing the essence of independence in a unified way.